A steep mountain is inclined 74 degrees to the horizontal and rises 3150 feet above the surrounding plain. A cable for a cable car is to be installed from a point 725 feet from the base to the top of the mountain. Find the length of cable needed.
Answer:
3546 ft
Step-by-step explanation:
First find length of base to center of mountain.
(3150*sin 16 deg)/(sin 74 deg) = ~903 ft
Then dist of point from centre of mountain
903+725=1628 ft
Then cable length
(3150^2 + 1628^2)^0.5 = ~3546 ft
What is the equation of the line that passes through the point (-6,8) and has an undefined slope?
Answer:
x = -6
Step-by-step explanation:
Slope is rise over run (change in y divided by change in x), and to have an undefined slope change in x must be zero. The line x = -6 is a vertical line that passes through the point (-6,8).
Fill in the blanks to solve 900 x 6
Answer:
The answer is 900 ×6= 5,400 u can use a calculator
1/3(x+6)=2/3(x-9)
multi step equation
[tex]\dfrac13(x+6) = \dfrac 23 (x-9) \\\\\\\implies x+6 = 2(x-9)~~~~;[ \text{Multiplying both sides by 3}]\\\\\implies x +6 = 2x -18\\\\\implies 2x -x = 6+ 18 \\\\\implies x = 24[/tex]
True or False (See Image)
The remainder theorem can be used to check if a binomial is a factor of a larger polynomial.
Answer: true
Step-by-step explanation:
Find the values of x and y that makes these triangles congruent by HL.
Answer:
What is HL? holey logic? hawk a loogy? half lies? honey lemon? heavenly lampshade? hand lotion?
Step-by-step explanation:
as AB = DE, the only options given where x = y - 1 are the the second and third.
as AC and AD are equal from ASA
3x - 2 = 2y + 1
3x - 3 = 2y
y = 1.5x - 1.5
the only x,y pair that fits is x = 5, y = 6
heeelllppp meeee please
Circle A was dilated with the origin as the center of dilation to creat circle b
Answer: The answer is B.)
Have a great Day/Night!
Molly tried to evaluate 93\times5193×5193, times, 51 using partial products. Her work is shown below.
\begin{array}{llrr} &&93 \\ &&\underline{{}\times51} \\ &\blueD{\text{Step 1}}&\blueD{3}& \blueD{1\times3\text{ ones}}\\ &\greenD{\text{Step 2}}&\greenD{90}& \greenD{1\times 9\text{ tens}}\\ &\maroonD{\text{Step 3}}&\maroonD{150}& \maroonD{50\times 3\text{ ones}}\\ &\goldE{\text{Step 4}}&\underline{{}+\goldE{ 4{,}500}}& \goldE{50\times 9\text{ tens}}\\ &\purpleD{\text{Step 5}}&\purpleD{4{,}743}& \end{array}
Step 1
Step 2
Step 3
Step 4
Step 5
93
×51
3
90
150
+4,500
4,743
1×3 ones
1×9 tens
50×3 ones
50×9 tens
Since molly's solution tally's with the given solution, hence Molly's solution is correct.
Given the working on a partial product of 93 and 51 carried out by Molly as shown:
[tex]\begin{array}{llrr} &&93 \\ &&\underline{{}\times51} \\ &\blueD{\text{Step 1}}&\blueD{3}& \blueD{1\times3\text{ ones}}\\ &\greenD{\text{Step 2}}&\greenD{90}& \greenD{1\times 9\text{ tens}}\\ &\maroonD{\text{Step 3}}&\maroonD{150}& \maroonD{50\times 3\text{ ones}}\\ &\goldE{\text{Step 4}}&\underline{{}+\goldE{ 4{,}500}}& \goldE{50\times 9\text{ tens}}\\ &\purpleD{\text{Step 5}}&\purpleD{4{,}743}& \end{array}[/tex]
This partial product can also be solved as shown below:
[tex]93 \times 51 = (90+3)\times (50+1)[/tex]
Applying the distributive law:
[tex]93 \times 51 = 90(50) + 90(1) + 3(50) + 3(1)\\93 \times 51 =4500 + 90 + 150 + 3\\93 \times 51 =4500+240+3\\93 \times 51 =4740+3\\93 \times 51 =4743[/tex]
Since molly's solution tally's with the given solution, hence Molly solution is correct.
Learn more about partial product at: https://brainly.com/question/24716925
PLEASE HELP I WILL GIVE BRAINLEST AND 20 POINTS PLEASEEEE
Answer:
Question 4: Which equation is parallel to the above equation and passes through the point (35, 30)
[tex]y=[/tex] [tex]\frac{5}{7} x + 5[/tex] is the correct answer, I found this by inputting the x and y value of the coordinate (35, 30) onto the equation and solving for y-intercept since the slope of all equations is the same (since it's traveling parallel)
[tex]30 = \frac{5}{7} (35) + y\\30 = 25 + y\\5 = y[/tex]
so the equation would be [tex]y=[/tex] [tex]\frac{5}{7} x + 5[/tex]
Question 5: Which equation is perpendicular to the above equation and passes through the point (35, 30)
[tex]y=\frac{-7}{5} x+79[/tex] is the correct answer, I found this using the same method as before, input coordinate values into the equation and solve for the y-intercept (The only thing changed from the last answer is the opposite reciprocal slope).
[tex]30 = \frac{-7}{5}(35) + y \\30 = -49 + y \\79 = y[/tex]
so the equation would be [tex]y=\frac{-7}{5} x+79[/tex]
Which fraction is the same as 3.375?
Answer: 27/8 or 3 3/8
Step-by-step explanation:
Write 3.375 as 3.375/1
then you take the numerator 3.375 and multiply it by 1000. Multiplying is to make 3.375 a whole number. Whatever you do to the numerator, you have to do to the denominator. So, we take 1x1000 aswell. Then our fraction would be 3375/1000.
Then, we would find the greatest common factor. The greatest common factor, or GCF, is the greatest factor that divides two numbers. To find the GCF of two numbers: List the prime factors of each number. The GCF is 125. Then you divid 125 by the fraction, (which means that you divid the number by both the numerator and denominator) and you get the answer, which is 27/8.
If the question is asking you to turn the fraction into a mixed number, you would have to find out how many times 8 going into 27. It goes in 3 times. That is ur whole number. Then do 8x3 to get 24. take 27 and subtract 24 to get 3. that 3 is your numerator. The denominator stays the same. ur final answer as a mixed number is 3 3/8.
.03 + six tenths equals
What is the solution to this equation? 1⁵+5²/25⁰-5¹=
Answer:
It is 21 first guy is no doubt correct.
Step-by-step explanation:
The expression results to 21.
What are Exponents and power?Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.
For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.
Given:
1⁵+5²/25⁰-5¹
So, 1⁵ = 1
5² = 25
25⁰ = 1
5¹ = 5
Now, 1⁵+5²/25⁰-5¹
= 1+ 25 / 1 - 5
= 1 + 20
= 21
Hence, the expression results to 21.
Learn more about exponents and power here:
https://brainly.com/question/15722035
#SPJ2
What is the slope and y-intercept that represents this table?
Answer:
[tex]m=-2\ 000; q=17\ 000[/tex]
Step-by-step explanation:
First of all, whoever formatted that table is a criminal.
Now, slope first, it's the easiest: the slope in a table like that is the difference between two consecutive position: ie [tex]13\ 000 - 15\ 000[/tex] or [tex]11\ 000-13\ 000[/tex], being careful of subtracting the higher position (not value!) minus the lower, or right minus left. Your slope thus is [tex]-2 \ 000[/tex]. Intercept is found in two ways. One is writing the line in point slope form based on any two values and the slope we found, or since we're jumping integer to integer, you can look at the table in reverse and notice that if you go backwards (ie from 4 to 3 to 2 to 1) the value is increasing by 2000 every time. The intercept [tex]q[/tex]will be the value at 0, or 17 000
AB:BD = 3:4
AC:CD = 3:2
Work out AB:BC:CD
Answer:
15:6:14
Step-by-step explanation:
AB:BD is split into a total of 3+4=7 parts.
AC:CD is split into a total of 3+2=5 parts.
So, if the two ratios are put on a number line together with the points A, B, C, and D, the number line would be split into a total of 35 parts (the LCM of 7 and 5).
AB would be (3/7)*35=15.
CD would be (2/5)*35=14
BC would be 35-(15+14)=6
So, the ratio is 15:6:14.
what is an equation of the line that passes through the points (2,-5) and (-3,-5)?
Answer:
y = -5
Step-by-step explanation:
yeah-ya....... right?
Answer:
Step-by-step explanation:
as both y values are -5, slope is zero and y intercept is -5
y = 0x - 5
y = -5
7+x÷y is a ______( type of polynomial)
I was absentee and i dont know how to solve it help plz
Answer:
-1/3 or 1/-3 (it doesn't matter which one you pick because its still the same)
Step-by-step explanation:
You find slope by doing rise over run. Its left to right so you start on the left dot and go down one. This makes it -1 because you're going down, not up. You move 3 to the right which makes it positive. Once you do this itll lead you right the the 2nd point. 1 down= -1
3 right= 3
-1/3
Put these fractions in order from greatest to least:
Answer:
[tex]\dfrac 34 , \dfrac 23 , \dfrac 35[/tex]
Step-by-step explanation:
[tex]\dfrac 34 >\dfrac 23 >\dfrac 35[/tex]
A nature preserve worker calculates there are 6,000 deer in Sharon Woods Park. She also estimates that 75 more deer die than are born each year.
a. Write a linear function to estimate how many deer will be in the park in x years.
b. Use the linear function to predict how many deer will be in the park in 3 years.
c. In how many years will there be 5,325 deer left in Sharon Woods Park?
The linear equation used to represent this situation is y = -75x + 6000
A linear equation is in the form:
y = mx + b;
where y, x are variable, m is the slope of the line and b is the y intercept.
Let y represent the amount of deer present in x years. There are 6000 deer presently, hence a = 6000. Also 75 more deer die than are born each year. Hence m = -75.
The linear equation is given by:
y = -75x + 6000
In 3 years:
y = -75(3) + 6000
y = 5775
For there to be 5325 deer:
5325 = -75x + 6000
x = 9 years
Find out more at: https://brainly.com/question/21105092
If Y varies directly as x and y= 49 when x= 40, find y if x =34
Answer:
y = 41.65
Step-by-step explanation:
Given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 49 when x = 40
49 = 40k ( divide both sides by 40 )
[tex]\frac{49}{40}[/tex] = k = 1.225
y = 1.225x ← equation of variation
When x = 34 , then
y = 1.225 × 34 = 41.65
Find the quotient.
32 ÷ 0.08
Answer:
The quotient of the equation is 400
Answer:
hi
Step-by-step explanation:
the correct answer is 400
For the line segment with endpoints M(m, 4) and N(-2, n) , the midpoint is (3, 1) . Find m and n.
Answer:
Step-by-step explanation:
(m + (-2)) / 2 = 3
(m + (-2)) = 6
m = 8
(4 + n) / 2 = 1
4 + n = 2
n = - 2
Write the expression in standard form,
(9+2i)(5-3i)
[tex](9+2i)(5-3i)\\\\=45-27i+10i-6i^2\\\\=45-17i+6~~~~~;[i^2 =-1]\\\\=51-17i[/tex]
[tex] \: \: \: \: \: \: [/tex]
[tex] = \: \: \: \: 51 - 17i[/tex]
refer to the attachment for explanationhope it helpsYou wish to buy a new skateboard. To earn money, you sell your baseball cards to
your friends for $2.50 each. If the new skateboard costs $98, what is the minimum number
of baseball cards you will have to sell?
simplify (x^4-4x^3+9x^2-5x) (x^3-3x^2+7) -30x^2+25x^4
Answer:
x^7-7x^6+21x^5-13x^3+33x^2-35x
Step-by-step explanation:
there you go!
Evaluate 3x + 34 if x = 5.
Answer:
49
Step-by-step explanation:
3x + 34
x = 5
3 * 5 + 34
15 + 34
49
Given logv5 3 ≈ 0.6826 and logv5 8 ≈ 1.2920, evaluate the expressions.
A) logv5 2
B) logv5 (75/8)
Write an equation in point-slope form for the line that passes through the given points (1,-3),(4,-15)
Answer: b=7
Step-by-step explanation:
PLEASE HELP! Look at the image and please help me
Answer:
Step-by-step explanation:
its b