Answer: The equation represents the value (in dollars) of a car t years after its purchase, so the purchase price of the car would have been the value of the car when t = 0. Plugging in t = 0 into the equation, we get:
V = 23900 * (0.91)^0
V = 23900
So the purchase price of the car was $23,900.
Regarding the rate of decrease in the value of the car, we can observe that the value decreases at a rate proportional to (0.91)^t, so the rate of decrease is proportional to 0.91.
Step-by-step explanation:
A 17-foot-long ladder leans on a wall, as shown in the accompanying figure. The bottom of the ladder is 8 feet from the wall. If the bottom is pulled out 3 feet farther from the wall, how far does the top of the ladder move down the wall?
(Round to the nearest thousandth as needed.)
The 17-foot-long ladder pulled out 3 feet farther from the wall from a distance of 8 feet, indicates, using Pythagorean Theorem that the top of the ladder moves about 2.039 feet down the wall.
What is the Pythagorean Theorem?Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the length of the legs of the right trianglde.
Length of the ladder = 17 foot ladder
Distance of the bottom of the ladder from the wall = 8 feet
The extra distance to which the bottom of the ladder is pulled = 3 feet
The ladder resting on the wall forms a right triangle, with the length of the ladder being the hypotenuse side.
The initial vertical distance reached by the ladder on the wall, h, can be found using Pythagorean Theorem as follows;
h² = 17² - 8² = 225 = 15²
h² = 15²
The initial vertical distance up the wall the ladder reaches, h, is therefore;
h = √(15²) = 15
The ladder initially reaches 15 feet high on the wall
The ladder is then pulled 3 feet farther, from which we get;
New horizontal distance of the ladder from the wall = 8 feet + 3 feet = 11 feet
The square of the new height the ladder reaches up to on the wall, h'², can therefore be found as follows;
h'² = 17² - 11² = 168
√h'² = h' = √(168) = 2·√(42)
The new height the ladder reaches up to on the wall, h' ≈ 2·√(42) feet
The distance the ladder moves down the wall, Δh = h - h', therefore;
Δh = 15 - 2·√(42) ≈ 2.039
The distance the top of the ladder moves down the wall is about 2.039 feetLearn more about Pythagorean Theorem here: https://brainly.com/question/66231
#SPJ1
1513 ÷ 3 Enter your answer by filling in the boxes. I need help.
Required value of (1513÷3) is 504R1.
What is division?
Division is the opposite of multiplication. If 3 groups of four are multiplied by 12, 12 divided into three equal groups gives 4 in each group.
The main purpose of distribution is to see how many equal groups are formed or how many are in each group in a fair distribution.
In the above example, to divide the 12 donuts into 3 similar groups, you need to put 4 donuts in each group. So, 12 divided by 3 is 4.
Here given two digits are 1513 and 3.
We want to find value of 1513 ÷ 3.
Now,
[tex]1513 ÷ 3 = \frac{1513}{3} = 504 R1[/tex]
Therefore, the quotient is 504 and the remainder is 1.
Learn more about division here,
https://brainly.com/question/30361089
#SPJ1
20 customers are eating dinner at a local restaurant. The restaurant accepts cash or credit as forms of payment. Of the 2020 customers, 44 have enough cash to pay for their meal, 1616 have a credit card, and 33 have enough cash and a credit card. Using this information, answer each of the following questions.
Let AA be the event that a randomly selected customer has enough cash and BB be the event that a randomly selected customer has a credit card.
What is P(A)P, left parenthesis, A, right parenthesis, the probability that a customer has enough cash?
the value of P(A∪B) is 17/20.
What is probability?Probability is a number expressing the likelihood or chance that a specific event will occur. Proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given, A neighborhood restaurant is serving dinner to 20 patrons.
Both cash and credit are accepted as modes of payment at the restaurant. Of the 20 customers, 3 have enough cash and a credit card to pay for their dinner, 16 have a credit card, and 4 have enough cash to cover the cost of their meal.
From the general formula of probability:
Probability = (desired outcomes)/(Total outcomes)
Let "A" represent the situation in which a randomly chosen consumer has enough cash,
"B" represents the situation in which a randomly chosen customer has a credit card.
thus,
P(A) = 4/20
P(A) = 1/5
P(B) = 16/20
Also given,
P(A∩B) = 3/20
Since,
P(A∪B) = P(A) + P(B) -P(A∩B)
P(A∪B) = 4/20 + 16/20 - 3/20
P(A∪B) = 17/20
therefore, the value of P(A∪B) is 17/20.
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ9
Find the global maxima and global minima of the function
f(x, y) =x^2 − 2xy + 2y on the rectangle D = {(x, y) ∶ 0 ≤ x ≤ 3, 0 ≤ y ≤ 2}
The required global maximum value is 4 and the global minimum value is 3.
What is implicit differentiation?The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol.
Here,
The critical points can be found by finding the partial derivatives of the function with respect to x and y and setting them equal to zero.
df/dx = 2x - 2y = 0
df/dy = -2x + 4y = 0
Solving the system of equations, we find that the critical points are (1, 2) and (2, 1).
Since (1, 2) is within the bounds of the rectangle D, we need to check the value of f(1, 2) to see if it is a local minimum or local maximum.
f(1, 2) = 1 - 2 + 4 = 3
(2, 1) is also within the bounds of the rectangle D, we need to check the value of f(2, 1) to see if it is a local minimum or local maximum.
f(2, 1) = 4 - 2 + 2 = 4
Since f(1, 2) < f(2, 1), the global maximum is at point (2, 1) and the global minimum is at point (1, 2).
The global maximum value is 4 and the global minimum value is 3.
Learn more about implicit differentiation;
https://brainly.com/question/11887805
#SPJ1
Sally saved $182 in March. Her father gave her $20 for every
$50 she saved. How much did Sally's father give her?
Answer:
$40
Step-by-step explanation:
We know
Her father gave her $20 for every $50 she saved
$50 + $20 = $70
$50 + 20 + 50 + 20 = $140
$182 - $140 = $42
It is not $50 yet, so her father only give her 2 times
So, her father gives her $40
Answer:
182÷50 = 3.64, 3.64x20=72.8$
her dad gave her 72.8$
seven times the quotient of 2 and 3
Answer:
4.666667, or you can round it to 4.67, depends on what it's asking!
Step-by-step explanation:
The quotient means to divide, so 2/3 = 0.666667
0.666667 * 7 = 4.666667
Hope that helps.
I NEED HELP ASAP PLEASE!!! Determine which integer will make the inequality x − 3 > 15 true.
S:{15}
S:{17}
S:{18}
S:{30}
Answer:
c) S : {30}
So, it is correct answer.
Step-by-step explanation:
mental math be like :-)
A crate is 3/4 yard long and 2/4 yard wide. The crate is also 2 feet tall. What is the area of the top of the crate?
(please explain the answer step by step if possible.)
Answer:
The area of the top of the crate can be found by multiplying the length by the width.
First, we need to convert all units to the same unit, either yards or feet. We will convert the length and width to yards:
3/4 yard = 9/12 yards
2/4 yard = 6/12 yards
2. Now we can find the area by multiplying the length by the width:
Area = 9/12 yards * 6/12 yards = (9/12) * (6/12) = 3/4 * 1/2 = 3/8 yards^2
So, the area of the top of the crate is 3/8 yards^2.
The phone company Splint has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 390 minutes, the monthly cost will be $178. If the customer uses 940 minutes, the monthly cost will be $398.
A) Find an equation in the form y=mx+b where x is the number of monthly minutes used and y is the total monthly of the Splint plan.
B) Use your equation to find the total monthly cost if 866 minutes are used.
Answer: If 866 minutes are used, the total cost will be ------ dollars
The equation can be given as y = 0.4x +22 and the monthly cost is $368.4
What is a linear equation?
A linear equation is an expression whose degree is one. The most general linear equation is y = mx + c. Where m is the slope and c is the y-intercept.
A) To find the equation in the form y = mx + b.
We are given two points (390, 178) and (940, 398).
Now we substitute these points into the standard equation y = mx + c
We get
y = mx + b
178 = m * 390 + b
398 = m * 940 + b
We subtract the two equation we get,
550m = 220
m =0.4
Now we substitute these values in the equation 1 we get
178 = 0.4 * 390 + b
178 = 156 + b
b = 22
So the equation is:
y = 0.4x + 22
B) We are asked to find the cost for 866 minutes we substitute x = 866 in the equation
y = 0.4x + 22
y = 0.4 * 866 + 22
y = 346.4 + 22
y = 368.4
So if 866 minutes are used, the total monthly cost will be $368.4.
The equation can be given as y = 0.4x +22 and the monthly cost is $368.4
The sample question about linear equation is given please refer the link below
https://brainly.com/question/2030026
#SPJ1
The Bitcoin economy had reported year-on-year growth from 2017 to 2019 at a yearly rate of 7%. In 2020 it went into a downward trend. That year the growth turned negative at -5%. If the negative growth doubled the next year, what was the approximate percentage increase or decrease of the bitcoin economy in that year, compared to 2018?
SELECT ONLY ONE
Approximately 9% decrease
Approximately 13% decrease
Approximately 3% increase
Approximately 5% increase
If the Bitcoin economy had a yearly growth rate of 7% from 2017 to 2019, then the value in 2019 would be $1.07^3 = $1.225. If the economy had a negative growth rate of 5% in 2020, then the value in 2020 would be $1.225 x 0.95 = $1.1638. If the negative growth rate doubled in the next year, then the value in the next year would be $1.1638 x 0.9 = $1.04742.
To calculate the percentage change from 2018 to the next year, we can compare the values of the Bitcoin economy in those two years. The value in 2018 would be $1.07^2 = $1.1449. The percentage change would be ((value in next year - value in 2018) / value in 2018) x 100%. Substituting the values, we get ((1.04742 - 1.1449) / 1.1449) x 100% = -8.5%.
Therefore, the approximate percentage decrease of the Bitcoin economy in the next year, compared to 2018, is approximately 9%. The closest option is "Approximately 9% decrease".
It’s math please help
Answer:
D because angle U is equal to angle W because it is diverting angle
graph f(x) = (x+2) (x-4)
Use the parabola tool then choose the vertex followed by one point on the parabola.
Answer:
The vertex of the parabola is at x = 3, and a point on the parabola can be (4, 0). Here is a Brainly link that can provide you with more information about graphing the function f(x) = (x+2) (x-4): https://brainly.com/question/31009433.
You pick a card at random. Without putting the first card back, you pick a second card at
random.
678
What is the probability of picking an 8 and then picking a number greater than 7?
Write your answer as a decimal.
The value of the probability is 0.167
How to determine the probabilityFrom the question, we have the following parameters that can be used in our computation:
6 7 8
The probability of picking a 8 on the first draw and then picking a number above 7 on the second draw is:
P(6 and then >7) = P(6) x P(>7 | 6)
Given that the cards are not replaced, we have
P(6 and then >7) = 1/3 * 1/2
Evaluate
P(6 and then >7) = 0.167
Hence, the probability is 1/6
Read more about probability at
brainly.com/question/251701
#SPJ1
The students in Class 6 vote to pick a class captain. The choice is Anton, Eva, Kofi or Petra. Anton gets 0.2 of the votes. Eva gets 10% of the votes. Petra gets of the votes. Kofi gets 9 votes. How many students are in class 6?
Answer:
There are 15 students in class 6
Step-by-step explanation:
Let's call the number of students in class 6 "n".
We know that:
Anton gets 0.2 * n votes
Eva gets 0.1 * n votes
Petra gets (1 - 0.2 - 0.1) * n votes
Kofi gets 9 votes
The total number of votes is n, so we can write:
n = 0.2 * n + 0.1 * n + (1 - 0.2 - 0.1) * n + 9
Simplifying this equation:
0.6 * n = 9
So:
n = 9 / 0.6
n = 15
Charlie buys 3 computer tables for $390. How much did he pay for each table?
Answer:
Step-by-step explanation:
If Charlie buys 3 computer tables for $390, then he paid $390 / 3 = $130 for each table.
Answer: 130 dollars for each table
Step-by-step explanation: Because 3 tables is 390 dollars, we have to divide 390 and 3 to see how much 1 table costs.
390 / 3 = 130
Anita attends a private school where she must wear a uniform. This year, the price of the uniform is $86.80, which is 9.6% more than it cost last year. How much were uniforms last year?
Help please
Answer:
The price of the uniforms last year was about $79.20.
Step-by-step explanation:
In order to calculate the price of the uniforms last year, it is important to understand two important thing that can be inferred by what is told in the problem. This year's uniforms are 9.6% more than last year's. The easiest way to understand this line of information is that if we view the prices of the uniform from the perspective of last year's price, we can set the price of last year's uniform as 100% of the original price, and this year's uniform as 109.6% of the original price. Essentially, this year's uniform price is 109.6% of what it would cost you to buy a uniform last year.
Since you are given the information that this year, the uniforms cost $86.80, you know that $86.80 is 109.6% of last year's uniform cost. Now you can write an equation to solve for last year's price.
Set last year's uniform price to be represented by the variable [tex]x[/tex], and you will have the function of [tex]109.6[/tex]% · [tex]x = 86.8[/tex]. In order to solve for [tex]x[/tex], you simply divide both sides of the equation by 109.6%, which you will then get [tex]x = 86.8[/tex] ÷ 109.6%, which can be rewritten as [tex]x=86.8[/tex] ÷ [tex]\frac{109.6}{100}[/tex] or [tex]x=86.8[/tex] · [tex]\frac{100}{109.6}[/tex] ≈ $79.20. Hence, last year's uniforms costed $79.20.
Have a great day! Feel free to let me know if you have any more questions :)
Consider the following three random experiments: Experiment 1: Toss a coin. Experiment 2: Toss a die. Experiment 3: Select a ball at random from an urn containing balls numbered 0 to 9. (a) Specify the sample space of each experiment. (b) Find the relative frequency of each outcome in each of the above experiments in a large number of repetitions of the experiment. Explain your answer.
To fully get the answer on the sample space and relative frequency, let's go directly to the analysis of the experiments as given.
The random experiments and their outcome(a) Sample space:
Experiment 1: Toss a coin: The sample space of this experiment is {heads, tails}.Experiment 2: Toss a die: The sample space of this experiment is {1, 2, 3, 4, 5, 6}.Experiment 3: Select a ball at random from an urn containing balls numbered 0 to 9: The sample space of this experiment is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.(b) Relative frequency of each outcome:
Relative frequency of an outcome is the number of times the outcome appears divided by the total number of trials. In a large number of repetitions of an experiment, the relative frequency of each outcome approaches the theoretical probability of that outcome.
Experiment 1: Toss a coin: Since each outcome (heads or tails) is equally likely, the theoretical probability of each outcome is 0.5. In a large number of repetitions of the experiment, the relative frequency of heads and tails would approach 0.5.Experiment 2: Toss a die: Since each outcome (1 to 6) is equally likely, the theoretical probability of each outcome is 1/6. In a large number of repetitions of the experiment, the relative frequency of each outcome (1 to 6) would approach 1/6.Experiment 3: Select a ball at random from an urn containing balls numbered 0 to 9: Since each outcome (0 to 9) is equally likely, the theoretical probability of each outcome is 1/10. In a large number of repetitions of the experiment, the relative frequency of each outcome (0 to 9) would approach 1Learn more on relative frequency here https://brainly.com/question/3857836
#SPJ1
Please answer my question. Find the SA (surface area) of the composite shape. Round to the nearest tenth. Please help.
The total surface area of the composite shape is 488.7 in².
What is a composite shape?
A composite shape is a shape that was produced from two or more fundamental shapes. Composite shapes are also referred to as compound and complex shapes frequently. Every day, composite shapes are around us.
The given composite shape can be divided into multiple shapes, to find the area easily.
For the given question, we can see that the lower portion of the shape is a cuboid and the upper portion is half of the cylinder cut vertically.
We find the areas of the figures separately.
Area of cuboid
Length l = 6 in.
Breadth b = 10 in.
Height h = 8 in.
Area = Area of each faces = 2(lb) + 2(bh) +2(lh)
= 2(6*10) + 2(10*8) + 2(6*8)
= 2*60 +2* 80 + 2* 48
= 376 in²
Area of cylinder
Radius of semicircles r = 5 in.
Height of cylinder h = 6 in.
Area = Area of semicircles + Area of half of the curved surface
= 2 *1/2 * πr² + 1/2 * 2πrh = πr² + πrh = 3.14 * 5² + 3.14 * 5 * 6
= 172.7 in²
The total surface area of the composite shape = Area of cylinder + Area of cuboid - Area of the common surface(rectangle)
= 172.7 + 376 - (l *b) = 548.7 - ( 10*6) = 488.7 in²
Hence the total surface area of the composite shape is 488.7 in².
To learn more about composite shapes, follow the link.
https://brainly.com/question/8370446
#SPJ1
38. PROBLEM SOLVING The paths of water from three
different garden waterfalls are given below. Each
function gives the height h (in feet) and the horizontal
distance d (in feet) of the water,
Waterfall 1h
-3.1d² + 4.8
Waterfall 2h-3.5d² + 1.9
Waterfall 3 h = -1.1d2 + 1.6
a. Which waterfall drops water
from the highest point?
b. Which waterfall follows the
narrowest path?
c. Which waterfall sends water the farthest?
Answer:
a. 1; b. 2; c. 1.
Step-by-step explanation:
1] if the given functions are:
[tex]1: \ h=-3.1d^2+4.8;\\2: \ h=-3.5d^2+1.9;\\3: \ h=-1.1d^2+1.6, \ then[/tex]
2] a. d=0, ⇒ max[h] is no.1 (h=-3.1d²+4.8);
b. h=0, ⇒ min[d] is no.2 (h=-3.5d²+1.9);
c. h=0, ⇒ max[d] is no.1 (h=-3.1d²+4.8).
The table and the graph below each show a different relationship between the same two variables, x and y:
A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 4,80 and 5,100 and 6,120 and 7,140. On the right of this table is a graph. The x-axis values are from 0 to 10 in increments of 2 for each grid line. The y-axis values on the graph are from 0 to 350 in increments of 70 for each grid line. A line passing through the ordered pairs 2, 70 and 4, 140 and 6, 210 and 8, 280 is drawn.
How much more would the value of y be on the graph than its value in the table when x = 12? (1 point)
a
20
b
90
c
150
d
180
Choose a new vehicle sold in the United States in December at random. The probability distribution for the type of vehicle chosen is given here. (a) What is the probability that the vehicle is a crossover? Round your answer to decimal places. Leave your answer in decimal form. (
b) Given that the vehicle is not a passenger car, what is the probability that it is a pickup truck? Round your answer to decimal places. Leave your answer in decimal form. (c) What is the probability that the vehicle is a pickup truck, SUV, or minivan? Round your answer to decimal places. Leave your answer in decimal form.
(a) The probability that the vehicle is a crossover is 0.30.
(b) Given that the vehicle is not a passenger car, the probability that it is a pickup truck is 0.50.
(c) The probability that the vehicle is a pickup truck, SUV, or minivan is 0.90.
Vehicle Type Probability CalculationI determined the probabilities based on the information provided in the problem. The problem states that the probability distribution for the type of vehicle chosen is given and lists the probabilities for each type of vehicle (crossover, pickup truck, SUV, minivan, and passenger car). To find the requested probabilities, I simply used basic probability formulas and the given probabilities for each type of vehicle.
For example, for part (a), the probability that the vehicle is a crossover is simply the given probability of 0.30.For part (b), given that the vehicle is not a passenger car, the probability that it is a pickup truck is found by using Bayes' Theorem:P(pickup truck | not passenger car) = P(not passenger car | pickup truck) * P(pickup truck) / P(not passenger car).
0.40 / (1 - 0.20) = 0.50.
The denominator P(not passenger car) is found by subtracting the probability of a passenger car (0.20) from 1, and the numerator P(not passenger car | pickup truck) is 1, since a vehicle can either be a pickup truck or not a pickup truck but not both. The requested probability is then equal to 0.50.
For part (c), the probability that the vehicle is a pickup truck, SUV, or minivan is found by adding the individual probabilities for each type of vehicle: 0.40 + 0.30 + 0.20 = 0.90.Learn more about Vehicle Type Probability Calculation here:
https://brainly.com/question/20723968
#SPJ4
NO LINKS!!! NEED URGENT HELP!!!
1. Describe the shape of the graph and any special features you see.
2. What is the greatest area possible for a rectangle with this perimeter? What are the dimensions of this rectangle?
3. What is the area of the rectangle whose length is 10 meters? What is the area of the rectangle whose length is 30 meters> How are these rectangles related?
Answers:
1. The graph is in the shape of a parabola, there is a vertex point at (20, 400), and the zeros (x-intercepts) of the graph are at the origin of the coordinate plane (0, 0) and (40, 0).
2. The greatest area possible for a rectangle with a perimeter of 80 meters is 400 [tex]m^2[/tex], and the dimensions of this rectangle will be 20 meters in length and 20 meters in width.
3. The area of the rectangle whose length is 10 meters and the area of the rectangle whose length is 30 meters are the same, both being 300 [tex]m^2[/tex]. This is because the perimeter is set as 80 meters total, and as they are both rectangles, the opposite sides must be the same length.
For the rectangle with a length of 10 meters, 2 of the 4 sides will use 20 meters of material, so there will be 60 meters of material left for the remaining 2 sides, or 30 meters per side. So the dimensions of that rectangle would be 10 meters in length and 30 meters in width.
For the rectangle with a length of 30 meters, it's the same thing, except the length is 30 meters, and the width is 10 meters. And for both rectangles, their areas are 30 meters multiplied by 10 meters, which equals 300 [tex]m^{2}[/tex], so the way these two rectangles are related is that they have the same area.
Have a great day! Feel free to let me know if you have any more questions :)
Answer:
1. See below.
2. 400 m²
20 m x 20 m
3. 300 m²
Step-by-step explanation:
Question 1The graph is a parabola that opens downwards.
Its vertex is (20, 400) and its axis of symmetry is x = 20.
Question 2From inspection of the given graph, the greatest possible area (y-value) is 400 m². This is when the length of the rectangle is 20 m.
The largest possible area of a rectangle is when the length equals the width. Therefore, the dimensions of the rectangle with the greatest area possible are:
width = 20 mlength = 20 mQuestion 3From inspection of the graph, when the length of the rectangle is 10 m, its area is 300 m².
Similarly, when the length of the rectangle is 30 m, its area is also 300 m².
A rectangle has two pairs of parallel sides of equal length.
Therefore, as both rectangles have the same area, this means that the one pair of parallel sides is 10 m in length and the other pair of parallel sides is 30 m in length. The dimensions of both rectangles are the same: 10 m x 30 m, where the width and length are interchangeable.
16. The elevation of City of Santa Clara is approximately 75 ft. What is the elevation in centimeters? (1ft = 12in; 1in = 2.54cm)
Answer:To convert the elevation of the City of Santa Clara from feet to centimeters, you can use the conversion factors:
1 ft = 12 in
1 in = 2.54 cm
First, convert feet to inches:
75 ft * 12 in/ft = 900 in
Then, convert inches to centimeters:
900 in * 2.54 cm/in = 2286 cm
So, the elevation of the City of Santa Clara is approximately 2286 cm.
Step-by-step explanation:
For what value of c is p(x) = 2x^4 - 5x^2 + cx - 1 divisible by x - 1? Show work.
Answer:
c = 4
Step-by-step explanation:
if (x - a) is a factor , that is divisible by, of f(x) then f(a) = 0
then for p(x) to be divisible by (x - 1) , p(1) = 0
then
2[tex](1)^{4}[/tex] - 5(1)² + c(1) - 1 = 0
2 - 5 + c - 1 = 0
- 4 + c = 0 ( add 4 to both sides )
c = 4
Let f(w) x 10x . We want to estimatef(1.07) using linear approximations. That is, using an appropriate tangent line_ First, we will build the tangent line at (€, y_ Enter as an ordered pair (a,6) The slope of the tangent line comes from f For this problem, f' (c) = And mtan The equation of the tangent line, in slope intercept form, is y = T(c) = Now, f(1.07) ~ T(1.07) Compare to actual value f(1.07)
The linear approximation of f(1.07) using the tangent line is T(1.07) is 10.77, which is slightly lower than the actual value f(1.07) = 11.77.
First, we need to find the derivative of the function f(x) = x + 10x.
The derivative is given by:
f'(x) = 1 + 10
Next, we need to find the tangent line at the point (a, 6), which means we need to find the value of "a" that makes the tangent line pass through (a, 6). To do this, we use the equation of the tangent line:
y - 6 = (1 + 10)(x - a)
y = (1 + 10)(x - a) + 6
Now we need to use the value of "a" to find the value of f(a) and then use this to find the value of the linear approximation of f(1.07).
Let's assume that the value of "a" is 1.
So, f(a) = f(1) = 1 + 10(1) = 11
And the equation of the tangent line is:
y = (1 + 10)(x - 1) + 6 = 11x - 4
Now, to find the value of the linear approximation of f(1.07), we use the equation of the tangent line:
T(1.07) = 11 * 1.07 - 4 = 10.77
Finally, we compare this value with the actual value of f(1.07), which is:
f(1.07) = 1.07 + 10 * 1.07 = 11.77
Read more about Approximation:
https://brainly.com/question/14291186
#SPJ4
Really stuck on this problem can someone help
The triangles are not similar because the dimensions of GDM are larger than those of PQR.
What are congruent shapes ?Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.
Even though triangles GDM and PQR have the same angle measure, the triangles are not congruent / similar because they are not the same size. Triangle GDM is larger than PQR and so is not congruent to it.
Find out more on congruent triangles at https://brainly.com/question/2938476
#SPJ1
Select the correct answer. Which expression is equivalent to this polynomial? x2 + 8
A. ( x + 2 2 ) ( x − 2 2 )
B. ( x + 4 i ) ( x − 4 i )
C. ( x + 2 2 ) 2 D.
Answer: C.
Step-by-step explanation:
1. The Corollary to the Polygon Angle-Sum Theorem finds the measure of each interior angle of a regular n-gon.
*Write a formula to find the measure of each interior angle using n=number of sides.
2. The Polygon Exterior Angle-Sum Theorem states that the exterior angles of any polygon add up to 360 degrees.
*Write a formula that can help you find the measure of each individual exterior angle in any polygon. Use n for the number of sides.
3. What is the most precise name for quadrilateral ABCD with vertices A(-2, -1), B(2, 2), C(1, -2), and D(-3, -3)?
1. The formula to find the measure of each interior angle of a regular n-gon is (180 * (n-2))/n degrees.
2. The formula to find the measure of each individual exterior angle in any polygon is 360/n degrees.
3. The most precise name for the quadrilateral ABCD with the given vertices is a parallelogram.
How did we arrive at these assertions?The formula to find the measure of each interior angle of a regular n-gon is given by:
(180 * (n-2))/n degrees
In a regular n-gon, all interior angles are equal.
The sum of the interior angles of a polygon can be found using the formula:
(n-2) * 180 degrees, where n is the number of sides in the polygon.
Dividing the sum of the interior angles by the number of sides (n) gives us the measure of each interior angle:
(180 * (n-2))/n degrees.
2. The formula to find the measure of each individual exterior angle in any polygon is:
360/n degrees.
In any polygon, the sum of the exterior angles is equal to 360 degrees.
3. To find the measure of each individual exterior angle, we divide the sum of the exterior angles (360 degrees) by the number of sides (n) in the polygon:
360/n degrees.
The precise name for the quadrilateral ABCD is a parallelogram because:
It has opposite sides that are parallel to each other.
It has equal opposite sides.
learn more about quadrilateral: https://brainly.com/question/23935806
#SPJ1
Joana is meeting her friend at the Fair and the admission to get in is $10. Each ride/food costs $1.25 each Create an equation for Joana to use so she can calculate how much money she will be spending while she’s at the fair.
Answer:
y=1.25x+10
Step-by-step explanation:
you can put this into the formula “y=mx+b”. y is the final amount, x is how many times joana gets food or goes on a ride. You can plug into the equation the two parts we know. We know that no matter what, if she goes into the fair, she is going to spend $10 on the admission, even if she does not go on any rides or gets any food. So we put 10 where the “b” is. Then each time she gets food or goes on a ride, she pays another $1.25. Therefore, you can plug 1.25 into where the m is. That leaves you with “y=1.25x+10”.
Arrange the following measurements from smallest to largest. Show the calculations. A. 1.5 cm B. 2.5 x 10^3 mm C. 3.5 x 10-5 m D. 4.5 km
The measurements arranged from smallest to largest are 0.15 cm, 2.5 mm, 0.000035 m, and 4.5 km.
A. 1.5 cm
B. 2.5 x 10^3 mm
C. 3.5 x 10-5 m
D. 4.5 km
Convert all units to the same unit type.
A. 1.5 cm = 15 mm
B. 2.5 x 10^3 mm
C. 3.5 x 10-5 m = 0.000035 m
D. 4.5 km = 4500 m
Arrange the measurements from smallest to largest.
A. 15 mm
B. 2.5 x 10^3 mm
C. 0.000035 m
D. 4500 m
Convert the measurements back to their original units.
A. 15 mm = 0.15 cm
B. 2.5 x 10^3 mm
C. 0.000035 m = 3.5 x 10-5 m
D. 4500 m = 4.5 km
Rearrange the measurements from smallest to largest.
A. 0.15 cm
B. 2.5 x 10^3 mm
C. 3.5 x 10-5 m
D. 4.5 km
Simplify the units to the same unit type.
A. 0.15 cm
B. 2.5 mm
C. 0.000035 m
D. 4.5 km
Rearrange the measurements from smallest to largest.
A. 0.15 cm
B. 2.5 mm
C. 0.000035 m
D. 4.5 km
To learn more about measurements visit:
https://brainly.com/question/27233632
#SPJ4
The measurements arranged from smallest to largest are:
C. 3.5 x 10^-5 m
A. 1.5 cm
B. 2.5 x 10^3 mm
D. 4.5 km
To arrange the measurements from smallest to largest, it is necessary to convert all the units to the same type. The units in the measurements A, C, and D are different, so they need to be converted.
Measurement A is 1.5 cm, which can be converted to millimeters by multiplying by 10: 1.5 cm x 10 mm/cm = 15 mm.
Measurement C is 3.5 x 10^-5 m, which can be converted to millimeters by multiplying by 1000: 3.5 x 10^-5 m x 1000 mm/m = 3.5 mm.
Measurement D is 4.5 km, which can be converted to millimeters by multiplying by 10^6: 4.5 km x 10^6 mm/km = 4.5 x 10^6 mm.
Now that all the units are in millimeters, the measurements can be arranged from smallest to largest:
Measurement C (3.5 mm) is smallest, followed by Measurement A (15 mm), Measurement B (2.5 x 10^3 mm), and finally Measurement D (4.5 x 10^6 mm) is largest.
Learn more about Measurements:
https://brainly.com/question/27233632
#SPJ4