The distance, In feet, from the base of the ladder to the base of the wall is 4.2 ft.
He needs to move the ladder 0.1 ft closer to the base of the building.
The situation forms a right angle triangle.
Right angle triangleRight angle triangle has one of its angles as 90 degrees. The sides and angle can be found using trigonometric ratios.
The length of the ladder is the hypotenuse of the triangle formed. Therefore, the distance, In feet, from the base of the ladder to the base of the wall can be calculated as follows;
cos 65° = adjacent / hypotenuse
cos 65° = d / 10
d = 10 × 0.42261826174
d = 4.22618261741
d = 4.2 ft
She needs to move the ladder so it reached a window 9.6 feet above the ground. Therefore, the distance from the base of the ladder and the wall is as follows;
cos 65 = d / 9.6
d = 9.6 × 0.42261826174
d = 4.05696
d = 4.1
Therefore, he needs to move the ladder 0.1 ft closer to the building.
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i) Find the first 4 terms in the expansion of
[tex](2 + x ^{2})^{6}[/tex]
in ascending powers of x.
ii) Find the term independent of x in the expansion of
[tex](2 + x ^{2})^{6}(1 - \frac{3}{x {}^{2} } ) {}^{2} [/tex]
Answer:
(i) [tex]64+192 x^2+240 x^4+160x^6[/tex]
(ii) 1072
Step-by-step explanation:
Part (i)
Using Binomial series formula:
[tex](2+x^2)^6=2^6+6C1 \cdot 2^{6-1}\cdot x^2+6C2 \cdot 2^{6-2}\cdot(x^2)^2+6C3 \cdot 2^{6-3}\cdot(x^2)^3[/tex]
[tex]=64+6 \cdot 32\cdot x^2+15 \cdot 16\cdot x^4+20 \cdot 8 \cdot x^6[/tex]
[tex]=64+192 x^2+240 x^4+160x^6[/tex]
Part (ii)
[tex](1-\frac{3}{x^2})^2=(1-\frac{3}{x^2})(1-\frac{3}{x^2})[/tex]
[tex]=1-\dfrac{6}{x^2}+\dfrac{9}{x^4}[/tex]
[tex](2+x^2)^6(1-\frac{3}{x^2})^2=(64+192 x^2+240 x^4+160x^6)\left(1-\dfrac{6}{x^2}+\dfrac{9}{x^4} \right)[/tex]
[tex]=64-\dfrac{384}{x^2}+\dfrac{576}{x^4}+192x^2-1152+\dfrac{1728}{x^2}+240x^4-1440x^2+2160+...[/tex]
There is no need to keep expanding since the remaining will include the variable.
Therefore, the term independent of x = 64 - 1152 + 2160 = 1072
One of the legs of a right triangle measures 2 cm and the other leg measures 17 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
17.1
Step-by-step explanation
a^2+b^2=c^2
2^2 + 17^2 = c^2
4 + 289 = c^2
293 = c^2
square root of 293 or 17.1
2) Jose bought a magazine for $10 and some erasers for $2 per eraser. He spent a total of $26. How many erasers
he buy?
I can solve it i just need to know the equation with X
A cuple travels 420 miles to dr0p their dughter off at summer camp. The trip back has a short cut and is only 360 miles. And the gas mileage is 50% better
due to a lighter load. Write an expression for the total gas used and simplify.
The expression for the simplified total gas used is 1.43x.
How to write the expression of the total gaslet the gas used on the way to camp "x"
Then the gas used on the way back can be calculated as follows:
360 / 420 × 0.5 × x
To calculate the total fuel used, We need to add this to the 'x' used on the way.
Therefore,
total gas used = x + 360 / 420 × 0.5 × x = x + 0.43x = 1.43x
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Brand 1 Brand 2 Brand 3 Store 1 Store 2 Store 3 Laptop Comparison Chart Criteria for laptop search: Laptop specifications: • At least 3GB of memory • At least 250 GB hard drive • At least 14” Screen • Weigh at most 7 pounds • At least a 1 year manufacturer warranty • Built-in wireless router • Must be new, not used of refurbished Spending Limit: $800 • Includes laptop, sales tax, and shipping • For the purpose of this project, use 7.5% sales tax
The total amount that will be paid for the products with a sales tax of 7.5% will be $1290.
How to compute the amount from the sales tax?Your information isn't complete as the table denoting the appropriate values aren't given.
Let's assume that the price of a product A is given as $800 ane product B is $400. If the sales tax is 7.5%, the total amount that will be paid will be:
= ($800 + $400) + (7.5% × $1200)
= $1200 + $90
= $1290
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Please help! These data show the number of miles each of the 9 members of a track team ran for the week.
11 11.5 10.5 17 14.5 14.5 18 17 19
What is the IQR (interquartile range) for these data?
6.25
7.00
14.50
17.50
Answer:
14.50
Step-by-step explanation:
i took the quiz on k12 truse me i wish luck
The IQR for these data is 6.25.
Answer choice A is correct.
What is the interquartile range?An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.
W can find the values of the upper and lower quartile and median from a box plot.
The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.
The formula used is Upper quartile - Lower quartile.
We have,
To find the IQR, we first need to find the first and third quartiles.
First, we need to order the data from smallest to largest:
10.5, 11, 11.5, 14.5, 14.5, 17, 17, 18, 19
Next, we find the median (middle value) of the data set.
Since we have an odd number of data points, the median is the middle number, which is 14.5.
To find the first quartile (Q1), we need to find the median of the lower half of the data set.
That is, we need to find the median of 10.5, 11, 11.5, and 14.5.
The median of this subset is (11 + 11.5) / 2 = 11.25.
To find the third quartile (Q3), we need to find the median of the upper half of the data set.
That is, we need to find the median of 17, 17, 18, and 19.
The median of this subset is (17 + 18) / 2 = 17.5.
Now we have the first quartile (Q1) = 11.25 and the third quartile (Q3) = 17.5. The IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1
= 17.5 - 11.25
= 6.25
Therefore,
The IQR for these data is 6.25.
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Find x on the triangle geometry please help
Answer:
[tex]\sf x=7\sqrt{6}[/tex]
Step-by-step explanation:
As the base angles of the triangle are the same, then the legs of the right triangle are also equal. Therefore, we can use Pythagoras' Theorem to calculate x.
Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse of the right triangle)
Given:
a = 7√3b = 7√3c = xSubstituting the given values into the formula:
[tex]\sf \implies (7\sqrt{3})^2+(7\sqrt{3})^2=x^2[/tex]
[tex]\sf \implies147+147=x^2[/tex]
[tex]\sf \implies x^2=294[/tex]
[tex]\sf \implies x=\sqrt{294}[/tex]
[tex]\sf \implies x=\sqrt{49 \cdot 6}[/tex]
[tex]\sf \implies x=\sqrt{49}\sqrt{6}[/tex]
[tex]\sf \implies x=7\sqrt{6}[/tex]
[tex]\\ \rm\Rrightarrow cos\theta=\dfrac{Base}{Hypotenuse}[/tex]
[tex]\\ \rm\Rrightarrow cos45=\dfrac{7\sqrt{3}}{x}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{\sqrt{2}}=\dfrac{7\sqrt{3}}{x}[/tex]
[tex]\\ \rm\Rrightarrow x=7\sqrt{3}\sqrt{2}[/tex]
[tex]\\ \rm\Rrightarrow x=7\sqrt{6}[/tex]
what is equivalent to 2
x
2
−
7
x
−
3
=
0
Answer:
I'm confused with this, I dont understand what you are asking.
Step-by-step explanation:
2 is equivalent with a lot of things,
1+1
3-1
92-90
7×7-47
4÷2
the list goes on...
Sally planted 3/8 rows of beans and 1/8 rows of Tyrion’s in a garden. In total how many rows of vegetables did sally plant?
Answer:
4/8 or 1/2 rows
Step-by-step explanation:
Hope this helps! ^^
Peyton's family took a road trip to the Grand Canyon. Peyton fell asleep 77% of the way through the trip. If the total length of the trip was 1000 miles, how many miles had they travelled when Peyton fell asleep?
The miles Peyton's family had travelled when he fell asleep is 770 miles
How many miles had they travelled when Peyton fell asleep?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. The sign used to represent percentages is %.
Miles when Peyton fell asleep = 77% x 1000 = 770 miles
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How much will the storage container
hold?
7 ft.
5 ft.
10 ft.
10 ft.
3 ft.
1 ft.
4 ft.
4 ft.
Answer:
The container will hold 190 ft^3 of volume of substance.
if the question means it.
the sum of three consecutive natural numbers is 1146, find the numbers.
the three numbers in increasing order are ______ , _____, and ________
[tex]\text{Let the 3 consecutive numbers be}~ x,~x+1~ \text{and} ~x+2.\\\\\text{According to the condition,}\\\\x+x+1+x+2 = 1146\\\\\implies 3x +3 = 1146\\\\\implies 3(x+1) = 1146\\\\\implies x+1 = \dfrac{1146}3 = 382\\\\\implies x= 382-1 = 381\\\\\text{Now, the numbers are}~ 381,~382~\text{and}~383[/tex]
Gena and her friends each estimated the quotient of –137.56 divided by –6.12 using compatible numbers. Which shows the best estimate using compatible numbers?
Answer:
23
Step-by-step explanation:
Compatible numbers : numbers that are easy to add, subtract, multiply, or divide mentally. They are close in value to the actual numbers, although they do not necessary need to be rounded numbers.
-138 is close to -137.56
-6 is close to -6.12
[tex]\implies \dfrac{-138}{-6}[/tex]
Divide the top and bottom by -2:
[tex]\implies \dfrac{69}{3}[/tex]
Divide the top and bottom by 3
[tex]\implies 23[/tex]
If this is too difficult to divide mentally, you could use -140 and -7:
[tex]\implies \dfrac{-140}{-7}[/tex]
As 2 x 7 = 14, then 20 x 7 = 140, so the answer is 20.
How could you demonstrate that the force of gravity acting on an object is proportional to the mass of the object?
Answer:
F = mg
Step-by-step explanation:
g is the constant of proportionality and force is the product of mass and the acceleration due to gravity
f is directly proportional to m, therefore, f = mg
I don't understand this problem
Answer:
Right angle (90°)
Step-by-step explanation:
Because, main Street and Oak Street are crossing each other at 90°.
Hope it helps you in your learning process.
Answer:
right angle
Step-by-step explanation:
because they're perpendicular lines
Complete the table below with the amounts of raspberry juice, apple
juice and soda needed to make the different quantities of Fruit Fizz.
mixture must taste exactly the same each time.
Evaluate 14 - (2x - y), when x = 3 and y = 2 - -
.A) -7
.B) 10
.C) 13
.D) 18
20 POINTSS
10
solve:
14 - (2(x) - y)
given x : 3, y : 2, insert the following
14 - (2(3) - 2)14 - (6-2)14 - 410[tex]\\ \rm\rightarrowtail 14-(2x-y)[/tex]
[tex]\\ \rm\rightarrowtail 14-2x+y[/tex]
Put values[tex]\\ \rm\rightarrowtail 14-2(3)+2[/tex]
[tex]\\ \rm\rightarrowtail 14-6+2[/tex]
[tex]\\ \rm\rightarrowtail 10[/tex]
find the zeros simplify all irrational and complex solutions
f(x)=x^4-11x^2-80
Answer:
Step-by-step explanation:
f(x)=x^4-11x^2-80=x^4-16x^2+5x^2-80
=x²(x²-16)+5(x²-16)
=(x²-16)(x²+5)
=(x-4)(x+4)[x²-(-5)]
=(x-4)(x+4)[x^2-(5i²)]
=(x-4)(x+4)(x-√5 i)(x+√5 i)
so zeros are 4,-4,√5 i,-√5 i
When a constant force acts
upon an object, the acceleration of the object varies Inversely with Its mass. When a certain constant force acts upon an object witt
mass 5 kg, the acceleration of the object Is 15 m/s-
If the same force acts upon another object whose mass is 3 kg, what is this object's acceleration?
Answer:
25
Step-by-step explanation:
First expression: A= k/M
when A = 15 and M = 5, k = A×M = 75
therefore, when M = 4, A = 75/3 = 25
What table represents the relationship “A video game designer makes $35 per hour”? A 2-column table with 3 rows. Column 1 is labeled hours with entries 35, 70, 105. Column 2 is labeled Dollars with entries 1, 2, 3. A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled Dollars with entries 35, 40, 45. A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled Dollars with entries 36, 37, 38. A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled Dollars with entries 35, 70, 105.
Answer:
d
Step-by-step explanation:
Let y=6 and z=2. Translate “z less than y” into an algebraic expression and solve it
Answer:
y - z; 6 - 2; 4
Step-by-step explanation:
z less than y means subtract z from y
y - z
Substitute the given values.
6 - 2
4
5h-2g=26
2h + 2g 2
find h and g
Answer:
g = -3, h = 4.
Step-by-step explanation:
5h - 2g = 26
2h + 2g = 2 Adding the 2 equations:
7h = 28
h = 4.
Substituting for h in the first equation:
5(4) - 2g = 26
-2g = 26 -20 = 6
g = -3.
Let w = width and 4 + w = length. Which equation represents the situation?
Answer:
Depends on whether you're looking for area or perimeter. Follow the equations below
Step-by-step explanation:
This depends on whether you're being asked to find perimeter of area
Perimeter is equal to 2(length) + 2(width)
In which case perimeter would be 2(4 + w) + 2(w)
Which can be simplified to 8 + 2w + 2w = 4w + 8
However, Area is equal to length times width
Which would be (4 + w) * w = 4w + w^2
Answer:
Step-by-step explanation:
✔ w(4 +w) = 60
Bottles of water are packaged with
24 bottles per case. A store has
365 cases to sell. How many bottles
of water does the store have to sell?
Step-by-step explanation:
1 case = 24 bottles
365 cases = 365×24 = 8,760 bottles
Help..........................
Hello! I believe your answer is x= -4 so B
===
Hope this helps and feel free to give feedback
Answer:
x = -4
Step-by-step explanation:
I’m stuck pls help me
Answer:
B and E
Step-by-step explanation:
Donte is making brownies. For one batch, the recipe requires 1 5/6 cups of chocolate chips, and 1/6 cup of sugar. What is the combined amount, in cups, of chocolate chips and sugar that is used in one batch of brownies?
Answer:
2
Step-by-step explanation:
1 ⅚ + ⅙ = 1 6/6, also known as, 2
A test requires two hours to attend five questions if a candidate spent 80 minutes on the first two question what fraction of the time did he spend on the remaining three question
Answer:
He spent ⅓ of the time on the remaining three questions.
Step-by-step explanation:
Let's first figure out what the question gives us, and what we need to find.
Given:
Test - 2 hours, 5 questions
Candidate - 80 minutes, 2 questions
Find:
Fraction of time he spent on remaining three questions
Start by finding the fraction of time that he spent on the first two questions.
Set up an unit converter to convert two hours to minutes.
[tex]2$ hours($\frac{60\text{ minutes}}{1 \text{ hour}})=2\cdot 60\text{ minutes}=120$ minutes[/tex]
Let "x" represent the fraction of time the candidate spent on the first two questions...
[tex]x=\frac{\text{Amount of Time spent on First Two Questions}}{\text{Total Time}}\\x=\frac{80\text{ minutes}}{120\text{ minutes}}[/tex]
[tex]x=\frac{80}{120}[/tex]
[tex]x=\frac{8}{12}[/tex]
[tex]x=\frac{2}{3}[/tex]
Let "y" represent the fraction of time the candidate spent on the remaining three questions...
[tex]y=1-\text{Fraction of Time spent on First Two Questions}\\y=1-\frac{2}{3}\\[/tex]
[tex]y=\frac{3}{3}-\frac{2}{3}\\[/tex]
[tex]y=\frac{1}{3}[/tex]
He spent ⅓ of the time on the remaining three questions.
It takes a boat 2 hours to go 16 miles downstream with the current and 4 hours to return against the current. Find the speed of the boat in still water and the speed of the current.
let's recall that d = rt, or namely distance = rate * time.
b = speed of the boat
c = speed of the current
now, we know that going downstream the boat went 16 miles total, that's going only one way, so the distance the boat travels downstream as well as upstream to return is 16 miles flat.
when going downstream, the boat is not really going at "b" speed, is really going at "b + c" speed, because the current is adding its speed to it, so is really going faster than "b".
when going upstream, the boat is not really going at "b" speed" either, is really going slower at "b - c" speed, because the current is against it and thus subtracting speed from "b".
let's take a look at those in a table
[tex]\begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Downstream&16&b+c&2\\ Upstream&16&b-c&4 \end{array}\qquad \qquad \begin{cases} 16=(b+c)(2)\\\\ 16=(b-c)(4) \end{cases} \\\\\\ \stackrel{16}{(b+c)(2)}~~ = ~~\stackrel{16}{(b-c)(4)}\implies 2b+2c~~ = ~~4b-4c\implies 2c=2b-4c[/tex]
[tex]6c=2b\implies \cfrac{6c}{2}=b\implies \boxed{3c=b} \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{16~~ = ~~(\stackrel{b}{3c}+c)(2)}\implies 16=4c(2)\implies 16=8c \\\\\\ \cfrac{16}{8}=c\implies \blacktriangleright \stackrel{mph}{2}=c \blacktriangleleft~\hspace{10em}3(2)=b\implies \blacktriangleright \stackrel{mph}{6}=b \blacktriangleleft[/tex]
Given g(x)
-2 – 2, find g(-3).
Answer:
The calculation of the function given shows that since g(x) = -2x² - 9, the value of g(3) will be -27.
How to calculate the function?From the complete function, it should be noted that the value of g(x) = -2x² - 9.
Therefore, the value of g(3) will be calculated thus:
= -2(3)² - 9
= -2(9) - 9.
= -18 - 9
= -27
In conclusion, g(3) is -27.
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