The length of the sides,MD, DK, and KM gives the measure of the angle m<D as c) 76°
Which method can be used to find the measure of angle m<D?In triangle ∆MDK, we have;
m = 16.4
d = 22
k = 19
Using cosine rule, we get;
d² = m² + k² - 2•m•k•cos(D)
Therefore;
2•m•k•cos(D) = m² + k² - d²
[tex]D = arccos \left( \frac{ {m}^{2} + {k}^{2} - {d}^{2} }{2 \cdot m \cdot k} \right)[/tex]
Which gives;
[tex]D = arccos \left( \frac{ {16.4}^{2} + {19}^{2} - {22}^{2} }{2 \times 16.4 \times 19} \right) \approx {76}^{ \circ} [/tex]
m<D = 76°The correct option is therefore;
c) 76°Learn more about the rule of cosines here:
https://brainly.com/question/4316134
#SPJ1
Answer:
76
Step-by-step explanation:
Use the Law of Cosines to find m∠D
.The figure shows the same triangle as in the beginning of the task. Angle M D K is highlighted in red.
Set up the equation for the Law of Cosines.
d2=k2+m2−2kmcosD
Substitute the given values and solve for m∠D
.222=192+16.42−2(19)(16.4)cosD
Simplify.
484=629.96−623.2cosD
Subtract 629.96
.−145.96=−623.2cosD
Divide by −623.2
0.234=cosD
Use the inverse cosine function to find m∠D
and round to the nearest degree.
The figure shows a screen of a graphical calculator. The inverse cosine of 0 point 2 3 4 is calculated. The result is 76 point 4 6 7 3 1 6 4 6.
m∠D=cos−1(0.234)≈76∘
Therefore, m∠D≈76∘
hope it helps you!
.
An open-faced box is to be constructed by cutting squares out of the corners of a 12in by 12in
sheet of tin and folding up the sides. Which of the following describes the volume of such a
box?* (5 Points)
Step-by-step explanation:
Volume= lbh
= (12-2h)(12-2h)h
= 144h-48h²+4h³
The volume of the open-faced box is described by the polynomial equation:Volume = 4x³ - 48x² + 144x
To determine the volume of the open-faced box, we need to consider the dimensions of the box after cutting squares out of the corners and folding up the sides.
Let's assume that each side of the square cutout has a length of x inches.
When the squares are cut out and the sides are folded up, the resulting box will have dimensions:
Length = 12 - 2x inches
Width = 12 - 2x inches
Height = x inches
The volume of the box can be calculated by multiplying these dimensions:
Volume = Length * Width * Height
Volume = (12 - 2x) * (12 - 2x) * x
Volume = 4x³ - 48x² + 144x
Therefore, the volume of the open-faced box is described by the polynomial equation:
Volume = 4x³ - 48x² + 144x
Learn more about Volume here:
https://brainly.com/question/28058531
#SPJ2
PLEASE ANSWER AS QUICK AS POSSIBLE
Answer:
(a) h^-1(x) = (x+6)/6
Step-by-step explanation:
The inverse relation can be found by solving for y: x = h(y).
Solutionx = h(y) . . . . . the inverse relation
x = 6y -6 . . . . . use the function definition
x +6 = 6y . . . . add 6
(x +6)/6 = y . . . . divide by 6
The inverse function is ...
[tex]\boxed{h^{-1}(x)=\dfrac{x+6}{6}}[/tex]
Complete the steps to solve this linear equation: 2x 9(x – 1) = 8(2x 2) – 5 1.apply the distributive property: 2x 9x– 9 = 16x 16 – 5 2.combine like terms on each side: 11x – 9 = 16x 11 3.use the subtraction property of equality to isolate the variable term: –9 = 5x 11 use the subtraction property of equality to isolate the constant: –20 = 5x 4. use the division property of equality to solve: = x
Answer:
x= 5/2
Step-by-step explanation:
Answer:
-4 =x
Step-by-step explanation:
Brainly.com
Dagogo uploads 333 videos on his channel every month. each video averages 151515 minutes in length and gets an average of 150{,}000150,000150, comma, 000 new views. the average ratio of likes-to-views of dagogo's videos is 1:51:51, colon, 5. dagogo wants to reach a total of 9{,}000{,}0009,000,0009, comma, 000, comma, 000 views on his channel. assuming these rates continue, for how many months does dagogo need to upload videos to get to 9{,}000{,}0009,000,0009, comma, 000, comma, 000 views on his channel?
To acquire 90000000 views on his channel, he has to upload 20 videos every month.
According to the given information:Every month, he posts 3 videos to his channel. An average number of people watch each video. = 1500000
In search of:
How many months must pass before he begins to receive 90,000,000 views on his channel?
Step 1
On his channel, he posts three videos each month.
The average number of views per video is.
3 Videos Receive Views
= 3 * 1500000
= 4,500,000 Views
Number of 4,500,000 views each month
Complete 90000000 Views
Step 2
Total Views/Months = Total Views/Total Views
Days in a month = 90000000/4500000
= 20
20 Monthly months in the number
To acquire 90000000 views on his channel, he has to upload 20 videos every month.
20 Months is the right response, so.
To know more about Average number's visit:
https://brainly.com/question/16956746
#SPJ4
If a polynomial function, f(x), with rational coefficients has roots 0, 4, and 3 startroot 11 endroot, what must also be a root of f(x)? 3 i startroot 11 endroot negative 3 i startroot 11 endroot 3 minus startroot 11 endroot negative 3 minus startroot 11 endroot
Answer:
C
Step-by-step explanation:
C
Answer:
Step-by-step explanation:
its c
grade 9 math
useing frist diff is this a linear relation yes or no show your work
Answer:
not linear since all first differences are not equal
Step-by-step explanation:
To find the first differences, subtract each y value from the next y value.
Use only y values.
here are the 4 first differences you need to calculate.
1 - 0 = 1
4 - 1 = 3
9 - 4 = 5
16 - 9 = 7
Now you place them in the appropriate column in the table.
x y first difference
0 0 1
1 1 3
2 4 5
3 9 7
4 16
If the first differences were all equal, the function would be a linear function.
In this case, the first differences are all different, 1, 3, 5, 7, so the function is not linear.
Hey guys please help? Trigonometry
So, the task is: find cos a, if:
1) sin a = (3√11)/10, a ∈ (0; π/2)
2) sin a = (3√11)/10, a ∈ (π/2; π)
Could someone please explain how to solve it? I can't figure out what difference a ∈ (0; π/2) and a ∈ (π/2; π) make in the way I have to solve it mmh... I'll pin my attempt to do the first one (failed for some reason)
Step-by-step explanation:
a ∈ (0; π/2) here means that our angle, a must lie between 0 and pi/2, exclusive.
So this mean our angle must be in between 0 and pi/2, but can not be neither 0 and pi/2.
Here we have
[tex] \sin( \alpha ) = \frac{3 \sqrt{11} }{10} [/tex]
We must find cos.
Using the Pythagorean theorem
[tex]( \sin( \alpha ) ) {}^{2} + ( \cos( \alpha ) ) {}^{2} = 1[/tex]
It is mostly notated as this,
[tex] \sin {}^{2} ( \alpha ) + \cos {}^{2} ( \alpha ) = 1[/tex]
But they mean the same thing, we know
[tex] \sin( \alpha ) = \frac{3 \sqrt{11} }{10} [/tex]
So we plug that in for sin a.
[tex]( \frac{3 \sqrt{11} }{10} ) {}^{2} + \cos {}^{2} ( \alpha ) = 1[/tex]
[tex] \frac{99}{100} + \cos {}^{2} ( \alpha ) = 1[/tex]
[tex] \cos {}^{2} ( \alpha ) = \frac{100}{100} - \frac{99}{100} [/tex]
[tex] \cos {}^{2} ( \alpha ) = \frac{1}{100} [/tex]
Since cos is Positve over the interval (0; π/2), we take the positive or principal square root.
[tex] \cos( \alpha ) = \frac{1}{10} [/tex]
2. We would get the same work for the second part, the only difference is that cosine is negative over the interval
(π/2, π)
So the answer for 2 is
[tex] \cos( \alpha ) = - \frac{1}{10} [/tex]
Disclaimer: Your work you did was correct, just remember for fractions like
[tex]1 - \frac{99}{100} [/tex]
Convert 1 into a fraction that has a denominator of 100.
[tex] \frac{100}{100} - \frac{99}{100} = \frac{1}{100} [/tex]
The given cylindrical container is used to fill the rectangular prism fish tank with water. what is the least number of full cylindrical containers needed to completely fill the fish tank?
30 full cylindrical containers are required to completely fill the fish tank.
What is a cylinder?A cylinder is a surface made up of all the points on all the lines that are parallel to a given line and pass through a set plane curve in a plane that is not parallel to the given line. Such cylinders have been referred to as generalized cylinders at times.To find what is the least number of full cylindrical containers needed to completely fill the fish tank:
We know the volume of the cylinder is given by: [tex]V=\pi r^{2} h[/tex]
The volume of a cylinder:
[tex]V=\pi (\frac{6}{2} )^{2} (8)\\V=75\pi inches^{3}[/tex]
The volume of cube V = 24 × 24 × 12 = 6912 cubic inches
A number of full cylindrical containers are needed to completely fill the fish tank:
6912/72π30.55 ≈ 30Therefore, 30 full cylindrical containers are required to completely fill the fish tank.
Know more about cylinders here:
https://brainly.com/question/24159177
#SPJ4
Select the correct answer. which function has a phase shift of to the right? a. b. c. d.
The function y = 2sin has a phase shift of pi/2 to the right (2x - pi).
What is a trigonometric function?An angle or angle function (such as the sine, cosine, tangent, cotangent, secant, or cosecant) is most simply defined in terms of the ratios of pairs of sides of a right-angled triangle.The inverse of a trigonometric function (such as arcsine, arccosine, or arctangent).To find the function which has a phase shift to the right:
The function has a phase shift of pi/2 to the right.
By definition, you have the phase shift is:
asin(bx+c)Phase shift = -c/bWhen you substitute the values from the function [tex]y=2sin(2x-\pi )[/tex], where [tex]c=-\pi[/tex] and [tex]b=2[/tex], you obtain:
Phase shift = [tex]-(-\pi )/2[/tex]Phase shift = [tex]\pi /2[/tex]Therefore, the function y = 2sin has a phase shift of pi/2 to the right (2x-pi).
Know more about trigonometric functions here:
https://brainly.com/question/1143565
#SPJ4
The complete question is given below:
Which function has a phase shift of pi/2 to the right?
Find the range of the function y=-x^2-3x when the domain is {-5, 0, 2}
The range of the function y = -x² - 3x when the domain is {-5,0,2} is:
{-10, 0}.
What is the range of a function?The range of a function is the set that contains the output values for the given domain of the function.
In this problem, the domain is:
{-5,0,2}.
Hence the output values are:
-(-5)² - 3(-5) = -25 + 15 = -10.-(0)² - 3(0) = 0.-(2)² - 3(2) = -4 + -6 = -10.Hence the range is:
{-10, 0}.
-10 repeats, but goes only once on the range.
More can be learned about the range of a function at https://brainly.com/question/10891721
#SPJ1
Gilbert plans to invest $14 000 into two types of bonds. one bond yields 8% interest each year and the other bond yields 12% interest each year. he needs to earn $1400 each year to consider the investment successful. how much should he invest in each bond?
invest in each bond = $7000
What is Profit and Loss?An income statement, also known as a profit and loss account, is one of a company's financial statements and displays the company's receipts and outlays for a specific time period. It explains how revenues are converted into net income or net profit.
According to the given data:
Let n be the amount invested at 8%
the amount invested at 12% would be : 14000-n
so,
8n+12(14000-n) = 1400
8n + 168000 - 12n = 1400 * 100
4n + 168000 = 140000
n = 28000/4
= 7000
Therefore,
At 12% amount invested
= 14000 - 7000
= $7000
To know more about Profit and Loss visit:
https://brainly.com/question/16198345
#SPJ4
Determine if diverges, converges, or converges conditionally.
By the alternating series test, this series converges: for [tex]k\in\Bbb N[/tex],
[tex]\dfrac{k^5+1}{k^6+11}[/tex]
is a positive, decreasing sequence that converges to 0.
However,
[tex]\displaystyle \sum_{k=2}^\infty \left| (-1)^{k+1} \frac{k^5+1}{k^6+11} \right| = \sum_{k=2}^\infty \frac{k^5+1}{k^6+11} \approx \sum_{k=2}^\infty \frac1k[/tex]
is a divergent series by comparison to the harmonic series.
So the given series is conditionally convergent.
The given series is conditionally convergent. This can be obtained by using alternating series test first and then comparing the series to the harmonic series.
Determine if diverges, converges, or converges conditionally:Initially we need to know what Absolute convergence and Conditional convergence,
If [tex]\sum|a_{n} |[/tex] → converges, and [tex]\sum a_{n}[/tex] → converges, then the series is Absolute convergence
If [tex]\sum|a_{n} |[/tex] → diverges, and [tex]\sum a_{n}[/tex] → converges, then the series is Conditional convergence
First use alternating series test,
[tex]\lim_{k \to \infty} \frac{k^{5} +1}{k^{6}+11 }[/tex] = [tex]\lim_{n \to \infty} \frac{5}{6k}[/tex] = 0,
The series is a positive, decreasing sequence that converges to 0.
Next by comparing the series to harmonic series,
[tex]\sum^{\infty} _{k=2}|(-1)^{k+1} \frac{k^{5} +1}{k^{6}+11 }|=\sum^{\infty} _{k=2}\frac{k^{5} +1}{k^{6}+11 }[/tex] ≈ [tex]\sum^{\infty} _{k=2}\frac{1}{k}[/tex] = 0
This implies that the series is divergent by comparison to the harmonic series.
First we got that the series is converging and then we got the series is divergent. Therefore the series is conditionally convergent.
[tex]\sum|a_{n} |[/tex] → diverges, and [tex]\sum a_{n}[/tex] → converges, then the series is Conditional convergence.
Hence the given series is conditionally convergent.
Learn more about conditionally convergent here:
brainly.com/question/1580821
#SPJ1
A lawn-mowing company is trying to grow its business. it had 30 clients when they started its business and wants to increase by 6 new clients each week. use an arithmetic sequence to write a function to represent this real-world situation and determine the range of the function for the first four weeks of data. f(x) = 6x 30; 0 ≤ y ≤ 4 f(x) = 6x 24; 0 ≤ y ≤ 4 f(x) = 6x 30; 30 ≤ y ≤ 48 f(x) = 6x 24; 30 ≤ y ≤ 48
The function to represent the problem is f(x)=6x+24 and the range is 30[tex]\leq[/tex]y[tex]\leq[/tex]48.
What is arithmetic sequence formula?If the terms of a sequence differ by a constant, we say the sequence is arithmetic. If the initial term ([tex]a_{0}[/tex]) of the sequence is a and the common difference is d, then we have,
[tex]a_{n}[/tex]=a+(n-1)d
Initial number of clients=30
Number increase per week= 6
So, we can make an arithmetic sequence fir six weeks
30,36,42,48
Here, first term, a=30
Common difference, d=6
Range is [30,48]
The explicit formula of an arithmetic sequence is
[tex]a_{n}[/tex]=a+(n-1)d
Put a=30, d=6, n=x
[tex]a_{x}[/tex]=30+(x-1)6
[tex]a_{x}[/tex]=30+6x-6
[tex]a_{x}[/tex]=6x+24
Therefore, The function to represent the problem is f(x)=6x+24 and the range is 30<=y<=48
To learn more about arithmetic sequence, visit: https://brainly.com/question/15412619
#SPJ4
The importance of mendel's work is that it made a connection between observed patterns of ____________ and probability.
Answer:
blank = inheritance
Step-by-step explanation:
Hope that helps
which recursive formula can be used to represent the sequence
2,6,10,14,18...?
Answer:
a(1) = 2
a(n) = a(n-1)+4
Step-by-step explanation:
Using the given arithmetic sequence,
a1 is 2
a2 is 6
a3 is 10
a4 is 14
a5 is 18
and to get from a1 to a2 you have to +4, to get from a2 to a3 you have to +4 and so on.
In a reclusive formula you need to find two pieces of information:
1. The first term of the sequence
2. The pattern rule to get any term from the term that comes before it
Using the given sequence, the first term is 2 and the rule to get any term from its previous term is +4.
So, putting that information in the form of a recursive formula will read as the following:
an+1 = an+4
a1 = 2, n is greater or equal to 1 (n is an interger)
Which can be rearranged to
a(1) = 2
a(n) = a(n-1)+4
If the 6am temperature in Durango, Colorado was -8° F and the temperature rose 15° by 2pm, then what would the temperature be at 2pm?
Select the reason that best supports statement 8 in the given proof. PLS ASAP. Ive been stuck on this for forever.
Answer:
C
Step-by-step explanation:
You are dividing BOTH sides by 3.
"The division property of equality states that when we divide both sides of an equation by the same non-zero number, the two sides remain equal."
Which of these is a simplified form of the equation 7p 4 = − p 9 2p 3p? 13p = 13 3p = 5 7 = 4 11 = 15
Answer:
[tex]\boxed{\sf{3p=5}}[/tex]Step-by-step explanation:
To find:
The value of pGiven:
7p + 4 = −p + 9 + 2p + 3p[tex]\sf{7p+4=-p+9+2p+3p}[/tex]
Isolate the term of p, from one side of the equation.
Combine like terms.
[tex]\rightarrow \sf{7p+4=-p+2p+3p+9}[/tex]
Add the numbers from left to right.
-p+2p+3p=4p
7p+4=4p+9
Then, you subtract by 4 from both sides.
[tex]\sf{7p+4-4=4p+9-4}[/tex]
Solve.
7p=4p+5
Subtract by 4p from both sides.
7p-4p=4p+5-4p
Solve.
[tex]\boxed{\sf{3p=5}}[/tex]
Divide by 3 from both sides.
3p/3=5/3
Solve.
p=5/3
Divide is another option.
5/3=1.6666
So, the final answer is 3p=5.
I hope this helps, let me know if you have any questions.
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex]denote \: by \: s \: the \: cost \: of \: a \: sweatshirt \\ denote \: by \: t \: the \: cost \: of \: a \: t \: shirt[/tex]
[tex]3t + 7s = 240.5 \\ 6t + 5s = 220[/tex]
[tex] - 6t - 14s = - 481 \\ 6t + 5s = 220[/tex]
[tex] - 9s = - 261 \\ s = \frac{ - 261}{ - 9} = 29 \: dollars[/tex]
[tex]3t + 7(29) = 240.5 \\ [/tex]
3t + 203 = 240.5
3t = 37.5
t = 12.5 dollars
If two coins are flipped and then a die is rolled, the sample space would have _________ different outcomes. (give your answer as a whole number. )
Answer:144
Step-by-step explanation: a coin has 2 possibilities so 2 coins have 2x2 = 4 possibilities. A normal six-sided dice has 6x6 = 36 possibilities. 4 x 36 = 144 (this might be wrong)
There is 1 pint of liquid in this container. if another pint were added, how much liquid would there be? a) 2 cups b) 1 pint c) 1 quart d) 2 gallons
Answer:
C: 1 Quart
Step-by-step explanation:
2 pints are the equivalent of 1 quart
Answer:1 Quart
Step-by-step explanation: Because 2 pints equals=1 quart
10) James earned $3,000 interest
on an investment that he put in
the bank for 6 years with a 5%
interest rate. How much was his
initial deposit?
Answer:
Step-by-step explanation:
assuming that he has an annual interest of 5% then his initial deposit would be rounded to $2,238.65
what is the volume of a triangular pyramid that is 12 feet tall and has a base area of 5 square feet
The volume of the triangular prism as described is; 20 cubic foot.
What is the volume of the triangular pyramid?A triangular pyramid refers to pyramid which has a triangular base
It follows from the formula for calculating the volume of a triangular prism that;
Volume = (1/3) × base area × height.
Consequently,
volume of the prism = (1/3) ×5 × 12
Volume = 20 cubic foot
Therefore, volume of the triangular prism as described is; 20 cubic foot.
Read more on triangular prism;
https://brainly.com/question/12807315
#SPJ1
Brayden has 24 feet of fence available to build a rectangular fenced in area. If the width of the rectangle is xx feet, then the length would be \frac{1}{2}(24-2x). 2 1 (24−2x). A function to find the area, in square feet, of the fenced in rectangle with width xx is given by f(x)=\frac{1}{2}x(24-2x).f(x)= 2 1 x(24−2x). Find and interpret the given function values and determine an appropriate domain for the function.
The maximum area is achieved when the rectangle is a square of side 6 feet, with a domain, 0 < x < 12.
The perimeter available with Brayden is 24 feet.
The width of the rectangle is assumed to be x feet.
The length can be calculated using the formula:
2(length + width) = perimeter,
or, 2length + 2width = perimeter,
or, 2length = perimeter - 2width,
or, length = (1/2)(perimeter - 2 width).
Substituting the values, we get:
length = (1/2)(24 - 2x).
The area can be calculated using the formula:
Area = length*width.
Substituting the values, we get:
Area = (1/2)(24 - 2x)x = (1/2)x(24 - 2x).
Now, we need to maximize the area for the given perimeter.
For that, we differentiate the area function, with respect to its width x.
d(Area)/dx = (1/2)(24 - 2x) + (1/2)x(-2),
or, d(Area)/dx = 12 - x - x = 12 - 2x ... (i).
To check for the point of inflection, we equate this to zero, to get:
12 - 2x = 0,
or, 2x = 12,
or, x = 6.
To check whether this is maximum or minimum, we differentiate (i) with respect to x to get:
d²(Area)/dx² = -2 which is less than 0, implying area is maximum at x = 6.
Thus, the maximum area is achieved when the width is 6 feet.
Length = (1/2)(24 - 2x) = (1/2)(24 - 2*6) = (1/2)12 = 6.
Thus, the maximum area is achieved when the length is 6 feet.
The area function is, area = (1/2)x(24 - 2x).
We know that the area is always greater than 0, thus, we can show that:
(1/2)x(24-2x) > 0,
or, x(24 - 2x) > 0,
or, x(12 - x) > 0, which is true when 0 < x < 12.
Thus, the domain of the area function is 0 < x < 12.
Thus, the maximum area is achieved when the rectangle is a square of side 6 feet, with a domain, 0 < x < 12.
Learn more about the area of a rectangle at
https://brainly.com/question/14569601
#SPJ1
The motion of an object was recorded by measuring the velocity of the object in meters per second at various times, as shown in the table. The scatterplot below was graphed from the data in the table, where t represents the time, and v represents the velocity. Based on the scatterplot, which equation BEST represents the relationship between velocity and time?
An equation which best represents the relationship between velocity and time is: B. v = 2.19x + 6.7.
What is a scatter plot?A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.
What is a linear function?A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the linear function is given by:
v = 2.0852x + 6.3978
Therefore, an equation which best represents the relationship between velocity and time is:
v = 2.19x + 6.7.
Read more on scatterplot here: brainly.com/question/6592115
#SPJ1
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
The equivalent expression of the radical expression ∛1080 is 6∛5
How to evaluate the radical expression?The radical expression is given as
∛1080
Express 1080 as 216 * 5
∛1080 = ∛(216 * 5)
Split the factors
∛1080 = ∛216 * ∛5
Evaluate the cube root of 216
∛1080 = 6 * ∛5
Evaluate the product
∛1080 = 6∛5
Hence, the equivalent expression of the radical expression ∛1080 is 6∛5
Read more about equivalent expression at
https://brainly.com/question/24734894
#SPJ1
Does anybody know this? The quotient of -45 and -5 is
Answer each question and tell your reasoning.
a. Is 60% of 400 equal to 87?
b. Is 60% of 200 equal to 87?
c. Is 60% of 120 equal to 87?
2. 60% of x
is equal to 87. Write an equation that expresses the relationship between 60%, x
, and 87. Solve your equation.
Equation:
x=
3. Write an equation to help you find the value of each variable. Solve the equation.
60% of c
is 43.2.
Equation:
c=
38% of e
is 190.
Equation:
e=
Answer:
Step-by-step explanation:
400*60% can be rewriten as 400×0.6 which is 240, so a is false.
the same steps can be repeated for b and c
b) 200*0.6=120, therefore is false
c) 120*0.6=72, therefore is false
2)
[tex]60 percent * x=87\\0.6x=87\\x=\frac{87}{0.6} \\\\x=145[/tex]
Now we check the answer by using the same steps in problems a,b,c
[tex]145*0.6=87\\87=87[/tex]
3)
[tex]0.6c=43.2\\c=\frac{43.2}{0.6} \\c=72[/tex]
and finally
[tex]0.38e=190\\e=\frac{190}{0.38} \\e=500[/tex]
What angle of descent ( depression) should the pilot use to safely bring the plane to the airport runway? The plane is 10,000 feet above the ground and is a little more than 30 miles ( approximately 160,000 feet) from the airport. Write an equation and show work . Round the angle measure to the nearest whole degree. ( Picture is not drawn to scale )
Answer:
4 degrees ( to nearest degree).
Step-by-step explanation:
The trig ratio you want is the tangent.
tan x = 10,000 / 160,000 where x is the angle of depression.
tan x = 0.0625
x = 3.576 degrees.
Shira's math test included a survey question asking how many hours students spent studying for the test. The scatter plot below shows the relationship between how many hours students spent studying and their score on the test. A line was fit to the data to model the relationship.
Which of these linear equations best describes the given model?
Answer:
Part 1) Option B. y = 10x + 45
Part 2) The score is 95
Step-by-step explanation:
Linear equation that best describes the given model
Let
x ---> number of hours students spent studying
y ---> their score on the test
Looking at the line that was fit to the data to model the relationship
The slope is positive
The y-intercept is the point (0,45)
For x=1, y=55 ----> point (1,55)
Find the slope
The formula to calculate the slope between two points is equal to
substitute the points (0,45) and (1,55)
Find the equation of the line in slope intercept form
we have
substitute
Part 2) Estimate the score for a student that spent 5 hours studying.
For x=5 hours
substitute in the linear equation and solve for y