a. The boat is currently 60.5 miles from its pier.
b. The boat could have originally taken a bearing of either N45°E or S45°W to arrive at the current spot.
a.How to determine the distance from the boat's pier?
To determine the distance from the boat's pier, we can use the Pythagorean theorem since we have a right triangle formed by the boat's original position, the current position, and the distance traveled to reach the current position.
Let's call the distance from the boat's pier to the current position "d", and let's call the distance traveled after the turn "x".
Using trigonometry, we can see that:
sin(35°) = x/d
Rearranging this equation, we get:
x = d×sin(35°)
Now we can use the Pythagorean theorem to solve for "d":
d² = 29²+ (d×sin(35°))²
d² = 841 + 0.77d²
0.23d² = 841
d² = 3661.74
d = 60.5 miles (rounded to one decimal place)
Therefore, the boat is currently 60.5 miles from its pier.
b. How to determine the original bearing?
To determine the original bearing, we can use trigonometry again. Let's call the original bearing "θ". Then we have,
cos(θ) = 29/d
Rearranging this equation,
d = 29/cos(θ)
Now we can substitute this expression for "d" into the equation we used to solve for "x" earlier:
x = d×sin(35°)
x = (29/cos(θ))×sin(35°)
We know that after traveling this distance, the boat is currently 14.6 miles away from its original position. So we can set up another equation:
cos(θ) = 14.6/(29/cos(θ))
Simplifying, we get:
cos²(θ) = 0.5
Taking the inverse cosine of both sides,
θ = 45° or θ = 315°
Therefore, the boat could have originally taken a bearing of either N45°E or S45°W to arrive at the current spot.
Learn more about boat here,
https://brainly.com/question/15394794
#SPJ1
a. The boat is currently 60.5 miles from its pier.
b. The boat could have originally taken a bearing of either N45°E or S45°W to arrive at the current spot.
a.How to determine the distance from the boat's pier?
To determine the distance from the boat's pier, we can use the Pythagorean theorem since we have a right triangle formed by the boat's original position, the current position, and the distance traveled to reach the current position.
Let's call the distance from the boat's pier to the current position "d", and let's call the distance traveled after the turn "x".
Using trigonometry, we can see that:
sin(35°) = x/d
Rearranging this equation, we get:
x = d×sin(35°)
Now we can use the Pythagorean theorem to solve for "d":
d² = 29²+ (d×sin(35°))²
d² = 841 + 0.77d²
0.23d² = 841
d² = 3661.74
d = 60.5 miles (rounded to one decimal place)
Therefore, the boat is currently 60.5 miles from its pier.
b. How to determine the original bearing?
To determine the original bearing, we can use trigonometry again. Let's call the original bearing "θ". Then we have,
cos(θ) = 29/d
Rearranging this equation,
d = 29/cos(θ)
Now we can substitute this expression for "d" into the equation we used to solve for "x" earlier:
x = d×sin(35°)
x = (29/cos(θ))×sin(35°)
We know that after traveling this distance, the boat is currently 14.6 miles away from its original position. So we can set up another equation:
cos(θ) = 14.6/(29/cos(θ))
Simplifying, we get:
cos²(θ) = 0.5
Taking the inverse cosine of both sides,
θ = 45° or θ = 315°
Therefore, the boat could have originally taken a bearing of either N45°E or S45°W to arrive at the current spot.
Learn more about boat here,
https://brainly.com/question/15394794
#SPJ1
Choose which sampling technique 1s used. (R) Random (STR) Stratined (CLS) Cluster
(CON) Convenience (SYS) Systematic
1. I ask everyone in my 5th period class who has more than one computer
at home in a study about all of my students for the year.
2. I collect data from every 15th student on my list of the entire school
population.
3. After using a random number table to generate two-digit numbers, I
decide on 10 people to choose from the population.
Answer:
1. CON (convenience sampling) - This sampling technique involves selecting participants who are readily available and willing to participate. In this case, the researcher is only selecting from their 5th period class, which is not a representative sample of the entire student population.
2. SYS (systematic sampling) - This sampling technique involves selecting every nth element from a population. In this case, the researcher is selecting every 15th student on their list of the entire school population.
3. R (random sampling) - This sampling technique involves selecting participants at random from the population. In this case, the researcher is using a random number table to generate two-digit numbers and selecting 10 people from the population.
Hope this helps!
Answer:
1. CON (convenience sampling) - This sampling technique involves selecting participants who are readily available and willing to participate. In this case, the researcher is only selecting from their 5th period class, which is not a representative sample of the entire student population.
2. SYS (systematic sampling) - This sampling technique involves selecting every nth element from a population. In this case, the researcher is selecting every 15th student on their list of the entire school population.
3. R (random sampling) - This sampling technique involves selecting participants at random from the population. In this case, the researcher is using a random number table to generate two-digit numbers and selecting 10 people from the population.
Hope this helps!
sketch the graphs y=|x|, y=|x|+2, y=|x|-1
The graph of y=|x| is a v-shaped graph that starts at the origin and continues infinitely in both the positive and negative x-directions. The graph of y=|x|+2 is the same v-shaped graph, but it has been shifted up two units so that it no longer intersects the x-axis. Finally, the graph of y=|x|-1 is a v-shaped graph that has been shifted down one unit so that it intersects the x-axis at (1,0) and (-1,0). All three graphs are symmetric with respect to the y-axis.
A quality control technician at a candle factory tested the eight 16-ounce candles, each 3 inches in diameter. These candles came from the same production run. The table shows the decrease in weight of each candle after burning for 3 hours. Candle makers believe that the rate at which the candles burn is constant.
Write an equation that can be used to model the weight,
of such a candle as a function of
, the number of hours burning. Then, explain how the equation can be used to predict the weight of a candle that has burned for 5 hours.
Enter your equation and your explanation in the box provided.
Answer:
According to the model. the weight of the candle after S hours of burning would be about 15.05 ounces
Step-by-step explanation:
If the burn rate is believed to be constant, determine the average burn rate for the eight candles as the ratio of weight loss per hour.
ounces lost over three hours
0.5+0.6+0.5÷0.7÷0.7÷0.5÷0.5÷0.6
8
* 0.575
0.575
ounces lost per hour on average
= 0.19
For 0 hours, the weight of each candle is 16 ounces. Therefore, w 16 - 0.19h.
This model can be used to predict the weight of the candle when h, the number of hours of burning, is 5.
W * 16 - 0.19(5)
W = 16 - 0.95
W = 15.05
According to the model. the weight of the candle after S hours of burning would be about 15.05 ounces.
Find the weighted mean. Round your answer to the nearest tenth.
The weighted mean of the deliveries each week can be found to be 5. 38 .
How to find the weighted mean ?The weighted mean is a type of mean that takes into account, the weight of the various items in question.
First, find the total frequency :
= 1 + 5 + 4 + 3
= 13
The weighted mean would then be:
= ∑ ( weight of delivery x number of deliveries )
= ( 1 / 13 x 2 ) + ( 5 / 13 x 4 ) + ( 4 / 13 x 6 ) + ( 3 / 13 x 8 )
= 0. 15 + 1. 54 + 1. 84 + 1. 85
= 5. 38
Find out more on weighted mean at https://brainly.com/question/18554478
#SPJ1
What is the area of this figure?
20 mi
3 mi
11 mi
7 mi
3 mi
4 mi
3 mil
Write your answer using decimals, if necessary.
square miles
3 mi
The area of the figure composed of two rectangles is 99 mi²
How to solve an equation?An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.
The area of a figure is the amount of space it occupies in its two dimensional state.
For the first rectangle:
Area = 11 mile * 5 mile = 55 mi²
For the second rectangle:
Area = 11 mile * 4 mile = 44 mi²
The area of figure = 55 mi² + 44 mi² = 99 mi²
The area of the figure is 99 mi²
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
In a game of cards you win $1 if you draw a heart (except the ace), $5 if you draw an ace (including the ace of hearts), $10 if you draw the king of spades and $0 for any other card. Let W be the amount you win playing this game, what the probability distribution of W?
There are four possible outcomes in this game: winning $1, winning $5, winning $10, or winning $0.
The probability of winning $1is the probability of drawing one of the 11 hearts that are not the ace of hearts. There are 52 cards in the deck, so the probability of drawing any one of them is 1/52. However, there are 11 hearts that win $1, so the probability of winning $1 is:
P(W = $1 ) = 11/52
The probability of winning $5 is the probability of drawing the ace of hearts, which is 1/52.
P(W = $5) = 1/52
The probability of winning $10 is the probability of drawing the king of spades, which is also 1/52.
P(W = $10) = 1/52
The probability of winning $0 is the probability of drawing any other card, which is 39/52.
P(W = $0) = 39/52
If the image is rotated about the x-axis, which of the following images best represents the result?
A. Y
B. Z
C. X
D. W
The images best represents the result is image W.
We have, the image is rotated about the x-axis.
Now, rotating around x axis can give the other half of the image.
Also, rotating about x axis gives the mirror image of the figure.
So, the rotation leads to a circle.
and, In three dimensional we can say that Sphere.
Thus, the required image is W.
Learn more about Rotation here:
https://brainly.com/question/1571997
#SPJ1
Which number line shows the solution set for |h-3| ≤5?
Answer:
Second number line
Step-by-step explanation:
(h-3)^2 <= 25
h^2 - 6h + 9 <= 25
h^2 - 6h - 16 <= 0
(h-8)(h+2) <=0
Using the graph of (x-8)(x+2),
-2 <= h <= 8
Hence, the answer is the second one (as it has shaded circles)
Hope this helps and be sure to mark this as brainliest! :)
A genetic experiment with peas resulted in one sample of offspring that consisted of 427 green peas and 154 yelow peas. a. Construct a 90% confidence interval to estimate of the percentage of yellow peas. b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25%, of the offspring peas would be yellow? a. Construct a 90% confidence interval. Express the percentages in decimal form.
how do I do 75% of 200
Answer:
150
Step-by-step explanation:
divide the percentage by 100 to make it decimal form,
75/100= .75
The multiple .75 by the total amount to find the 75%,
200 x .75 = 150
Which means 75% of 200 is 150
Triangle D has been dilated to create triangle D′. Use the image to answer the question.
image of a triangle labeled D with side lengths of 3.8, 4.8, 4.2 and a second triangle labeled D prime with side lengths of x, 2.4, 2.1
Determine the scale factor used.
one half
2
one fourth
3
Answer:
To determine the scale factor used, we need to find the ratio of corresponding side lengths in both triangles.
Let's compare the length of the first side in both triangles:
x/3.8 = 2/4.8
Cross-multiplying, we get:
4.8x = 7.6
Dividing both sides by 4.8, we get:
x = 1.58
Now, let's compare the length of the second side in both triangles:
2.4/4.2 = 0.57
Finally, let's compare the length of the third side in both triangles:
2.1/4.8 = 0.44
Since the scale factor is the same for all corresponding side lengths, we can take the average of the ratios:
(scale factor) = (1.58/3.8 + 0.57 + 0.44)/3
(scale factor) = 1.01
Therefore, the scale factor used is approximately 1.
↑
tructor
Watch the video and then answer the problem given below.
Click here to watch the video.
The circle graph represents a sample of 600 people who were asked which one automobile accessory they would most
prefer to have on a family trip. How many people indicated Bluetooth capability?
people
CEFF
Automobile Accessories for a Family Road Trip
Bluetooth capability 29%
Other 21%
Clear all
Roof rack 8%
Extra cup holders 15%
DVD player 27%
Check answer
Based on the above, about 174 people out of the sample of 600 people indicated Bluetooth capability.
What is the graph about?To know the number of individuals who shown Bluetooth capability, we have to to begin with calculate the division of individuals who chose this choice from the circle chart.
Note that:
People who Bluetooth capability =29%
Number of people = Percentage × Total sample size
= 0.29 × 600
= 174
So, 174 individuals shows that the Bluetooth capability is their favored option for the family trip.
Learn more about sample from
https://brainly.com/question/24466382
#SPJ1
The graph of f(x) and table for g(x)= f(kx) are given.- WORTH 40 BRAINLY POINTS PLEASE ANSWER FAST
The graph shows an upward opening parabola labeled f of x that passes through a point negative 2 comma 8, a point negative 1 comma 2, a vertex 0 comma 0, a point 1 comma 2, and a point 2 comma 8.
x g(x)
−6 8
−3 2
0 0
3 2
6 8
What is the value of k?
k = 3
k is equal to one third
k = 6
k is equal to negative one sixth
The value of k include the following: B. k is equal to one third.
What is the vertex form of a quadratic equation?In Mathematics, the vertex form of a quadratic function can be modeled by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about the quadratic function f(x), we can logically deduce that its vertex is at (0, 0);
f(x) = a(x - h)² + k
2 = a(1 - 0)² + 0
2 = a
f(x) = 2(x - 0)² + 0
f(x) = 2x²
For the quadratic function g(x), we have;
g(x) = f(kx)
g(x) = 2(kx)²
g(x) = 2k²x²
By using the point (3, 2) from the table, we have:
2 = 2k²3²
1 = k²9
k² = 1/9
k = √(1/9)
k = 1/3 i.e one third.
Read more on vertex here: brainly.com/question/14946018
#SPJ1
View photo below. This is timed.
Answer: ∠EFB, ∠DFE, and ∠CFB
Step-by-step explanation:
Starting Angle: ∠CFD
Since its in an X formation: ∠EFB, ∠DFE, and ∠CFB would all work.
SAT/ACT An arc has a central angle of
radians and a length of 6. What is the
circumference of the circle?
A 12T
B 15T
30T
D 36л
Answer: D 36л
Step-by-step explanation:
s = θr
where r is the radius of the circle. given that the arc length is 6, and the central angle is π/3 radians r:
6 = (π/3)r
r = 6/(π/3) = 18/π
the circumference of the circle is given by:
C = 2πr
Substituting r = 18/π, we get:C = 2π(18/π) = 36
A sample of n = 64 scores has a mean of M = 68. Assuming that the population mean is μ = 60, find the z-score for this sample:
If it was obtained from a population with σ = 16
z =
If it was obtained from a population with σ = 32
z =
If it was obtained from a population with σ = 48
z =
c) Population [tex]\sigma = 48[/tex]
Z = [tex]\frac{68-60 }{\frac{48 }{\sqrt{64}}}[/tex]
Z-score= 1.3333
How to solveAccording to the question , sample size n=64 , mean M = 68 , population mean [tex]\mu= 60[/tex]
Z = [tex]\frac{M-\mu }{\frac{\sigma }{\sqrt{n}}}[/tex]
where M = Sample Mean
[tex]\mu[/tex] = Population Mean
[tex]\sigma[/tex] = Population Standard Deviation
n = Sample Size
a) Population [tex]\sigma[/tex] = 16
Z = [tex]\frac{68-60 }{\frac{16 }{\sqrt{64}}}[/tex]
Z-score = 4
b) Population [tex]\sigma[/tex] = 32
Z = [tex]\frac{68-60 }{\frac{32 }{\sqrt{64}}}[/tex]
Z-score = 2
c) Population [tex]\sigma[/tex]= 48
Z = [tex]\frac{68-60 }{\frac{48 }{\sqrt{64}}}[/tex]
Z-score= 1.3333
Read more about sample mean here:
https://brainly.com/question/31101410
#SPJ1
Use the graph below to answer the question.
Money Spent on Food
dinner
42%
lunch
30%
snacks
10%
breakfast
18%
A shopper spent $100 at the store. How many dollars did the shopper spend on snacks?
A. $10
B. $18
C. $30
D. $42
For each of the following, place a decimal point in the number to make the sentence reasonable. a. The basketball player is 1950 cm tall. b. A new piece of chalk is about 8100 cm long. c. The speed limit in town is 400 km/hr.
a. The basketball player is 19.50 cm tall. (Assuming you meant to write
195 cm instead of 1950 cm)
b. A new piece of chalk is about 81.00 cm long.
c. The speed limit in town is 40.0 km/hr. (Assuming you meant to write 40 km/hr instead of 400 km/hr).
What is the equivalent expression?Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
By placing a decimal point in the appropriate location, we can make the numbers more reasonable.
a. The basketball player cannot be 1950 cm tall, as that is almost 20 meters or over 65 feet.
The average height of a basketball player in the NBA is around 6'7'' (or about 2 meters).
Therefore, we can assume that the correct height of the basketball player is 195 cm, or about 6'5''.
b. A piece of chalk that is 8100 cm long is over 80 meters long, which is clearly too long for a piece of chalk.
Therefore, we can assume that the correct length of the chalk is 81.00 cm or about 32 inches.
c. A speed limit of 400 km/hr is unreasonably high, as it is equivalent to over 248 miles per hour.
The highest speed limits in the world are typically around 80-85 mph (130-140 km/hr), so 400 km/hr is clearly incorrect.
Therefore, we can assume that the correct speed limit is 40.0 km/hr, which is a more reasonable speed limit for a town or residential area.
Hence,
a. The basketball player is 19.50 cm tall. (Assuming you meant to write
195 cm instead of 1950 cm)
b. A new piece of chalk is about 81.00 cm long.
c. The speed limit in town is 40.0 km/hr. (Assuming you meant to write 40 km/hr instead of 400 km/hr).
To learn more about the decimal point visit:
https://brainly.com/question/20753759
#SPJ1
Find the sum of 10x² + 7x + 6 and 6x + 5.
Answer:
Submit Answer
M
DELL
10x² + 13x + 11 is the sum of linear equation .
What is a linear equation in mathematics?
The algebraic equation y=mx+b is known as a linear equation. All of its terms are constant, first-order linear ones. where m denotes the slope and b the y-intercept.
The aforementioned is occasionally referred to as a "linear equation in two variables" where y and x are variables. One or more variables may be present in a linear equation. The term "bivariate linear equation" refers to a linear equation with two variables.
two equations are 10x² + 7x + 6 and 6x + 5.
now add both equations
= (10x² + 7x + 6 )+ (6x + 5)
= 10x² + 7x + 6 + 6x + 5
= 10x² + 13x + 11
Learn more about linear equation .
brainly.com/question/11897796
#SPJ1
A room is 18 feet long and 12 feet wide. At $13.25 per square yard, what will be the cost for wall-to-wall
carpeting?
The cost for wall-to-wall carpeting is equal to $ 318.
How to compute the cost for wall-to-wall carpeting
In this problem we need to compute the cost for wall-to-wall carpeting, that is, the cost of covering the floor of the entire room. This can be done by using the following formula:
C = (1 / 9) · c · w · l
Where:
C - Cost, in monetary units. c - Unit cost, in monetary units per yard.w - Width, in feetl - Length, in feetIf we know that c = 13.25, w = 12 and l = 18, then the cost of the wall-to-wall carpeting is:
C = (1 / 9) · 13.12 · 12 · 18
C = 318
To learn more on costs of carpets: https://brainly.com/question/29061014
#SPJ1
At Downtown Pizza, 4 of the last 6 pizzas sold had pepperoni. What is the experimental probability that the next pizza sold will have pepperoni?
The answer of the given question based on the experimental probability is the next pizza sold at Downtown Pizza will have pepperoni is 2/3 or approximately 0.67.
What is Experimental probability?Experimental probability is ratio of number of times event occurs to the total number of trials or observations conducted in experiment or real-life situation. It is based on actual observations or data and is also known as empirical probability.
Experimental probability is used when it is not possible or feasible to determine the theoretical probability of an event, or when the theoretical probability does not match the actual outcomes observed in a given situation. In such cases, experimental probability provides an estimate of the likelihood of an event occurring based on real-life data.
The experimental probability that the next pizza sold will have pepperoni is the ratio of the number of pepperoni pizzas sold to the total number of pizzas sold in the recent past.
According to the problem, 4 of the last 6 pizzas sold had pepperoni. So, the experimental probability of the next pizza sold having pepperoni is:
experimental probability = number of pepperoni pizzas sold / total number of pizzas sold
experimental probability = 4 / 6
experimental probability = 2 / 3
Therefore, the experimental probability that the next pizza sold at Downtown Pizza will have pepperoni is 2/3 or approximately 0.67.
To know more about Empirical probability visit:
https://brainly.com/question/29776548
#SPJ1
What’s the equation of the line shown above ? A y=2x+3 B y=2x+1/3 C y=3x+2 D y=1/3x+2
It should be noted that to find the equation of a line, two pieces of information are necessary: the slope and coordinates of a point on the line.
How to find the equationAlso, to acquire this, one can leverage either the point-slope form or the slope-intercept form to compose it.
If both the slope (m) and coordinates of the point (x1, y1) on the line are known, then one can express the equation in its point-slope style as follows:
y - y1 = m(x - x1)
Or, if only the slope (m) and the y-intercept (b), which is the value of y where the line crosses the y-axis, are accessible, then the equation can be expressed via the slope-intercept form with: y = mx + b
Learn more about equations on
https://brainly.com/question/18831322
#SPJ1
A ribbon is 29 centimeters long. How many millimeters long is the ribbon?
2.9 millimeters
2,900 millimeters
290 millimeters
58 millimeters
Answer: The 290 millimeters long is the ribbon.
Step-by-step explanation:
To convert centimeters to millimeters
1 cm =10 millimeters
therefore,
29cm= 290 millimeters
Therefore, the ribbon is 290 millimeters long.
To learn more about Ribbon length
https://brainly.in/question/50652931?
) Find the average gold medal winnings of those NOCs who have been
awarded fewer than ten bronze medals.
Count the number of those NOCs that have been awarded ten or more
silver medals.
This question requires the construction and interpretation of a pie chart based
on the data throughout this task.
a) Create a suitable and fully labelled pie chart to show the total medal
winnings of the Top 10 NOCs at the Beijing 2022 Winter Olympic games.
Interpret the pie chart produced in Question 8a). Discuss two probable
justifications for the behaviour of the data.
a. To create a pie chart to show the total medal winnings of the Top 10 NOCs at the Beijing 2022 Winter Olympic games:
Obtain the data for the medal winnings of the Top 10 NOCs
Find the average gold medal winnings of those NOCs who have beenawarded fewer than ten bronze medals.?Calculate the total medal winnings for each NOC (i.e., the sum of gold, silver, and bronze medals)
Create a pie chart in Excel or any other software by selecting the data and choosing the pie chart option
Add a title and labels to the chart to show the NOCs and their corresponding medal winnings
b. The interpretation of the pie chart produced in Question 8a) depends on the shape and distribution of the chart. Two probable justifications for the behavior of the data are:
Dominance of certain NOCs: The pie chart may show that certain NOCs have a significantly higher share of medal winnings compared to others. This may be due to the dominance of these NOCs in specific sports or events, or due to their superior training and preparation.
Balanced distribution of medals: The pie chart may show a relatively balanced distribution of medal winnings among the Top 10 NOCs. This may indicate a high level of competitiveness and equal opportunities for success among the NOCs.
to know more about Olympic
brainly.com/question/29376067
#SPJ1
sine law vector method
Answer: Well that wouldn't work quite as well.
Step-by-step explanation:
(4a-ts)(2a+2ts) what is the solution
Answer:
8a^2 + 6ats - 2t^2s^2
Step-by-step explanation:
(4a-ts)(2a+2ts)
4a(2a+2ts) -ts(2a+2ts)
8a^2 + 8ats - 2ts - 2t^2s^2
= 8a^2 + 6ats - 2t^2s^2
In the diagram shown, ABC is equilateral. AD is an altitude.
10). ABD = _____.
11). ADB = _____.
12). BAD = _____.
13). CAD = _____.
Suppose AB = 6. Find:
14). BD
15). AD
16). Area of ABC
All the correct values are,
⇒ ∠ABD = 60°
⇒ ∠ADB = 90°
⇒ ∠BAD = 30°
⇒ ∠CAD = 30°
⇒ BD = 3
⇒ AD = √27
⇒ The value of area of triangle ABC is, 3√27
Given that;
In the diagram shown, ABC is equilateral. AD is an altitude.
Hence, We get;
All the angles of a equilateral triangle are,
⇒ 60°
Thus, We get;
⇒ ∠ABD = 60°
Since, AD is an altitude.
⇒ ∠ADB = 90°
And,
⇒ ∠BAD = 60 / 2 = 30°
⇒ ∠CAD = 60/2 = 30°
By Pythagoras theorem;
AB² = AD² + BD²
6² = AD² + 3²
36 = AD² + 9
AD² = 27
AD = √27
Thus, The value of area of triangle ABC is,
⇒ 1/2 × AD × BC
⇒ 1/2 × √27 × 6
⇒ 3√27
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ1
Write an equation for the transformed logarithm shown below, that passes through (1,0) and (-3,3)
The equation of the transformed logarithmic function that passes through the points (1,0) and (-3,3) is f(x) = 4.366*log10(x+4)
To find the equation of the transformed logarithmic function that passes through the points (1,0) and (-3,3), we need to determine the values of a, b, h, and k.
First, we know that the function passes through (1,0), so we can substitute x=1 and y=0 in the general equation of the transformed logarithmic function to get:
0 = a x log b(1-h) + k
Since log b(1-h) = 0 for any base b and any value of h, we can simplify the equation to:
0 = k
Therefore, k=0 and the equation becomes:
f(x) = a x log b(x-h)
Now, we have two equations with two unknowns (a and h), which we can solve by substitution or elimination. For simplicity, we can substitute b=10 (base 10 logarithm) since it is a common base and the values of a and h do not depend on the base of the logarithm. We get:
10⁶/ᵃ = 3-h
Since h is the horizontal shift of the graph, we can choose any value of h that makes the expression inside the logarithm positive. For example, we can choose h=-4, which makes x-h=-3-(-4)=1, the same as the x-coordinate of the point (1,0).
Taking the logarithm of both sides with base 10, we get:
log(4) = (6/a)*log(10)
Solving for a, we get:
a = 6/(log(4)*log(10)) ≈ 4.366
Now, we can substitute the values of a and h in the equation of the transformed logarithmic function to get:
f(x) = 4.366*log10(x+4)
To know more about equation here
https://brainly.com/question/10413253
#SPJ1
Find The volume of this 7th Grade Mathematical 3D Triangular Prism!!!!!!!!
The volume of the triangular base prism is 120 inches³.
How to find the volume of a triangular prism?The prism above is a triangular base prism. The volume of the triangular base prism can be calculated as follows:
volume of the prism = base area × height
Therefore,
base area = 1 / 2 bh
base area = 1 / 2 × 8 × 10
base area = 80 / 2
base area = 40 inches²
Therefore,
volume of the prism = 40 × 3
volume of the prism = 120 inches³
learn more on volume here: brainly.com/question/22907480
#SPJ1
This shows a number line. Which point is located at 90 ?
Answer:
incomplete question bru