solve the given question Divide Rs 400 in ratio of 1:3
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In order to divide the segment RS in a ratio of 1:3, let's divide it by 4, this way we can use 1 part to the left and 3 parts to the right:
Dividing the length by 4, we have:
[tex]\frac{400}{4}=100[/tex]That means we can use a point X on the segment RS, where RX = 100 and XS = 300.
Related Questions
find the surface area of the outside of the block. taking out the drilled holes.
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The surface area of the outside of the block is determined by the difference of cube and cylinder.
The surface area of cylinder is,
[tex]S_c=\text{ 2}\Pi rh+2\Pi(r^2)[/tex]The radius is 2 ft and height is 6 ft.
[tex]S_c=2\Pi(2\times6+2^2)[/tex][tex]S_c=\text{ 2}\times3.14\times(12+4)[/tex][tex]S_c=100.48ft^{2^{}}[/tex]The surface area of cube is,
[tex]S_a=6s^2[/tex]The sidde of cube is 6 ft.
[tex]S_a=\text{ 6}\times6^2[/tex][tex]S_a=216ft^2[/tex]The surface area of the outside of the block is,
[tex]S=S_a-S_c[/tex][tex]S=\text{ 216-100.48}[/tex][tex]S=115.52ft^2[/tex]The formula for the volume of a cone is V=\frac{1}{3}\pi r^2 h,
where r is the radius of the cone and h is the height of the cone. Rewrite the formula to solve for the positive value of r in terms of h and V.
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The formula for calculating r's positive value in terms of h as well as V for the volume of cone is; r = (1/2)√3V/πh.
What is defined as the cone?A cone is a distinct three-dimensional dimensional figure with such a flat as well as curved surface pointing upward.Radius is described as the distance from the center of a circular base to every point on its circumference.The height is indeed the distance from the cone's apex to the center of the base.For the given question.
The volume of a cone is calculated as follows:
V = (4/3)πr²h
In which r is the radius of the cone as well as h is the height of the cone.
The formula for calculating r's positive value in terms of h as well as V is;
V = (4/3)πr²h
r² = 3V/4πh
Taking square root both side;
r = ± √3V/4πh
r = ± (1/2)√3V/πh
Only positive value is to be considered. Thus, Neglecting the negative value.
Thus, the formula for calculating r's positive value in terms of h as well as V is; r = (1/2)√3V/πh.
To know more about the cone, here
https://brainly.com/question/28967200
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Find the zeros of each function by factoring. F(x)=x^2+9x+18
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We have the following:
[tex]F\mleft(x\mright)=x^2+9x+18[/tex]factoring:
[tex]\begin{gathered} \mleft(x+3\mright)\mleft(x+6\mright)=0 \\ x+3=0 \\ x=-3 \\ x+6=0 \\ x-6 \end{gathered}[/tex]A quadrilateral has two angles that measure 150° and 140°. The other two angles are in aratio of 3:4. What are the measures of those two angles?o ando
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Solution
Let the quadrilateral be
From the above
[tex]\begin{gathered} x+y+140+150=360 \\ x+y+290=360 \\ x+y=360-290 \\ x+y=70 \\ \text{Multiply through by 4} \\ 4x+4y=280\ldots\ldots\ldots\text{.}(1) \end{gathered}[/tex]Without the loss of generality, let
[tex]\begin{gathered} x\colon y=3\colon4 \\ \frac{x}{y}=\frac{3}{4} \\ \text{cross multiply} \\ 4x=3y \end{gathered}[/tex]Substitute 4x = 3y into equation (1)
[tex]\begin{gathered} 4x+4y=280 \\ 3y+4y=280 \\ 7y=280 \\ y=\frac{280}{7} \\ y=40 \end{gathered}[/tex]From
[tex]\begin{gathered} x+y=70 \\ x=70-y \\ x=70-40 \\ x=30 \end{gathered}[/tex]Therefore, the two angles are
[tex]30^{\circ},40^{\circ}[/tex]3-5b + 2b = -2 -2(1-5)
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our first step is to operate what we can on each side
[tex]undefined[/tex]If 1/4 + 1/8 + n + 1/2 = 1, find the value of n.
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Given:
[tex]\frac{1}{4}|+\frac{1}{8}|+n+\frac{1}{2}|=1[/tex]To Determine: The value of n
Solution:
[tex]\begin{gathered} \frac{1}{4}|+\frac{1}{8}|+\frac{1}{2}|+n=1 \\ \frac{2+1+4}{8}|+n=1 \\ \frac{7}{8}|+n=1 \end{gathered}[/tex][tex]\begin{gathered} n=1-\frac{7}{8}| \\ n=\frac{8-7}{8}| \\ n=\frac{1}{8}| \end{gathered}[/tex]Hence, the value of n is
[tex]n=\frac{1}{8}|[/tex]One month lashonda rented 3 movies and 2 video games for a total of $19. The next month she rented 5 movies and 6 video games for a total of $47. Find the rental cost for each movie and each video game
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We are given that:
Lashonda rented 3 movies and 2 video games for a total of $19. If "x" is the cost per movie and "y" the cost per video game, then we can write this mathematically as:
[tex]3x+2y=19,(1)[/tex]This is our first equation.
We are also given that:
She rented 5 movies and 6 video games for a total of $47. This can be written mathematically as:
[tex]5x+6y=47,(2)[/tex]This is our second equation.
To solve the system we will solve for "x" in equation (1). To do that we will subtract "2y" from both sides:
[tex]3x=19-2y[/tex]Now we divide both sides by 3:
[tex]x=\frac{19-2y}{3}[/tex]Now we substitute this in equation (1):
[tex]5(\frac{19-2y}{3})+6y=47[/tex]Now we use the distributive law on the parenthesis:
[tex]\frac{95-10y}{3}+6y=47[/tex]Now we multiply both sides by 3, we get:
[tex]95-10y+18y=141[/tex]Now we add like terms:
[tex]95+8y=141[/tex]Now, we subtract 95 from both sides:
[tex]\begin{gathered} 8y=141-95 \\ 8y=46 \end{gathered}[/tex]Dividing both sides by 8:
[tex]y=\frac{46}{8}=5.75[/tex]Now we substitute this value in equation (1), the one where we have solved for "x", we get:
[tex]x=\frac{19-2(5.75)}{3}[/tex]Solving the operations we get:
[tex]x=2.5[/tex]Therefore, each movie costs $2.5 and each video game costs $5.75.
Use the given function value and the trigonometric identities to find the exact value of each indicated trigonometric function. (I already have the csc I need the others)
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b.
In order to calculate the cotangent of 60°, we can use the relation below:
[tex]\cot (90\degree-x)=\frac{1}{\cot x}=\frac{1}{\frac{1}{\tan x}}=\tan x[/tex]So we have:
[tex]\begin{gathered} \cot (90\degree-30\degree)=\frac{1}{\cot (30\degree)} \\ \cot (60\degree)=\frac{1}{\frac{1}{\tan30\degree}}=\tan 30\degree \\ \cot (60\degree)=\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]c.
To calculate the cosine of 30°, we can use the relation below:
[tex]\tan x=\frac{\sin x}{\cos x}[/tex]So we have:
[tex]\begin{gathered} \tan 30=\frac{\sin 30}{\cos 30} \\ \frac{\sqrt[]{3}}{3}=\frac{\frac{1}{2}}{\cos 30} \\ \sqrt[]{3}\cos 30=\frac{3}{2} \\ \cos 30=\frac{3}{2\sqrt[]{3}}=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]d.
Calculating the cotangent of 30°, we have:
[tex]\cot (30\degree)=\frac{1}{\tan(30\degree)}=\frac{1}{\frac{\sqrt[]{3}}{3}}=\frac{3}{\sqrt[]{3}}=\sqrt[]{3}[/tex]What happens to the function when x gets close to zero?What happens to the function as y gets very large, we say x'"approaches infinity"?What happens as x gets very small (approaches -∞)?
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According to the graph:
* Domain:
[tex](-\infty,0)\cup(0,\infty)[/tex]* Range:
[tex](-\infty,0)\cup(0,\infty)[/tex]* When x gets close to zero on the left, the function approaches negative infinity.
And when x gets close to zero on the right, the function approaches to infinity.
* When y gets very large x approaches zero.
* When x gets very small, y is close to zero.
Let f(x) = x^2and g(x) = x – 6, find:a. (fog)(x) =b. (gof)(x) =c. (fog)( - 1) = d. (gof)( - 1) =
Answers
Answer:
Given that,
[tex]\begin{gathered} f(x)=x^2 \\ g(x)=x-6 \end{gathered}[/tex]To find,a. (fog)(x)
b. (gof)(x)
c. (fog)( - 1)
d. (gof)( - 1)
we know that,
The composition of a function is an operation where two functions say f and g generate a new function say h in such a way that h (x) = g (f (x)). It means here function g is applied to the function of x that is f(x).
It is represented as (gof)(x), i.e)
[tex](g\circ f)(x)[/tex]a)(fog)(x)
[tex](f\circ g)(x)=f(g(x))[/tex][tex]=f(x-6)[/tex]Put x=x-6 in the function f(x),
[tex]=(x-6)^2[/tex]we get,
[tex](f\circ g)(x)=(x-6)^2-----(1)[/tex]b)(gof)(x)
[tex](g\circ f)(x)=g(f(x))[/tex][tex]=g(x^2)[/tex]Put x=x^2 in the function g(x),
[tex]=x^2-6[/tex]we get,
[tex](g\circ f)(x)=x^2-6----(2)[/tex]c) (fog)( - 1)
using equation (1), Put x=-1, we get
[tex](f\circ g)(-1)=(-1-6)^2[/tex][tex]=(-7)^2=49[/tex][tex](f\circ g)(-1)=49[/tex]d) (gof)( - 1)
using the equation (2), Put x=-1, we get
[tex](g\circ f)(-1)=(-1)^2-6[/tex][tex]=1-6=-5[/tex][tex](g\circ f)(-1)=-5[/tex]What is sin θ if cos θ= √2/2 And θ is in 0< θ< π /2?
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(2 points) In the state of Indiana, 471700 people don't drive. If this is 8.9% of the population of Indiana residents aged 5 years and older, estimate the population of Indiana residents aged 5 years and older. Express your answer rounded to the nearest hundredth of a million.
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You have that in the state of Indiana, 471700 people don't drive. And this population corresponds to the 8.9% of the total population of Indiana resident aged 5 years and older.
In order to calculate the Indiana residents aged 5 years and older, you can use the information about people don't drive and the percentage about it. You can write the given specification as follow:
x(8.9/100) = 471700
where the unknown value x is the total population. When this factor x is multiplied by 8.9/100 you are calculating the 8.9% of that value, which in this case is equal to 471700.
Then, you solve the last equation for x, just as follow:
x(8.9/100) = 471700
x(0.089) = 471700
x = 471700/0.089 = 5300000
Hence, the total population of Indiana resident aged 5 years or older are 5,300,000
Sheila is 1.7 m tall her son is 109 cm tall how many meters tall are shield their son
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express 24,010 in scientific notation
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24,010 = 24.010 x 1000 = 2.4010 x 10000 = 2.401 x 10^4
[tex]2.401x10^4[/tex]Answer:
2.401x10(power4)
A drug manufacturer produces 7,000,000mg of a certain drug. How many kg is thisequal to?
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1 mg = 1/1,000,000 kg =10^-6 kg
multiply 7,000,000 by 1/1,000,000
7,000,000 x (1/1,000,000) = 7 kg
Can someone help me with this geometry question?The first box has four options: cylinder, square pyramid, cone, triangular prism
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Answer:
The shell is best modeled by a cone.
[tex]SA=32\pi=100.6\text{ square inches}[/tex]By the given choices, since the surface area is not a perfect cone, it has a small alteration at the bottom which increases the area. The approximate surface area of the shell is 107.4 square inches.
Step-by-step explanation:
The seashell is best represented by a cone. The surface area of a cone is represented by the following equation:
[tex]\begin{gathered} SA=\pi rs+\pi\cdot r^2 \\ \text{where,} \\ \\ r=\text{radius} \\ s=\text{ slant height} \end{gathered}[/tex]Then, use the Pythagorean theorem to find the slant height:
[tex]\begin{gathered} s=\sqrt[]{2.5^2+10^2} \\ s=\frac{5\sqrt[]{17}}{2} \end{gathered}[/tex]Now, solve for the surface area. If s=10.3, r=2.5
[tex]\begin{gathered} SA=\pi\cdot2.5\cdot\frac{5\sqrt[]{17}}{2}+\pi\cdot(2.5)^2 \\ SA=25.75\pi+6.25\pi \\ SA=32\pi=100.6\text{ square inches} \end{gathered}[/tex]By the given choices, since the surface area is not a perfect cone, it has a small alteration at the bottom which increases the area. The approximate surface area of the shell is 107.4 square inches.
The sum of the interior angles of a polygon with n sides is 1980°. Find n.
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We can relate the sum of the interior angles of a polygon S with its number of sides n as:
[tex]S=(n-2)\cdot180[/tex]Then, if S=1980 degrees, we can find n as:
[tex]\begin{gathered} 1980=(n-2)\cdot180 \\ n-2=\frac{1980}{180} \\ n-2=11 \\ n=11+2 \\ n=13 \end{gathered}[/tex]Answer: the polygon has 13 sides (n=13)
Assume that we are competing different sizes of same brand
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Explanation:
First, we find the unit price of a frozen orange juice which costs $1.63 for 14 ounces.
[tex]Unit\text{ Price}=\frac{1.63}{14}=\$0.116\text{ per ounce}[/tex]Next, we find the unit price of a frozen orange juice which costs $0.63 for 4 ounces.
[tex]Un\imaginaryI t\text{ Pr}\imaginaryI\text{ce}=\frac{0.63}{4}=\operatorname{\$}0.158\text{ per ounce}[/tex]The better buy is $1.63 for 14 ounces since it has a lower unit price. Option A is correct.
Answer:
• (a)$0.116 per ounce
,• (b)$0.158 per ounce
,• (c) A. $1.63 for 14 ounce
I need help please it’s due today and I don’t want to fail please help!! I’m in 8th grade just so you know
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Using distribution property:
5 (3m - 6) = 5(3m) + 5 (-6) = 15m - 30
(-6p + 7) (-4) = (-6p)(-4) + (7)(-4) = 24 p - 28
5 (b - 1) = 5 (b) + 5(-1) = 5b - 5
(x + 9) 5 = x(5) + 9 (5) = 5x + 45
Simplify completely: 12x11y · 1848062" y? 16O 6x^y? V6xO 6x"y? 6xO 216'ya
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Given:
[tex]\sqrt[]{12x^{11}y^6}.\sqrt[]{18y^8}[/tex]To simplify this, we can follow the steps below
[tex]\sqrt[]{12x^{11}y^6}.\sqrt[]{18y^8}=\sqrt[]{12\times18\times x^{11}\times y^6\times y^8}[/tex]This can be simplified further
[tex]\sqrt[]{216\times x^{11}\times y^{14}}[/tex]Then we will obtain
[tex]\sqrt[]{216\text{ }}\text{ x }\sqrt[]{x^{11}}\text{ x}\sqrt[]{y^{14}}[/tex]=>
[tex]6\sqrt[]{6}\times x^{\frac{11}{2}}\times y^{\frac{14}{2}}[/tex]=>
[tex]6\sqrt[]{6}\text{ }\times(x^{5+\frac{1}{2}})\times y^7[/tex]=>
[tex]6\sqrt[]{6}\text{ }\times x^5\times x^{\frac{1}{2}}\times y^7[/tex]=>
[tex]6\sqrt[]{6}\text{ }\times x^5\times\sqrt[]{x}\text{ }\times y^7[/tex]=>
[tex]6x^5y^7\sqrt[]{6x}[/tex]estimate the probability that the next three songs to playare all country songs.Which simulation design could Carlos use to estimate the probability?O A. Number cubeLet even number = countryLet odd number = not countryRoll cube three times. Repeat.O B. Number cubeLet 1, 2 = classicalLet 3,4 = countryLet 5, 6 = popRoll cube three times. Repeat.O C. Random digitsLet 1,2,3 = classicalLet 4,5,6 = country17 On-OnPREVIOUS
Answers
Explanation
Since the personal music player have equal numbers of classical songs, country music, and pop songs.The probability must be symmetric that is;
[tex]\begin{gathered} pr(pop)=\frac{1}{3} \\ pr(country)=\frac{1}{3} \\ pr(classic)=\frac{1}{3} \end{gathered}[/tex]The above must hold regardless of the number of songs. The right answer that correlates to this is:
Answer: Option B
Write the first five terms of the sequence whose general term, a_n, is given as a_n= -3n+9
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To find the terms, substitute n by the number of the term, according to the steps.
Step 01: Find a₁.
To do it, substitute n by 1.
[tex]\begin{gathered} a_n=-3n+9 \\ a_1=-3\cdot1+9 \\ a_1=-3+9 \\ a_1=6 \end{gathered}[/tex]Step 02: Find a₂.
[tex]\begin{gathered} a_2=-3\cdot2+9 \\ a_2=-6+9 \\ a_2=3 \end{gathered}[/tex]Step 03: Find a₃.
[tex]\begin{gathered} a_3=-3\cdot3+9 \\ a_3=-9+9 \\ a_3=0 \end{gathered}[/tex]Step 04: Find a₄.
[tex]\begin{gathered} a_4=-3\cdot4+9 \\ a_4=-12+9 \\ a_4=-3 \end{gathered}[/tex]Step 05: FInd a₅.
[tex]\begin{gathered} a_5=-3\cdot5+9 \\ a_5=-15+9 \\ a_5=-6 \end{gathered}[/tex]In summary:
a₁ = 6
a₂ = 3
a₃ = 0
a₄ = -3
a₅ = -6
Part A. 0.3 is 30% of what number ?
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Let be "x" the number that represents 100%.
According to the information given in the exercise, 30% of the number "x" is:
[tex]0.3[/tex]Then, you can set up the following proportion:
[tex]\frac{0.3}{30}=\frac{x}{100}[/tex]Now you can solve for "x" in order to find the number:
[tex]\begin{gathered} (100)(\frac{0.3}{30})=x \\ \\ \frac{30}{30}=x \\ \\ x=1 \end{gathered}[/tex]Therefore, the answer is:
[tex]1[/tex]Describe the vertical asymptote(s) and hole(s) for the graph of y= (x+2) / (x^2+8x+15).a) asymptotes: x = 3 and 5 and hole: x = - 2b) asymptotes: x = 3 and 5 and no holesc) asymptotes: x = - 5, - 3 and hole: x = - 2d) asymptotes: x = - 5, - 3 and no holes
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we have the function
[tex]y=\frac{x+2}{x^2+8x+15}[/tex]Simplify
[tex]x^2+8x+15=(x+5)(x+3)[/tex]substitute
[tex]y=\frac{x+2}{(x+5)(x+3)}[/tex]Remember that
The denominator cannot be equal to zero
so
The domain of the given function, are all real numbers, except for x=-5 and x=-3
that means
There are vertical asymptotes at x=-5 and at x=-3
No holes in the graph
therefore
The answer is the option DA slope of 2 and passes through (2,3)
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The equation of a Straight Line can be found knowing a point and the slope, as follows:
y-yo=m(x-xo)
Where:
m=2
(2,3)=(xo,yo)
xo=2
yo=3
Therefore:
y-3=2(x-2)
y-3=2x-4
y=2x-1
The Chinese Postman Problem question! 60 points
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Answer:
if it travels a longer distance it will clear up more than it is supposed to and maybe go the wrong direction
Step-by-step explanation:
You randomly select one of the marbles from the jar shown below. What is the probability that you will select a red marble? R marbles red, G marbles are green, and B marbles are blue.3/101/21/53/7
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In the jar, we have:
• # of R marbles = 3,
,• # of G marbles = 2,
,• # of B marbles = 5,
,• total # of marbles = 3 + 2 + 5 = 10.
The probability of randomly selecting a red marble is:
[tex]P(\text{red})=\frac{\#\text{ of R marbles}}{\text{total \# of marbles}}=\frac{3}{10}.[/tex]Answer
3/10
3.Consider this dilation. (a)Is the image of the dilation a reduction or an enlargement of the original figure? Explain. (b)What is the scale factor? Explain.
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a)
Image VMS is reduced to image M'V'S'.
b) the scale factor is 2/3
M(-3,3)
Multiply -3 and 3 with 2/3 your result = -2 and 2.
Scale factor for coordinate M = (-3,3) andN = (-2,2)
Since it is reduction, -2/-3 or 2/3
Therefore, scale factor = 2/3
what is the relationship between angle A and angle B in the picture below?
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From the given figure, let's determine the relationship between angle A and angle B.
Angle A and angle B can be said to be vertical angles.
Since angle A and angle B are opposite each other where two lines cross, they are vertical angles.
Vertically opposite angles can be said to be congruent angles.
ANSWER:
Angle A and B are vertical angles
x-(x+7) What is the simplified expression?
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EXPLANATION
Given the expression x-(x+7), removing the parentheses give us:
= x - x - 7
Adding like terms:
= -7
The simplified expression is -7