Answer:
x < -28
Step-by-step explanation:
5x < -28
x < -28/5
Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that ∠A1 is smaller than ∠A2.)
b = 121, c = 162, ∠B = 48°
The values of triangle ABC are
< A = 47.8 < C = 84.2a = 120.6How to find the angels in triangle ABCThe angles in triangle ABC is calculated using the sine rule which sates that the ratio of a side and the opposite angles are equal to each other
This represented by the formula
Sine A / a = Sine B / b = Sine C / c
applying the formula for the problem
Sine B / b = Sine C / c
Sine 48 / 121 = Sine C / 162
cross multiplying
Sine C = 162 * Sine 48 / 121
Sine C = 0.99495
C = arc sine (0.99495)
C = 84.2
Applying sum of angles in a triangle
< A + < B + < C = 180
< A + 48 + 84.2 = 180
< A = 180 - 48 - 84.2
< A = 47.8 degrees
side a
Sine A / a = Sine B / b
Sine 47.8 / a = Sine 48 / 121
121 * sine 47.8 / Sine 48 = a
a = 120.6
Learn more about sine rule at:
https://brainly.com/question/29625488
#SPJ1
32. Solve the equation and check your solution: 3(x + 6) = 18 + 3x
Answer:
4
Step-by-step explanation:
18 = 3x + 6
18 - 6 = 3x
12=3x
12/3 = x
4 = x
Hope this helped, please mark the brainliest if it did! I put a lot of effort into my answers
What is the rate of change
The rate of change of the table is 3
How to calculate the rqte of change of the table?From the question, we have the following parameters that can be used in our computation:
The table of values
On the table, we have the following ordered pairs
(9, -6) and (11, -12)
The rate of the table is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (9, -6) and (11, -12)
Substitute the known values in the above equation
So, we have the following equation
Slope = (-12 + 6)/(11 - 9)
Evaluate
Slope = -3
Hence, the rate of the table is -3
Read more about slope at
brainly.com/question/3493733
#SPJ1
adam is standing next tot he palmetto building in columbia, south carolina. he is 6 feet tall and the length of his shadow is 9 feet. if the length of the shadow of the building is 322.5 feet, how tallis the building?
He stands 6 feet tall, and his shadow extends 9 feet. if the building's shadow extends for 322.5 feet.
Now 6/9 = X/322.5
9X = 1935
X = 215ft
The Height of the building = 215ft
Consider an object AB of height h such that its shadow of length s is formed and angle of elevation is θ.
The object AB depicts a right triangle in which ∠ABO = 90o.
Now we know that in trigonometry, the tangent ratio for an angle is equal to the opposite side to that angle divided by its adjacent side.
So, for the angle of elevation θ, we have
=> tan θ = AB/OB
Putting AB = h and OB = s, we get
=> tan θ = h/s
=> s/h = 1/tan θ
=> s = h/tan θ
Learn more about Shadow here:
https://brainly.com/question/15021258
#SPJ4
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
3 cm
Step-by-step explanation:
Given
Triangle ABC and Triangle DEF are similar
BC=4cm
EF = 16cm
FD = 12cm
ED = 10cm
Since we know that the triangles are similar,
AB/DE = BC/EF = CA/FD as they are the corresponding sides of the similar triangles
or
BC/EF = AC/FD
or
4/16 = AC/12
1/4 = AC/12
12/4 = AC
3 = AC
Therefore the value of AC is 3 cm
please help me to find this!!!!!!
ASAP.............
9x _ 7i ≥ 3 ( 3x _7u )
Step-by-step explanation:
9x-7i > 3(3x-7u)
-9x-7i > 9x-21u
-7i > -21u
-i > -3u
i < 3u
Antonia visits the park every 6 days and goes to the library every 7 days. If Antonia does both of these today, how many days will pass before Antonia gets to do them both on the same day again?
Antonia will have to wait 42 days before she gets to do both activities on the same day again.
The smallest positive integer that is a multiple of both 6 and 7 is the least common multiple (LCM) of 6 and 7. This is the number of days that will pass before Antonia does both of these activities on the same day again.
We can find the LCM of 6 and 7 using the formula as follows -
LCM(6, 7) = 6 * 7 / GCD(6, 7)
where GCD is the greatest common divisor.
The GCD of 6 and 7 is 1, so we can write -
LCM(6, 7) = 6 * 7 / 1 = 42
Therefore, Antonia will have to wait 42 days before she gets to do both activities on the same day again.
Read more about LCM:
brainly.com/question/16054958
#SPJ4
HELP
The mean daily pocket money of 35 pupils in another class is m cents. Given that the mean daily pocket money of the 80 pupils from these two classes is 72.25 cents, calculate the value of m.
Answer:-0.696
Step-by-step explanation:Let the total daily pocket money of the 35 pupils in the other class "A" and the total daily pocket money of all 80 pupils "B".
The mean daily pocket money of the 35 pupils in the other class is m cents, so:
A = 35 * m
The mean daily pocket money of all 80 pupils is 72.25 cents, so:
B = 80 * 72.25
Since we know the total pocket money of both classes, we can use this information to solve for m:
A + B = 115 * m
35 * m + 80 * 72.25 = 115 * m
35 * m = 115 * m - 80 * 72.25
35 * m = 115 * m - 5780
5780 = 115 * m - 35 * m
5780=80 * m
Finally, we can solve for m:
m = 5780/80
m = 72.25
according to the u.s. census bureau, 5% of americans age 25 or older had completed a bachelor's degree or higher in 1940. write this percent as a ratio and do not simplify.
5% as a ratio not in simplified form is 5/100 or 5:100.
To write a percent as a ratio, we can divide it by 100 and express the result as a fraction. For example, 5% can be written as 5/100.
So, according to the U.S. Census Bureau, 5% of Americans age 25 or older had completed a bachelor's degree or higher in 1940 can be written as a ratio as:
= 5/100
This fraction represents the ratio of Americans age 25 or older who had completed a bachelor's degree or higher in 1940 to the total number of Americans age 25 or older.
To know more on percentage and ratio
https://brainly.com/question/30033832
#SPJ4
Here are 2 polygons. Select all sequences of translations, rotations, and reflections below that would take polygon P to polygon Q
The sequences of translations, rotations, and reflections bthat would take polygon P to polygon Q will be:
C Translate so that Ais taken to J. Then reflect over line BA
E Reflect over line BAand then translate by directed line segment BA.
What is translation?A function is translated when it is moved from where it was before. In geometry, a function that moves an object a specific distance is referred to as translation. Nothing else is done to change the object.
It is not scaled, reflected, rotated, or refracted. Every point of the object must be translated by the same amount and in the same direction.
Learn more about translation on:
https://brainly.com/question/12861087
#SPJ1
Given: number of free throws made by a basketball player varies directly with
number of attempts the player has. If she makes 12 out of 40 attempts, how
many would she make during the season if she had 135 total attempts?
If she makes 135 attempts, the number of throws will be 40.5 .
How to find the number she makes?Number of free throws made by a basketball player varies directly with number of attempts the player has. If she makes 12 out of 40 attempts, the amount of throws she will make during the season if she made 135 total attempts can be calculated as follows:
Therefore,
y ∝ x
y = kx
where
k = number of free throwsx = number of attemptsTherefore,
12 = 40k
k = 12 / 40
k = 6 / 20 = 3 / 10
Hence,
y = 3 / 10 × 135
y = 405 / 10
y = 40.5
Therefore, the number of throws will be 40.5.
learn more on proportional relationship here: https://brainly.com/question/19059146
#SPJ1
Find the volume of a cone with a base diameter of 8 cm and a height of 6 cm .
Use the value 3.14 for π, and do not do any rounding.
Be sure to include the correct unit in your answer.
The volume of a cone with a diameter of 8 cm and a height of 6 cm is
100.48 cm³.
What is a cone?A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.
The volume of a cone is (1/3)πr²h.
The total surface area of a cone is πr(r + l).
The curved surface area is πrl.
Given, The height of the cone is 6 cm.
Also given the diameter of the base 2r = 8 cm hence r = 4 cm.
Therefore, The volume of this cone is,
= (1/3)π(4)²×6 cm³.
= 32π cm³.
= 100.48 cm³
learn more about cones here :
https://brainly.com/question/23863102
#SPJ1
D) If fx)=-x-11; find the following
1) 4f(-2) +5f(1) =
3) -5f12)-2f-9) =
2) 3f(5) x (2)
4)f(9)/f(-6)=
Pls I need help quick
To find 4f(-2) + 5f(1), we need to first find the values of f(-2) and f(1). Using the given equation, we have:
An easy definition of a function
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
f(-2) = -(-2) - 11 = 9
f(1) = -1 - 11 = -12
So, 4f(-2) + 5f(1) = 4 * 9 + 5 * -12 = 36 - 60 = -24.
To find 3f(5) * 2, we need to first find the value of f(5). Using the given equation, we have:
f(5) = -5 - 11 = -16
So, 3f(5) * 2 = 3 * -16 * 2 = -96
To find -5f(12) - 2f(-9), we need to first find the values of f(12) and f(-9). Using the given equation, we have:
f(12) = -12 - 11 = -23
f(-9) = -(-9) - 11 = 2
So, -5f(12) - 2f(-9) = -5 * -23 - 2 * 2 = 115 + 4 = 119
To find f(9)/f(-6), we need to first find the values of f(9) and f(-6). Using the given equation, we have:
f(9) = -9 - 11 = -20
f(-6) = -(-6) - 11 = 5
So, f(9)/f(-6) = -20 / 5 = -4.
Learn more about function
https://brainly.com/question/11624077
#SPJ1
In a circle with radius 8, an angle intercepts an arc of length 16pi/3. Find the angle in radians in simplest form.
The angle in radians in simplest form is 2π/3 radians.
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.
Given the radius of the circle = 8
and length of arc = 16π/3
the relation between angle and arc is given by,
s = rθ
where r = radius, s = arc length and θ = angle in radians,
so, θ = s/r
θ = (16π/3)/8
θ = 2π/3 radians
Hence the angle is 2π/3 radians.
Learn more about circles;
https://brainly.com/question/29142813
#SPJ1
PLEASE HELP WHAT TYPE OF FUNCTION
the given function y = 3(4)ˣ, is an exponential function.
What is a logarithmic function?The opposite of an exponential function is a logarithmic function. A log function and an exponential function both use the same base. An exponent is a logarithm. f(x) = bx is how the exponential function is expressed. The formula for the logarithmic function is f(x) = log base b of x.
Given a function y = 3(4)ˣ
An exponential function is defined by the formula f(x) = a, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The exponential function is an important mathematical function which is of the form
f(x) = aˣ
therefore, we can say that the given function is an exponential function.
Learn more about logarithmic functions here:
https://brainly.com/question/3181916
#SPJ1
The line with equation a + 2b = 0 coincides with the terminal side of an angle θ in standard position and cos θ<0. What is the value of sinθ?
The value of sin( tetha) is -2/√5
What is intersection value?Point of intersection is the point where two lines meet.
a+2b = 0 can be related to x+2y = 0
Line x + 2y = 0 is end side of angle θ and cos θ < 0 means x < 0. Line is y = -x/2, slope -1/2 and the Line intersects unit circle when :
b = -1/2 a
therefore the slope is -1/2
Line intersect unit circle when:
x²+y² = 1
a²+b² = 1
a² +( - 1/2a)² = 1
a²+ a²/4 = 1
5a²/4 = 1
a² = 4/5
a = √ 4/5
the value of sin(tetha) at the point of intersection is y
y = -1/2a
y = -1/2√4/5
y = -2/√ 5
learn more about intersection of line from
https://brainly.com/question/1906467
#SPJ1
a company starts to track the number of phone calls received
Answer:
pls give more detail
Step-by-step explanation:
Travelling to America, Jenny received 88 cents American for each Australian dollar. When she returned from America, she had n American dollars. What is this amount equivalent to in Australian dollars?
Answer:
Australian dollar = n * 100 / 88
Step-by-step explanation:
n = American dollars
1 Australian dollar = 88 cents American
• On Dec. 9, Rick worked from half past seven o'clock a.m. to half past four o'clock p.m. He took a half-hour lunch break.
On Dec. 10, Rick worked from seven o'clock a.m. to half past four o'clock p.m. He took a half-hour lunch break.
On Dec. 11, Rick worked from half past eleven o'clock a.m. to five o'clock p.m. He did not take a lunch break.
•
On Dec. 12, Rick worked from half past seven o'clock a.m. to half past five o'clock p.m. He took a one-hour lunch break.
• On Dec. 13, Rick worked from half past seven o'clock a.m. to seven o'clock p.m. He took a one and a half-hour lunch break.
On Dec. 14, Rick worked from eight o'clock a.m. to five o'clock p.m. He took a one and a half-hour lunch break.
On Dec. 15, Rick did not work.
The timesheet of Rick's working hours is given below.
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
From the given data points of Rick's working hours:
Date Start Time End Time Time away Regular hours
Dec. 9, 7:30 am 4:30 pm 30 minutes 8.5
Dec. 10, 7:00 am 4:30 pm 30 minutes 8.5
Dec. 11, 11:30 am 5:00 pm - 5.5
Dec. 12, 7:30 am 5:30 pm 60 minutes 9
Dec. 13, 7:30 am 7:00 pm 90 minutes 10
Dec. 14, 8:00 am 5:00 pm 90 minutes 4.9
Dec. 15, - - - -
Therefore, the timesheet is given.
To learn more about the addition;
brainly.com/question/29464370
#SPJ1
The complete question:
Make a timesheet for the following dates and times: Dec. 9, Rick...
Make a timesheet for the following dates and times:
Dec. 9, Rick worked from 7:30am to 4:30 p.m. He took a 30 min lunch break
Dec. 10, Rick worked from 7 am to 4:30 p.m. He took a 30 min lunch break
Dec. 11, Rick worked from 11:30 am to 5:00 p.m. He didn't take a lunch break
Dec. 12, Rick worked from 7:30 am to 5:30 p.m. He took an hour lunch break
Dec. 13, Rick worked from 7:30 am to 7:00 p.m. He took an hour and a half lunch break
Dec. 14, Rick worked from 8 am to 5 p.m. He took an hour and a half lunch break
Dec. 15, Rick did not work.
Which situation can be represented by the equation x + 14 = 25?
The situation that can be represented using the equation x + 14 = 25 is
illustrated below.
What is a linear equation?An equation of degree one is known as a linear equation.
A linear equation of two variables can be represented by ax + by = c.
Given an equation x + 14 = 25.
A situation can be represented as,
Joy and John are two friends, Joy has 14 chocolates, and together they have a total of 25 chocolates, How many chocolates John has?
learn more about linear equations here :
https://brainly.com/question/29739212
#SPJ1
Is 20 - 5x = 50- 10x true ?
Answer:
Step-by-step explanation:
that is incorrect.
if it were to be equal, one side should equal each other when multiplied to make the ratio equal.
20-5x=40-10x (when multiplied by 2 on each side)
It CANNOT equal 50, if it were there would not be -10x
20-5x=100-25x
DIVIDE BY 2 to get 50 WOULD GIVE:
20-5x=50-17.5x
Answer:
Yes
Step-by-step explanation:
solve the equation for x , then evaluate and compare both sides
20 - 5x = 50 - 10x ( add 10x to both sides )
20 + 5x = 50 ( subtract 20 from both sides )
5x = 30 ( divide both sides by 5 )
x = 6
then
left side = 20 - 5x = 20 - 5(6) = 20 - 30 = - 10
right side = 50 - 10x = 50 - 10(6) = 50 - 60 = - 10
since both sides are equal then
20 - 5x = 50 - 10x is true
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 8 above 10 to 19, up to 6 above 20 to 29, up to 2 above 30 to 39, and up to 2 above 50 to 59. There is no shaded bar above 40 to 49.
Which measure of center should the charity use to accurately represent the data? Explain your answer.
The median of 22.7 is the most accurate to use to show that they have plenty of money.
The mean of 20 is the most accurate to use to show that they need more money.
The median of 20 is the most accurate to use, since the data is skewed.
The mean of 22.7 is the most accurate to use, since the data is skewed.
Answer: C. The most accurate measure of center to represent the data in this case is the median of 20.
Step-by-step explanation: The median is the middle value in a dataset when the data is arranged in ascending or descending order. In this case, the donations are: 10, 10, 10, 10, 15, 15, 15, 19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55.
When we arrange these values in ascending order, we get: 10, 10, 10, 10, 15, 15, 15, 19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55.
The median is the value that separates the dataset into two equal halves. In this case, there are 18 values, so the middle value is the 9th value, which is 20.
The reason the median is the most accurate measure of center to use in this case is because the data is skewed. Skewness refers to the asymmetry in the distribution of data. In this case, the data is skewed to the right because there are a few large values (55) that pull the mean higher than the majority of the values.
Using the mean, which is calculated by summing all the values and dividing by the total number of values, would be influenced by these large values and may not accurately represent the typical donations received by the charity.
Are the domain and range of function F? F(x)=x-6\x^2-3x-18
Answer:
domain: all x except -3, 6range: all y except 0, 1/9Step-by-step explanation:
You want the domain and range of the function ...
F(x) = (x -6)/(x² -3x -18)
DomainWe can simplify the function to ...
[tex]F(x) = \dfrac{x-6}{x^2-3x-18}=\dfrac{x-6}{(x-6)(x+3)}\\\\F(x)=\dfrac{1}{x+3}\quad x\notin\{-3,6\}[/tex]
The domain is the set of x-values for which the function is defined. It is undefined where the denominator is zero. So, x=-3 and x=6 are excluded from the domain, which would otherwise be all real numbers.
RangeThe range is the set of values that the function may have. Here, the function can have any y-value except 0 (the value of the horizontal asymptote), and 1/9, the location of the "hole" at x=6.
The range is all real numbers except 0 and 1/9.
g what is the root-mean-square speed (urms) of a co2 molecule that has an average ke of 5.44 x 10-21 j/molecule?
The root mean square speed of a carbon dioxide molecule at mentioned average kinetic energy is 1.57× [tex] {10}^{-11} [/tex].
The formula to find root mean square speed of carbon dioxide molecule using average kinetic energy is as follows -
c = ✓2KE/m, where c is root mean square speed, KE is kinetic energy and m is molecular mass
Keep the values in formula to find the root mean square speed.
c = ✓2×5.44×[tex] {10}^{-21} [/tex]/44
Performing multiplication and division on Right Hand Side of the equation
c = ✓2.47×[tex] {10}^{-22} [/tex]
Taking square root on Right Hand Side of the equation
c = 1.57× [tex] {10}^{-11} [/tex]
Learn more about root mean square speed
https://brainly.com/question/25959744
#SPJ4
18. Pilihan ganda30 detik1 ptQ. Year Consumption (million barrels per day)1986 621987 631988 651989 661990 661991 671992 671993 671994 681995 701996 721997 74What was the approximate percent increase in consumption from 1986 to 1997?Pilihan jawaban10%20%30%50%80%
The approximate percent increase in consumption from 1986 to 1997 is:
B. 20%
What is the percentage increase in consumption?The initial consumption level for the year, 1986 is 62 million barrels per day and by 1997, the percent increase in consumption shot up to 74 million barrels per day.
When we subtract the latter consumption levels from the former, we will have a total of 12 million barrels per day. So, the percentage increase will be:
12 million barrels per day/ 62 million barrels per day × 100
= 19.35 %
Thus, we can arrive at the conclusion that the total consumption levels per day increased by 19.35%, which is approximately 20%.
Learn more about percentage increments here:
https://brainly.com/question/28398580
#SPJ1
In a group, 40% of the items are red. Of all the red items in the group, 30% also have stripes. What percentage of the items in the group are red and have stripes?
Answer:
12% of the items in the group are red and have stripes.
Step-by-step explanation:
Aassume that there is 100 items, 40 items red.
In the 40 items, 30% are striped.
40×(30/100)=12%
12% of the items in the group are red and have stripes. This is found by multiplying the proportion of red items (40%) by the proportion of these red items that also have stripes (30%).
Explanation:We are given that 40% of items in a group are red. This is represented as 40/100, or 0.40. The question mentions that out of these red items, 30% also have stripes. This can be represented as 30/100, or 0.30. The question requires us to find out what percentage of the total items in the group are red and have stripes. To find this, we multiply 0.30 (the proportion of red items that are striped) by 0.40 (the proportion of items that are red).
So, 0.30 x 0.40 = 0.12 or 12%.
Therefore, 12% of the items in the group are red and have stripes.
Learn more about Percentage Calculation here:https://brainly.com/question/329987
#SPJ2
For a moving object, the force acting on the object varies directly with the objects acceleration. When a force of 40 N acts on a certain object, the acceleration of the object is 4 m/s^2. If the acceleration of the object becomes 9 m/s^2, what is the score?
Answer:
Step-by-step explanation:
We can use the proportionality relationship between force and acceleration, which is given as:
force = constant × acceleration
Let's call the constant of proportionality k. Then we can write:
40 N = k × 4 m/s^2
Solving for k, we get:
k = 40 N / 4 m/s^2 = 10 Ns^2/m
Now we can use this value of k to find the force required for an acceleration of 9 m/s^2:
force = k × acceleration = 10 Ns^2/m × 9 m/s^2 = 90 N
Therefore, the force required for an acceleration of 9 m/s^2 is 90 N.
3. you want to determine whether the race of the defendant has an impact on jury verdicts. you assign participants to watch a trial with either a hispanic or caucasian defendant, and you measure on a 1 (not at all) to 7 (very) scale how guilty the defendant is. what is the best dv scale of measurement?
The best discrete variable of measurement for the situation is an interval.
What is the Scale of Measurement?Finding the scale of measurement for the variables is the next step in selecting a statistical test after identifying the independent and dependent variables. The dependent variable must be measured using an interval or ratio scale for each of the parametric tests that we have covered so far. Many psychologists also subject variables with roughly interval scales of measurement to parametric tests. You must decide whether to use "scale" or "interval" scores when performing parametric tests of means.
Given the condition about whether the race of the defendant has an impact on jury verdicts,
and measure on a 1 (not at all) to 7 (very) scale how guilty the defendant,
The best scale of measurement for the condition is an interval.
Although the interval scale has characteristics of nominal and ordered data, it also allows for the quantification of data point differences. The variables' actual positions in the order as well as their differences are both displayed by this form of data. They can be combined or split, but not added to or subtracted from.
The fact that zero is an existing variable adds another characteristic to this scale. Zero in the ordinal scale indicates that there is no data.
Hence the scale of measurement is an interval.
Learn more about the Scale of Measurement;
https://brainly.com/question/17893821
#SPJ1
Compare using
>
,
<
,
>,<,is greater than, comma, is less than, comma or
=
=equals.
72
×
3
7
72×
7
3
72, times, start fraction, 3, divided by, 7, end fraction, space
72
72space, 72
How do you know your answer is correct?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Because we are multiplying
72
7272 by a fraction that is less than
1
11.
(Choice B)
B
Because we are multiplying
72
7272 by a fraction that is equal to
1
11.
(Choice C)
C
Because we are multiplying
72
7272 by a fraction that is greater than
1
11.
The examination of the results of the two numerical articulations, 72 × 3 and 72 × 7, can be resolved utilizing the duplication administrator (×). 72 × 3 = 216 and 72 × 7 = 504.
While contrasting the results of these two expressions, we can see that 504 is more prominent than 216. This can be addressed as 504 > 216.
This implies that when 72 is duplicated by 7, the outcome is more prominent than when 72 is increased by 3.
This is on the grounds that 7 is a bigger number than 3, and thus, when it is increased by 72, the outcome will be bigger. All in all, the expression 72 × 7 delivers a more noteworthy worth than the expression 72 × 3.
All in all, the examination between 72 × 3 and 72 × 7 outcomes in 72 × 7 being more prominent than 72 × 3, or 504 > 216.
Learn more about the fraction at
https://brainly.com/question/10354322
#SPJ4
General Sherman, a tree located in Sequoia National Park, stands 275
feet tall. To see the top of the tree, Carlos looks up at a 15° angle of elevation. If Carlos is 6 feet tall, how far is he from the base of the tree to the nearest foot? There are 4 options A.1004 B.1020 C.1026 D.1049
Answer:
Step-by-step explanation:
If Carlos is 6ft tall and looks up at the tree that is 275 ft tall, subtract those two.
275 - 6 = 269
Use tangent with the given angle and the new height. The distance is x.
tan15 = 269/x
x = 269/tan15
x = 1004ft
The distance from Carlos to the tree, given he is 6 feet tall and looks up at a 15° angle of elevation to see the top of a 275-foot tall tree located in Sequoia National Park, is 1026.
Hence option C is correct.
According to the information given,
We can set up a right triangle with Carlos's eye level, the top of the tree, And the base of the tree as the three points of the triangle.
Carlos's height of 6 feet can be used as one side of the triangle,
And we can use the tangent function to find the length of the adjacent side.
A tangent of 15 degrees is equal to the opposite side (height of the tree) divided by the adjacent side (distance from Carlos to the tree).
So, we can solve for the adjacent side by multiplying the height of the tree by the tangent of 15 degrees:
tan(15) = height of the tree / distance from Carlos to the tree
Distance from Carlos to the tree = height of the tree / tan(15)
Plugging in the values given:
Distance from Carlos to the tree = 275 / tan(15)
≈ 1026
Therefore,
The nearest foot to the distance from Carlos to the tree is option C. 1026.
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ2