The height of the tree is 5.4 m
Step-by-step explanation:
Let the height of the tree be 'h'
Angle of elevation= 34°
distance from the rock on the ground
to the base of the tree = 8 m
we can use the tan function of trigonometry to find the height of the tree,
tan 34° = h/8
tan 34° = 0.67
tan 34° = h/8
0.67 = h/8
h = 8 x 0.67
h = 5.4m
The height of the tree is 5.4 m
The height of the tree to the nearest tenth of a meter is approximately 5.6 meters.
To calculate the height of the tree, we can use trigonometry, specifically the tangent function since we have the angle of elevation and the distance from the observer to the base of the tree.
Let's denote:
h as the height of the tree,d as the distance from the observer to the base of the tree.According to trigonometry,
[tex]\[ \tan(\text{angle of elevation}) = \frac{\text{height of the tree}}{\text{distance to the tree}} \][/tex]
Substituting the given values:
[tex]\[ \tan(34^\circ) = \frac{h}{8} \][/tex]
Now, let's solve for h:
h = 8 × tan(34°)
Using a calculator, we find:
h ≈ 8 × 0.6947
≈ 5.5576
Therefore, the height of the tree to the nearest tenth of a meter is approximately 5.6 meters.
Write an equation that represents “The sum of a number and two, divided by 5 is equal to the number plus four.”
Answer:
[tex]\frac{x+2}{5} = x+4[/tex]
Step-by-step explanation:
"sum of a number and two" => addition of x and 2
"divided by 5" => division by 5
"equal" => "="
"plus four" => add 4
The value of the number such that the given phrase satisfy will be -4.5 and the equation will be (x + 2)/5 = x + 4.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Suppose that number is x.
The Sum of x and 2 will be x + 2.
It is divided by 5 thus, (x + 2)/5
It is equal to x + 4.
(x + 2)/5 = x + 4
(x + 2) = 5(x + 4)
x + 2 = 5x + 20
5x - x = 2 - 20
4x = -18
x = -4.5
Hence "The value of the number such that the given phrase satisfy will be -4.5 and the equation will be (x + 2)/5 = x + 4".
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PLEASE HELP ME!!! 30 POINTS
Select the statement that correctly completes the sentence. When using more than one adjective, ________.
A. an order only needs to be followed sometimes
B. there is an order, but it should never be followed
C. there is an order that should be followed
D. there is not an order that should be followed
Final answer:
When using multiple adjectives, there is a specific order that should be followed to make sentences sound natural and to convey descriptions clearly. Therefore, the correct answer is option D
Explanation:
When using more than one adjective, there is an order that should be followed (option D). In English grammar, adjectives are typically arranged in a specific order when they are used together before a noun. The general sequence is opinion, size, age, shape, color, origin, material, and purpose. Following this adjective order helps sentences sound natural to native speakers and makes the description clearer and easier to understand. For example, you might describe a sweater as a 'beautiful, small, old, red woolen sweater' to adhere to the standard adjective order.
Explain how to add decimals to the thousandths?
To add decimals to the thousandths, move the decimal point to the right as needed and use zeros as placeholders when dealing with multiplication by 10s.
Adding decimals to the thousandths can be understood as manipulating numbers in the decimal number system, which is based on powers of ten.
For example, when multiplying 2.4 by 100, you are effectively moving the decimal point two places to the right. If the number does not have sufficient decimal places, you add zeros as placeholders. So, 2.4 becomes 240.
Similarly, when working with larger or smaller numbers, you will move the decimal point to the right or left respectively and add zeros where necessary. For instance, if we are to multiply 45.86 by 100, we move the decimal point two places to the right to get 4586.
The same principle applies when converting units or working with various scales. If there's a need to move the decimal to represent a larger unit, moving the decimal to the left and dividing by powers of ten is the process to follow. The process is reversed when converting to a smaller unit.
If the units for x are years, and x = 5 represents the year 2015, what is the y-value for 2010?
Given:
The given graph passes through the points (-3,4) and (3,2)
The x - axis represents the years. The value x = 5, year 2015.
We need to determine the y - value for 2010.
Slope:
The slope of the line can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the points (-3,2) and (3,2), we get;
[tex]m=\frac{2-4}{3+3}[/tex]
[tex]m=\frac{-1}{3}[/tex]
Thus, the slope of the line is [tex]m=\frac{-1}{3}[/tex]
y - intercept:
The y - intercept in the graph is the point in the line that crosses the y - axis.
Thus, from the graph, it is obvious that the y - intercept is b = 3.
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y=mx+b[/tex]
Substituting the values, we have;
[tex]y=-\frac{1}{3}x+3[/tex]
Thus, the equation of the line is [tex]y=-\frac{1}{3}x+3[/tex]
The y - value for 2010:
Since, it is given that x = 5 represents 2015 and 2010 is 5 years before 2010.
Hence, the value of x for 2010 is given by
[tex]x=5-5=0[/tex]
Thus, x = 0 represents the year 2010.
To determine the y - value, let us substitute x = 0 in the equation [tex]y=-\frac{1}{3}x+3[/tex], we have;
[tex]y=-\frac{1}{3}(0)+3[/tex]
[tex]y=3[/tex]
Thus, for 2010 the value of y is 3.
pls help and dont ignore if you do help i will actually cry bc im failing math rn
pls help
Answer:
1700
300
Step-by-step explanation:
Let X be the investment at 7%,
Then 2000-X is invested at 4%
0.07X + 0.04(2000 - X) = 131
0.07X - 0.04X = 131 - 80
0.03X = 51
X = 1700
2000 - X = 300
In this problem, you're multiplying 7 by 10. What is 10 called in this math problem?
Answer:
the first digit like 10 x 7
Step-by-step explanation:
ur multiplying it byyyyyy 10
Answer:
multiplier
Step-by-step explanation:
7 is what's multiplying
10 is called the multiplier
Salim had a flock of 300 chickens 15%
Answer:
what is the question
Step-by-step explanation:
Salim has a flock of 300 chickens, and 15% of them are infected with a virus. He plans to take a Simple Random Sample (SRS) of 7 chickens to test for the virus.
Salim has a flock of 300 chickens, and 15% of them are infected with a virus. This means there are 45 infected chickens in the flock. To test for the virus, Salim plans to take a Simple Random Sample (SRS) of 7 chickens from the entire flock.
A Simple Random Sample involves selecting a subset of individuals from a larger population in such a way that each individual has an equal chance of being selected. This ensures that the sample is representative of the entire population.
Salim's decision to take a sample of 7 chickens is based on the practical constraints of time, resources, and cost. Testing all 300 chickens would be time-consuming and expensive. By taking a smaller sample, Salim can still obtain valuable information about the prevalence of the virus in his flock while minimizing costs and resources.
However, it's important to note that the accuracy of the sample depends on how well it represents the entire population. To ensure the sample is truly random and representative, Salim should use a random selection method, such as drawing names from a hat or using a random number generator.
Once Salim selects his sample, he can conduct tests to determine the presence of the virus in these chickens. The results of these tests will provide valuable insights into the overall prevalence of the virus in his flock, helping him make informed decisions about disease management and control.
The complete question is:
Salim had a flock of 300 chickens 15% of which are infected with a virus he plans on taking a SRS of 7 chickens to test for the virus.
Use the graph.
a. Which plant was the tallest at the beginning?
b. Which plant had the greatest rate of change over the 6 weeks?
1.) plant 3; plant 1
2.) plant 2; plant 2
3.) plant 3; plant 3
4.) plant 1; plant 3
Answer:
3) plant 3; plant 3
Step-by-step explanation:
it was 3 inches at the beginning and grew up to 7 by the end, while the others were shorter and grew less over the time period.
Answer:
hmmmmm
Step-by-step explanation:
A long jumper leaves the ground at an angle of
22
°
above the horizontal, at a speed of
9
/
m
s
. The height of the jumper can be modeled by
=
h
x
+
−
0.046
x
2
0.362
x
, where
h
is the jumper's height in meters and
x
is the horizontal distance from the point of launch.
Answer:
a) = 3.96
b) = 0.72
c) = 7.94
Step-by-step explanation:
Complete question.
(A long jumper leaves the ground at an angle of 20° above the horizontal, at a speed of 11 m/sec. The height of the jumper can be modeled by h(x) = -0.046x2+ 0.364x, where h is the jumper's height in meters and x is the horizontal distance from the point of launch. a. At what horizontal distance from the point of launch does the maximum height occur? Round to 2 decimal places. b. What is the maximum height of the long jumper? Round to 2 decimal places. c.What is the length of the jump? Round to 1 decimal place.)
Solution.
Data
Θ = 20
v = 11m/s
h(x) = -0.046x² + 0.364x
x = horizontal distance
h = height
a.
h(x) = -0.046x² + 0.364x
at maximum height,
d / dx (h) = 2(-0.46x) + 0.364
d / dx (h) = -0.092x + 0.364
at maximum height d / dx (h) = 0
0 = -0.092x + 0.364
0.092x = 0.364
x = 3.96.
b).
Hmax = -0.046x² + 0.364x
Hmax = -0.046(3.96) + 0.364(3.96)
Hmax = -0.72 + 1.44
Hmax = 0.72
c) the length of the jump can be calculated using the formula for range of a projectile
R = v² sin2Θ / g
g = 9.8m/s²
R = 11² * sin 2(20) / 9.8
R = 121 * sin40 / 9.8
R = 77.777 / 9.8
R = 7.936 = 7.94
a. The maximum height occurs at a horizontal distance of 3.96 meters.
b. The maximum height of the long jumper is 0.72 meters.
c. The length of the long jumper's jump is approximately 7.94 meters.
a. The maximum height occurs when the derivative of the height function with respect to horizontal distance is equal to zero.
Given h(x) = -0.046x² + 0.364x
Taking the derivative of h(x) with respect to x:
dh/dx = -0.092x + 0.364
Setting dh/dx to zero and solving for x:
0 = -0.092x + 0.364
0.092x = 0.364
x = 3.96
Therefore, the maximum height occurs at a horizontal distance of 3.96 meters.
b. To find the maximum height, substitute x = 3.96 into the height function h(x):
h(3.96) = -0.046(3.96)² + 0.364(3.96)
h(3.96) = -0.72 + 1.44
h(3.96) = 0.72
The maximum height of the long jumper is 0.72 meters.
c. The length of the jump, also known as the range, can be calculated using the formula for the range of a projectile:
R = v^2 * sin(2θ) / g
Given:
v = 11 m/s
θ = 20°
g = 9.8 m/s²
Substitute these values into the formula:
R = 11^2 * sin(40°) / 9.8
R = 121 * sin(40°) / 9.8
R = 121 * 0.6428 / 9.8
R = 77.777 / 9.8
R ≈ 7.94
Therefore, the length of the long jumper's jump is approximately 7.94 meters.
Complete question :
(A long jumper leaves the ground at an angle of 20° above the horizontal, at a speed of 11 m/sec. The height of the jumper can be modeled by h(x) = -0.046x2+ 0.364x, where h is the jumper's height in meters and x is the horizontal distance from the point of launch. a. At what horizontal distance from the point of launch does the maximum height occur? Round to 2 decimal places. b. What is the maximum height of the long jumper? Round to 2 decimal places. c.What is the length of the jump? Round to 1 decimal place.)
Solution.
Data
Θ = 20
v = 11m/s
h(x) = -0.046x² + 0.364x
x = horizontal distance
h = height
a.
h(x) = -0.046x² + 0.364x
at maximum height,
d / dx (h) = 2(-0.46x) + 0.364
d / dx (h) = -0.092x + 0.364
at maximum height d / dx (h) = 0
0 = -0.092x + 0.364
0.092x = 0.364
x = 3.96.
b).
Hmax = -0.046x² + 0.364x
Hmax = -0.046(3.96) + 0.364(3.96)
Hmax = -0.72 + 1.44
Hmax = 0.72
c) the length of the jump can be calculated using the formula for range of a projectile
R = v² sin2Θ / g
g = 9.8m/s²
R = 11² * sin 2(20) / 9.8
R = 121 * sin40 / 9.8
R = 77.777 / 9.8
R = 7.936 = 7.94.
A civil engineer is making a scale model of a highway on ramp. The length is 4 inches. The actual length on the ramp is 500ft. Ik scale model is 1/125 but how many times as long as the actual on ramp is the model?
Answer:
1500 Time the multiple of model scale is the actual length of the ramp.
Step-by-step explanation:
Given:
Actual length of ramp is 500ft
Modelling scale is 1/125.
To Find:
how many times as long as the actual on ramp is the model.
Solution:
Actual length is 500 ft
When Civil engineer is modelling the ramp on model then it is about 1/125 of the actual length present at that site.
So
=500*1/125
=4 inches
So on model scale engineer took inches as a unit for scale.
Actual length is 500 ft and model length is 4 inches
So 1 ft corresponds to 12 inches hence 500*12=6000 inches
6000 inches corresponds to 4 inches on model scale
i.e it is about 1500 time multiple of the model scale.
To find out how many times longer the actual on-ramp is than the model, we can use the following steps:
1. **Convert the model length to the same unit as the actual on-ramp:** Since the model's length is given in inches and the actual length is given in feet, we need to convert one of the measurements to the other unit so that they are comparable. Here, we will convert the model's length into feet. There are 12 inches in 1 foot, so to convert inches to feet, we divide by 12.
Model length in feet = Model length in inches / 12
Model length in feet = 4 inches / 12 inches per foot
Model length in feet = 1/3 foot
2. **Compare the actual length to the model length:** Once both lengths are in the same unit, we divide the actual on-ramp length by the model length to find out how many times longer the actual on-ramp is.
Times longer = Actual length / Model length
Times longer = 500 feet / (1/3 foot)
3. **Solve the division:** Now we solve the division by multiplying the actual length by the reciprocal of the model length.
Times longer = 500 feet * (3/1)
Times longer = 1500
So, the actual on-ramp is 1500 times longer than the model.
As for the mention of a scale of 1/125, this doesn't come into play in this specific comparison, as we are only comparing lengths. However, if we want to double-check the work, we can ensure that the scale is consistent with our findings.
Given a scale of 1/125, it means that 1 unit on the model represents 125 units in reality. If our model is 4 inches, that would mean:
Actual length at this scale = Model length * Scale factor
Actual length at this scale = 4 inches * 125
Actual length at this scale = 500 inches
Now, to convert this into feet:
Actual length at this scale in feet = 500 inches / 12 inches per foot
Actual length at this scale in feet = 41.6667 feet (approximately)
Now, this is not the actual length we've been given for the on-ramp (which is 500 feet), so it seems there might be some confusion with the scale provided. The scale factor is not needed when directly comparing the model's length to the actual on-ramp's length, as long as we convert into the same units for a fair comparison.
Johnny started a lawn mowing company to make some extra money over the summer. Johnny charges a one-time maintenance fee of $25 plus he charges $15 per yard mowed. Write an equation that can be used to help us determine how much Johnny would make over the summer.
Answer:
$25 + 15x
Step-by-step explanation:
$25 is the maintenance fee +
$15x (x will be the number of yards)
What is the value of 5(y +3)–3x² when x=4 and y=2?
OA) -23
OB) –10
OC) 10
OD) 23
Answer:
-23
Step-by-step explanation:
Plug in the x and the y into the equation:
5((2)+3)-3(4)^2
On the left side of the equation distribute the 5 to the 2 and the three to get:
(10+15)-3(4)^2
which would give us
(25)-3(4)^2
lets solve the other side now
4^2 is 16 and multiply that by 3 to get 48
so it should look like this:
25-48
=-23
Answer: The answer is -23
5(2+3)-3(4)^2 = -23
Step-by-step explanation:
:)
What is the degree measure of f?.
A) 56°
B) 58°
C) 60°
D) 64°
Answer:
C. 60
Step-by-step explanation:
i need help i cant get this right :(
Complete the sentence:
If Angle J X M has a value of 57 degrees, then Angle N X P has a value of
Answer:
33 is the correct answer.
Step-by-step explanation:
Answer:
33
Step-by-step explanation:
please give brainliest
1. The range between the highest and lowest temperatures recorded in
Houston is 78 °F. If the record high is 100 °F, what is the record low
temperature? *
Answer:
58 °F
have a wonderful day you are amazing :)
Answer:
22 degrees
Step-by-step explanation:
100-78=22
If a 4x 16 rectangle has the same area as a square, what is the length of a side of the square?
Ο Α. 10
Ο B. 12
Ο C. 6
Ο D. 8
Answer:
D
Step-by-step explanation:
4*16=64
8*8=64
Answer:
D. 8
Step-by-step explanation:
8*8= 64 =4*16
Graph the image of QRS after a rotation 270º counterclockwise around the origin.
Answer:
Q=(1,-5)
R=(5,-5)
S=(2,-7)
Step-by-step explanation:
1
Given f(x) = -3x – 2, find the following.
a. f(3)
b. f(-1)
c. f(-2)
Answer:
Step-by-step explanation:
f(x) = -3x -2
a) f(3) = -3*3 - 2 = -9 - 2 = -11
b)f(-1) = (-3*-1) - 2 = 3 - 2 = 1
c)f (-2) = (-3 * -2 ) - 2 = 6 - 2 = 4
Answer:
a.-11
b.1
c.4
Step-by-step explanation:
the explanation is in the picture
please like and Mark as brainliest
If g(x) is the graph of f(x) shifted up 5 units and right 1 units, write formula for g(x)
Answer:
( x+1, y+5 )
Step-by-step explanation:
x+1 because adding 1 to the x coordinate would shift it over 1
y+5 because adding 5 to the y coordinate would shift it up 5
Formula for g(x) is g(f(x)) = ( x+1, y+5 )
What is graph?
A graph can be defined as a pictorial representation or a diagram that represents data or values.
Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.
For example, If shift up by 1 unit, add 1 to function
If shift down by 4 units, subtract 4 from function
x+1 because adding 1 to the x coordinate would shift it over 1
y+5 because adding 5 to the y coordinate would shift it up 5
g(f(x)) = ( x+1, y+5 )
Hence, formula for g(x) is g(f(x)) = ( x+1, y+5 )
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Find the slope, Y-intercept, and equation (make sure there is no decimals if there is a decimal make it into a fraction)!
Answer:
Slope is 5/3
y-intercept = -3
y = 5/3x - 3
Step-by-step explanation:
To find the slope, take to coordinates and use the equation below
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
7-2 = 5
6-3= 3
Now you have your slope which is 5/3
Then take the slope and input it into point slope form to get your y-intercept.
y-y₁=m(x-x₁)
y-2 = 5/3(x-3)
y-2=5/3x-5
add two to both sides to get Y by itself
y = 5/3x - 3
now you have your y-intercept, which is -3
Then check your answer by inputing two different coordinates for X and Y
7 = 5/3(6)-3
7=7
12= 5/3(9)-3
12=12
You park you car in a pay lot. Because you have a coupon, you get the first 4 hr and 45 min free. You pay for an extra 1 1/2hr. How long did you park?
Answer:
6 hours and 15 minutes
Step-by-step explanation:
4 hours + 45 minutes + 1 hour + 30 minutes = 5 hours + 75 minutes = 6 hours + 15 minutes
Answer:
The answer is 6 hours and 15 minutes.
Step-by-step explanation:
You just need to add the 4 hours and 45 minutes to the extra 1 hour 30 minutes you had to pay for. So 4 hours and 45 minutes plus 1 hour 30 minutes gives you 6 hours 15 minutes.
Find the circumference of the circle. Round to the nearest tenth.
Formula for the circumference of a circle: C = pi x diameter
We are given the radius here, but we need the diameter. The diameter of a circle is equal to two times the radius.
diameter = 40 x 2 = 80 in
C = pi x 80
C = 80pi = 251.3 in
Hope this helps!! :)
Answer:
251.3 in
Step-by-step explanation:
The formula for circumference is π·d
Double 40 to get your radius, 80
Then, multiply π·80
The circumference is about 251.3 in
A graph in the form y = ax2 will have a vertex at __
Answer: For a given quadratic y = ax2 + bx + c, the vertex (h, k)
Step-by-step explanation:
A graph in the form y = ax2 will have a vertex at h, k.
PLS ANSWER FAST!!!!Which sentences contain phrases that are hyphenated correctly? Select 3 options
Answer:
The middle three sentences are hyphenated correctly.
Step-by-step explanation:
2. Jessica is a waitress. Her customer’s bills totaled $300. She earned $45 in tips. What percent did her customers tip her? ___
Answer:
15%
Step-by-step explanation:
$45/$300 = 0.15 = 15%
Solve 2(3∕4z + 2) = 2(1∕8z – 1∕2) for z.
Question 1 options:
A)
z = –4
B)
z = –3
C)
z = 5
D)
z = 2
Answer:
A) z= -4
Step-by-step explanation:
Answer:
z= -4
Step-by-step explanation:
Which equation could be used to solve for the length of XY?
XY = (22)sin(41°)
XY = (22)cos(41°)
XY = StartFraction 22 Over cosine (41 degrees) EndFraction
XY = StartFraction 22 Over sine (41 degrees) EndFraction
Answer:
Step-by-step explanation:
(D) XY= 22/sin(41 degrees)
Which equation could be used to solve for the length of XY?
Answer:
XY 22/sin(41o)
Step-by-step explanation:
Circle C has intersecting chords AB and DE as shown.
A) type the equation needed to solve for X?
B) what is the value of X in the diagram?
Please help!
Answer:
x = 30
Step-by-step explanation:
The measure of the chord- chord angle is one half the the sum of the arcs intercepted by the angle and its vertical angle, that is
A
[tex]\frac{1}{2}[/tex] (2x + 10 + x + 20) = 60
B
Multiply both sides by 2 to clear the fraction
2x + 10 + x + 20 = 120, that is
3x + 30 = 120 ( subtract 30 from both sides )
3x = 90 ( divide both sides by 3 )
x = 30
please help urgent I will mark brainliest
Answer:
∠ BCD = 28°
Step-by-step explanation:
The centre angle BOD is twice the angle on the circumference ∠ BFD, thus
∠ BOD = 2 × 76° = 152°
The sum of the interior angles of quadrilateral BODC = 360°
The angles at the point of contact of the tangents and the radii are 90°
Sum the interior angles and equate to 360
∠ BCD + 90 + 152 + 90 = 360
∠ BCD + 332 = 360 ( subtract 332 from both sides )
∠ BCD = 28°
A 15-minute TV program consists of one commercial of 1
1
4
minutes long, and two equal‐length entertainment segments. How long is each entertainment segment? Enter your answer as a mixed fraction.
Answer:
6 7/8 minutes
Step-by-step explanation:
Say the entertainment segments are each x minutes long. Then, we have the equation:
x + x + 1 1/4 = 15
2x + 1 1/4 = 15
2x = 15 - 1 1/4
We need a common denominator. 1 1/4 = 5/4 and 15 = 60/4, so we now have:
60/4 - 5/4 = 55/4. Then: 2x = 55/4
Divide by 2 from both sides:
(55/4) / 2 = 55/8 = 6 7/8
Thus, each entertainment segment is 6 7/8 minutes long.
Hope this helps!
Answer:
6⅞ minutes
Step-by-step explanation:
15 - 1¼
60/4 - 5/4
55/4
Each segment:
55/4 ÷ 2
55/8
(48 + 7)/8
6 ⅞