Answer:
742
Step-by-step explanation:
4x203
Therefore , the solution of the given problem of function comes out to be g(x) is given by g(x) = (x-4)² + 6
What is function ?A function is a mathematical representation of the relationship between a set of inputs, each of which has an associated output. A function is a group of inputs that, when combined, result in a single, recognized output for each input.
Here, we have,
Given the graph of the original function f(x), whose vertex is at (0, 0), and indeed the graph of the translating function g(x), whose vertex is at (0, 0), (5, 2).
Be aware that the translated function's vertex is 2 units higher and 5 units to the right of the f graph's graph (x).
The function f(x) is then translated 5 units toward the right и 2 units up to arrive at g(x).
Recall that provided a function, f(x), is characterized as a parabola with a vertex at (h, k).
=> f(x) = (x-h)² + k
The outcome of translating a unit to the right with b unit up is
=>f'(x) = (x-h-a)² + k + b
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Una empresa embotelladora de gaseosas lanzará su propia bebida "Delicia" de un litro a un costo variable de S/ 2.50 por unidad, los costos fijos son S/ 18,500. Cada unidad tiene un precio de venta de S/ 4.50. Entonces, determine el número de botellas de un litro que deben venderse para que la empresa obtenga utilidades de S/ 30 000.
Por la ecuación de utilidad, necesitamos una producción de 7,667 botellas de un litro de capacidad para obtener un total de utilidades de S/ 30.000.
¿Cómo determinar las utilidades por la venta de bebidas gaseosas?
Las utilidades (U') se obtienen de sustraer los costes de producción (Cp) a las utilidades netas (U). Los costes de producción (Cp) son la suma de costes variables (C') y costes fijos (C). y la utilidades netas proceden de la venta de botellas. En consecuencia, tenemos la siguiente expresión:
U' = U - Cp
U' = U - C' - C
A continuación, desarrollamos y resolvemos la ecuación resultante:
30000 = 4.50 · x - 2.50 · x - 18500
1.50 · x = 11500
x = 7667
Por la ecuación de utilidad, necesitamos una producción de 7,667 botellas de un litro de capacidad para obtener un total de utilidades de S/ 30.000.
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Marc mixes blue and yellow paint to make his favorite shade of green, which he'll use to paint his house. He has 14 cans of blue paint and 20 cans of yellow paint when he starts.
He wants the same green color every time he mixes, so the amounts of blue and yellow must always be proportional to the original mixture.
On day 1, he mixes 4 cans of blue and 6 cans of yellow.
On day 2, he mixes 6 cans of blue and 9 cans of yellow.
Fill in the blanks to find the highest number of cans of each color Marc can mix to make the same shade of green on day 3.
The ratio of blue paint to yellow paint is 2 : 3.
The total number of blue paint he used on the first and second day is 10.
The number of yellow paint he used on the first and second day is 15.
On the third day, the highest number of can of blue paint he can use is 2
On the third day, the highest number of can of yellow paint he can use is 3.
What is the highest number of blue and yellow paint he can use?The ratio of blue paint to yellow paint can be determined by determining the simplest form of the paints used: 4 : 6 = 2: 3
Total blue paint cans used on the first and second day = 4 + 6 = 10
Blue paint cans remaining = 14 - 10 = 4
Total yellow paint cans used on the first and second day = 6 + 9 = 15 cans
Yellow paint cans remaining = 20 - 15 = 5 cans
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There are currently 3000 moose in the state of Colorado. Their population is increasing at a rate of 2% per year. How many years will it be before there are 6000 moose in the state of Colorado. Round your answer to the nearest year.
Answer:
35 years from now.
Step-by-step explanation:
The quantity of moose as a function of time is as follows:
[tex]M(t) = 3000(1.02)^{t}.[/tex]
Thus, for [tex]M < 6000:[/tex]
[tex]3000(1.02)^{t} < 6000\\\\1.02^{t} < 2\\\\t < \frac{log\,2}{log\,1.02}\\\\ t < 35.003\,\,years.[/tex]
f(x) = 3/x+2-√x-3
The domain for f(x) is all real numbers ___ than it equal to 3
The domain of f(x) is all real numbers > than it equal to 3, for f(x) = 3/x + 2 - √(x - 3).
The domain of a function f(x) is the set of all real values of x, for which real f(x) exists.
In the question, we are asked to find the domain of the function f(x) = 3/x + 2 - √(x - 3).
To find the domain of f(x), we need to check the real values of x, for which real f(x) exists.
We check each part of f(x):
For 3/x, every x gives a real value except x = 0.
For 2, every x gives a real value as it is not dependent on x.
For √(x - 3), real values exist when x - 3 ≥ 0, as negative square roots are not real.
Therefore, after assessing each term, we can say that the domain for f(x) is x - 3 ≥ 0, or x ≥ 3.
Therefore, the domain of f(x) is all real numbers > than it equal to 3, for f(x) = 3/x + 2 - √(x - 3).
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A graph shows the proportional relationship between the number of test questions a student gets correct, x, and the student’s test score, y. The ordered pair (1,5/4) is on the graph. What does the y- coordinate of the ordered pair represent in this relationship.
Answer:
The y-coordinate is 5/4, it represents a test score for one correct answer
Step-by-step explanation:
Proportional relationship is:
y = kx, where k is coefficient of proportion.We have the ordered pair (1, 5/4), which represents:
5/4 = k*1 k = 5/4When x = 1, the y- coordinate is equal to the coefficient of proportionality.
In this case it represents a score for one correct answer.
Please help!! Simplify the following expression in terms of fractional exponents and write it in the following form.
Answer:
[tex]\huge{\boxed{ \huge{\sf 10^{\frac{4}{5} } x^\frac{1}{5} }}}[/tex]
Explanation:
Exponent rules:
[tex]\sqrt[\sf n]{\sf x^b} = \sf x^{\sf \frac{b}{n} }[/tex]Given expression:
[tex]\sqrt[\sf 5]{\sf 10^4 x}[/tex]breakdown
[tex]\sqrt[\sf 5]{\sf 10^4} \sqrt[\sf 5]{\sf x}[/tex]rewrite expression
[tex]\sf 10^{\frac{4}{5} } x^\frac{1}{5}[/tex]A line passes through the point (-3,4) and has a slope of -5. Find an equation of this line
Answer:
y = -5x - 11
Step-by-step explanation:
We are given that a line passes through the point (-3,4) and also has a slope of -5.
We want to write an equation of this line.
The equation of the line can be written in 3 different ways:
Slope-intercept form, which is written as y=mx+b, where m is the slope and b is the y intercept.Standard form, which is written as ax+by=c, where a, b, and c are free integer coefficients (but a and b cannot be 0, and a cannot be negative). Slope-point form, which is written as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope, and [tex](x_1, y_1)[/tex] is a pointSince the question did not specify, any of these 3 options will be valid, however, the most common way to write the equation of the line is in slope-intercept form, so let's do it that way.
Because we are already given the value of the slope, we can immediately plug that into the equation.
Replace m with -5.
y = -5x + b
Now we need to find b.
As the equation passes through the point (-3, 4), we can use its values to help solve for b.
Substitute -3 as x and 4 as y.
4 = -5(-3) + b
Multiply
4 = 15 + b
Subtract 15 from both sides.
-11 = b
Substitute -11 as b in the equation.
y = -5x - 11
Topic: finding the equation of the line
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What is the point-slope form of a line with slope 3/2 that contains the point
(-1, 2)?
A.y+2=(x + 1)
B. y-2-(x-1)
C. y+2=(x-1)
D. y-2-(x+1)
Answer:
[tex]\boldsymbol{\rm{y-2=\dfrac{3}{2}(x+1)}}[/tex], or DStep-by-step explanation:
Hello
If a line's equation has the form [tex]\boldsymbol{\rm{y-y1=m(x-x1)}}[/tex], then it's considered to be in point-slope form.
In that formula,
[tex]\boldsymbol{\rm{y1}}[/tex] is the y co-ordinate (2nd co-ordinate) of the point (here it's given as 2)[tex]\boldsymbol{\rm{m}}[/tex] is the slope, here it's 3/2[tex]\boldsymbol{\rm {x1}}[/tex] is the x co-ordinate (the first co-ordinate) of the point.Now you know why this equation is called point-slope form!
Now that we're familiar with the equation, let's plug in the information that's given to us...
[tex]\boldsymbol{\rm{y-2=\displaystyle\frac{3}{2}(x-(-1)}}[/tex] | simplify
[tex]\boldsymbol{\rm{y-2=\displaystyle\frac{3}{2}(x+1)}}[/tex]
[tex]\pmb{\tt{done~!!}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
[tex]\displaystyle \rm \int_{1 - \sqrt{\pi x} \large \frac{ {d}^{ {1/2 }} }{ {dx}^{1/2} } \small(1) }^{ \sum \limits_{n = 1}^ \infty \frac{4}{4 {n}^{2} - 1 } } \frac{arctan( \frac{2 - x}{1 + 2x}) }{ {x}^{2} - 4x - 1} dx[/tex]
There's nothing particularly tricky about the limits of integration. The upper limit is a telescoping series converging to 2,
[tex]\displaystyle \sum_{n=1}^\infty \frac4{4n^2-1} = 2 \sum_{n=1}^\infty \left(\frac1{2n-1} - \frac1{2n+1}\right) \\\\ ~~~~~~~~ = 2 \left(\left(1-\frac13\right)+\left(\frac13-\frac15\right) + \left(\frac15 - \frac17\right) + \cdots\right)[/tex]
The lower limit reduces to 0 using the Riemann-Liouville definition of the fractional derivative. For [tex]q\in\Bbb Q[/tex], let
[tex]\displaystyle \frac{d^q}{dx^q} f(x) = \frac1{\Gamma(\lceil q\rceil-q)} \frac{d^{\lceil q\rceil}}{dx^{\lceil q\rceil}} \int_a^x (x-t)^{\lceil q\rceil-q-1} f(t) \, dt[/tex]
With [tex]a=0[/tex], [tex]q=\frac12[/tex] and [tex]\lceil q\rceil=1[/tex], it follows that
[tex]\displaystyle \frac{d^{1/2}}{dx^{1/2}} 1 = \frac1{\Gamma\left(\frac12\right)} \frac d{dx} \int_0^x (x-t)^{-1/2} \, dt = \frac1{\sqrt{\pi x}}[/tex]
Let
[tex]\displaystyle I = \int_0^2 \frac{\tan^{-1}\left(\frac{2-x}{1+2x}\right)}{x^2-4x-1} \, dx[/tex]
Observe that
[tex]f(x) = \dfrac{2-x}{1+2x} = f^{-1}(x)[/tex]
is its own inverse, so by substituting [tex]\frac{2-x}{1+2x}\mapsto x[/tex], we get the equivalent integral
[tex]\displaystyle \int_0^2 \frac{\tan^{-1}(x)}{x^2-4x-1} \, dx[/tex]
We have the identity
[tex]\tan^{-1}(x) + \tan^{-1}\left(\dfrac{2-x}{1+2x}\right) = \tan^{-1}(2)[/tex]
so that
[tex]\displaystyle I + I = \int_0^2 \frac{\tan^{-1}\left(\frac{2-x}{1+2x}\right) + \tan^{-1}(x)}{x^2-4x-1} \, dx[/tex]
[tex]\implies \displaystyle I = \frac{\tan^{-1}(2)}2 \int_0^2 \frac{dx}{(x-2)^2-5}[/tex]
The remaining integral is trivial,
[tex]\displaystyle \int_0^2 \frac{dx}{(x-2)^2-5} = \int_{-2}^0 \frac{dx}{x^2-5} \\\\ ~~~~~~~~ = \frac1{2\sqrt5} \int_{-2}^0 \left(\frac1{x-\sqrt5} - \frac1{x+\sqrt5}\right) \, dx \\\\ ~~~~~~~~= -\frac{\ln(2+\sqrt5)}{2\sqrt5} \\\\ ~~~~~~~~ = -\frac1{\sqrt5} \tanh^{-1}\left(\dfrac2{\sqrt5}\right)[/tex]
Then the integral we want is
[tex]I = \displaystyle \int_0^2 \frac{\tan^{-1}\left(\frac{2-x}{1+2x}\right)}{x^2-4x-1} \, dx = \boxed{-\frac1{2\sqrt5} \tan^{-1}(2) \, \tanh^{-1}\left(\dfrac2{\sqrt5}\right)} \approx -0.357395[/tex]
4cos(-5B) sin3B is equivalent to
The trigonometric identity 4cos(-5B) sin3B is equivalent to 2[sin(8B) - sin(2B)]
How to find the trigonometric identity 4cos(-5B) sin3B is equivalent to?Since we have 4cos(-5B) sin3B
Using the trigonometric identity
sin(x + y) - sin(x - y) = 2cosxsiny
So, cosxsiny = [sin(x + y) - sin(x - y)]/2
Since we have 4cos(-5B) sin3B, comparing cos(-5B) sin3B with cosxsiny, we have
x = -5B and y = 3B
So, we have cos(-5B)sin3B = [sin(-5B + 3B) - sin(-5B - 3B)]/2
= [sin(-2B) - sin(-8B)]/2
= [-sin(2B) - {-sin(8B)}]/2 [since sin(-2B) = -sin(2B)]
= [-sin(2B) + sin(8B)]/2
= [sin(8B) - sin(2B)]/2
So, 4cos(-5B)sin3B = 4 × [sin(8B) - sin(2B)]/2
= 2[sin(8B) - sin(2B)]
So, the trigonometric identity 4cos(-5B) sin3B is equivalent to 2[sin(8B) - sin(2B)]
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If 15 buses can carry 795 passengers, what is the total number of passengers that can be carried by 18 buses?
Answer:
954 passengers
Step-by-step explanation:
We can use ratios to solve
15 buses 18 buses
-------------- = ---------------
795 passengers x passengers
Using cross products
15 * x = 18 * 795
15x = 14310
Divide each side by 15
15x/15 = 14310 /15
x =954
18 buses can carry 954 passengers
Q. 2 Find the HCF of 16, 44 and 84 by listing the factors.
Hey brainly gang I'm having trouble could someone help me out. Solve for x.
Answer: x=9
Step-by-step explanation:
Since this shape is a parallelogram, the diagonals perpendicularly bisect each other. So EH =HG
5x-3=2x+24
3x=27
x=9
Substituing x=9 to EH and HG
EH: 5(9)-3=42
HG: 2(9)+24=42
The table shows all possible outcomes for rolling two sixed numbers cubes
The probability of rolling an even number first and an odd number second is 1/4.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability of rolling an even number first and an odd number second = (numbers that have the even number first and odd number second / total sample space)
9/36 = 1/4
Here is the complete question:
The table below shows all of the possible outcomes for rolling two six-sided number cubes. What is the probability of rolling an even number first and an odd number second?
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First accurate answer gets brainliest
Answer: C, (-1, -5)
Step-by-step explanation:
A = 2, B = 4, C = -3
We know the graph opens up because a is positive.
This rules out A and D
We are left with B and C as options.
Let's change this into vertex form
[tex]y=a(x-h)^2[/tex]
Complete the square
[tex]2(x+1)^2-5[/tex]
now a = 2, h = 1, k = -5
The vertex is (h, k)
plug in values:
(-1, -5)
10.3 was subtracted from a number then that difference was multiplied by 7 after which the result was divided by 2.5. if the result of that divison is -7 then what was the initial number
Answer:
6
Step-by-step explanation:
i took the test
Two bikers meet at a park. Biker A needs to stop at the store that is 12 miles east of the park. Biker B heads southeast at a 61° angle at the same time for 24 miles. Once biker A leaves the store he heads southwest at an angle of 89° for 21 miles. Do NOT use the law of cosines, use your knowledge from the content of this course.
Two bikers meet at a park at A
The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°
Biker A needs to stop at the store that is 12 miles east of the park. Biker B heads southeast at a 61° angle at the same time for 24 miles. Once biker A leaves the store he heads southwest at an angle of 89° for 21 miles.
By following of the above statement the triangle is formed shown in the image attached below.
Thus, without using cosine formula, by drawing the triangle according to
the statement. At point A both the bikers were meet
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Find y
please please please help
Answer: [tex]y=26^{\circ}[/tex]
Step-by-step explanation:
Using linear pairs, we can determine the two angles in the picture attached.
Thus, as angles in a triangle add to [tex]180^{\circ}[/tex], [tex]y=26^{\circ}[/tex]
100 POINTS!!! Find the exact length of side a.
Has to be one of the four options
Answer: a = 2√3
First method (Pythagoras theorem):
a² + b² = c²
a² + 2² = 4²
a² = 16 - 4
a = √12
a = 2√3
Second method (sine rule):
opposite/hypotenuse = sin(x)
a/4 = sin(60)
a = 4sin(60)
a = 2√3
Third method (tan rule):
opposite/adjacent = tan(x)
a/2 = tan(60)
a = 2tan(60)
a = 2√3
Answer:
2√3
Step-by-step explanation:
From inspection of the given triangle:
Side a is opposite angle A ⇒ a = BCSide b is opposite angle B ⇒ b = ACSide c is opposite angle C ⇒ c = ABAs we cannot be sure that ΔABC is a right triangle since it is not marked as such, use the cosine rule to find the exact length of side a.
Cosine Rule
[tex]a^2=b^2+c^2-2bc \cos A[/tex]
where a, b and c are the sides and A is the angle opposite side a
Given:
A = 60°b = 2c = 4Substitute the given values into the formula and solve for a:
[tex]\implies a^2=2^2+4^2-2(2)(4) \cos 60^{\circ}[/tex]
[tex]\implies a^2=4+16-16\left(\dfrac{1}{2}\right)[/tex]
[tex]\implies a^2=20-8[/tex]
[tex]\implies a^2=12[/tex]
[tex]\implies a=\sqrt{12}[/tex]
[tex]\implies a=\sqrt{4 \cdot 3}[/tex]
[tex]\implies a=\sqrt{4}{\sqrt{3}[/tex]
[tex]\implies a=2\sqrt{3}[/tex]
Therefore, the exact length of side a is 2√3.
To find out if ΔABC is a right triangle, use Pythagoras Theorem to solve for side a:
[tex]\implies a^2+b^2=c^2[/tex]
[tex]\implies a^2+2^2=4^2[/tex]
[tex]\implies a^2+4=16[/tex]
[tex]\implies a^2=12[/tex]
[tex]\implies a=\sqrt{12}[/tex]
[tex]\implies a=2\sqrt{3}[/tex]
As the measure of side a is the same as the solution found when using the cosine rule, we can conclude that ΔABC is a right triangle.
Please help me with problem 3 (a-d). Thank you!
Using the spread sheet we can easily get the answers:
The statistical section helps find answers by putting the accurate formula or the graphing calculator.
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 1471.33 2 735.68 11.59 0.001072834 3.7389
Within Groups 888.55 14 63.4677
Total 2359.882 16
The APA style refers to Times New Roman Font 12 pts.
The effect size of the result is 0.6233 medium
Part A
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 1471.33 2 735.68 11.59 0.001072834 3.7389
Within Groups 888.55 14 63.4677
Total 2359.882 16
1) The null and alternative hypotheses are
H0: u1=u2=u3
Ha: Not all means are equal
2) The significance level is alpha = 0.05
3) The test statistic F = sb²/sw²
Which if H0 is true has an F distribution with ν1=2 and v2= 14 degrees of freedom.
The computations are
Anova: Single Factor
Groups Count Sum Average Variance
Column 1 6 373 62.16666667 78.96666667
Column 2 4 324 81 60.66666667
Column 3 7 402 57.42857143 51.95238095
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 1471.33 2 735.68 11.59 0.001072834 3.7389
Within Groups 888.55 14 63.46768707
Total 2359.882353 16
5) The critical region is F ≥ F(0.05)(2,14) = 3.74
6) Conclusion:
Since the computed value F= 3.73 does not fall in the critical region F> 3.74 so we accept H0 and conclude that there is no significant difference in the three means.
Part D: The effect size of the result is 0.6233 medium and calculated by
η²= ss between/ ss between + ss error
η²= 1471/1471+889
η²= 0.6233
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Please can somebody help me with this question
Answer:
the answer is=21
Step-by-step explanation:
u have to sum all of its sides
(length+breadth+height).
From a group of 6 men and 4 women, how many committees of 2 men and 3 women can be formed?
The number of ways committees of 2 men and 3 women can be formed is 60.
What is Permutation and Combination ?The method of arranging objects in order is called Permutation and the method of selecting things from a group of objects such that the order doesn't matter is called Combination.
Total Men = 6
Total Women = 4
Committee should consists of 2 men and 3 women
2 men from 6 men can be selected in [tex]\rm ^6 C _2[/tex] ways
3 women from 4 women can be selected in [tex]\rm ^4C_3[/tex] ways
The number of ways committees of 2 men and 3 women can be formed can be determined by Multiplication Principle
[tex]\rm ^6 C _2[/tex] * [tex]\rm ^4C_3[/tex]
15 * 4
= 60 ways
Therefore the number of ways committees of 2 men and 3 women can be formed is 60.
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Geometry
Round volume to nearest tenth
Answer:
volume= [tex]912.9ft^{3}[/tex] (not sure how you want to round the answer. it could be rounded to 913 or left as 912.9)
Step-by-step explanation:
volume of cone: to find the height of the cone, subtract the cylinder height from the total height (H-h= cone height)
[tex]V=\pi r^2\frac{h}{3} \\V=\pi (5.6)^2(\frac{6.8}{3} )\\V=\pi (31.36)(2.2666...)\\V=71.08057\pi \\V=223.3062[/tex]
volume of cylinder:
[tex]V=\pi r^2h\\V=\pi (5.6)^2(7)\\V=\pi (31.36)(7)\\V=219.52\pi \\V=689.6424[/tex]
add them together:
[tex]V=223.3062+689.6424\\V=912.9486[/tex]
60% of a rectangular garden measuring 3 by 6 is covered by snow. What area of the garden is not covered by snow?
What is 11 3/8 divided in half
Answer:
in fraction form it is : 5 11/16
Decimal form it is : 5.6875
Step-by-step explanation:
convert the mixed number into improper fractions: 11 3/8 = 91/8
= 91/8 / 8/2
Apollyon the fraction rule: a/b / c = a / b * c
= 91/8 * 2
Multiply the numbers: 8 * 2 = 16
= 91/15
convert the improper fractions into mixed numbers: 91/16 = 5 11/16
Final answer of:
= 5 11/16
Solve for the missing item in the following. (Do not round intermediate calculations. Round your answer to the nearest whole percent.)
Principal 5,000 time 6 months simple interest 300
Rate?
The rate is 1.2%.
What is Simple interest?Simple interest is interest calculated on the principal portion of a loan or the original contribution to a savings account.
Given:
P = 5000
T =6 month= 1/2 year
SI= 300
We know,
SI= P*R*T/100
300= 500* R * 1 /200
60000= 500R
R= 60000/500
R= 120
R= 1.2%
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Which of the following is the best strategy to support children in learning about shapes?
a. Purchase a complete, wooden collection of two-and three- dimensional shapes from educational supply catalog.
b. Plan opportunities for children to talk about what is and what is not a shape and identify attribo les that define shapes.
C. Provide multiple worksheets with pictures of the basic shapes for children to color.
The best option is C. Provide multiple worksheets with pictures of the basic shapes for children to colour.
What does the learning process in children involve?The process of learning has often been described to include all but not limited to the following:
gaining new understanding, learning new behaviours,skills,values, attitudes, andpreferences.Children according to experts learn faster and easily remember what they see. Hence, providing multiple worksheets with pictures of the basic shapes for children to colour is the most cost-efficient strategy to support children in learning about shapes.
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EXTREMELY URGENT!!! The angles of elevation of the top of two vertical towers as seen from the
middle point of the lines joining the foot of the towers are 45° & 60°. The ratio of the height of the towers is:
Since the angles of elevation of the top of two vertical towers is 45° & 60°, the ratio of the height of the towers is 0.58:1
How to find the ratio of the height of the towersSince the angles of elevation of the top of two vertical towers as seen from the middle point of the lines joining the foot of the towers are 45° & 60°.
The height of the tower, the line of sight and the ground form a right angled trangle
Height of first towerLet
h = height of first tower, d = distance of tower to middle point = L/2 where L = distance between tower and Ф = angle of elevation of tower from midpoint = 45°Using trigonometric ratios, we have that
tanФ = h/d
= h/L/2
= 2h/L
So, h = LtanФ/2
= Ltan45°/2
= L/2 × 1
= L/2
Height of second towerLet
h' = height of first tower, d = distance of tower to middle point = L/2 where L = distance between tower and Ф' = angle of elevation of tower from midpoint = 60°Using trigonometric ratios, we have that
tanФ' = h'/d
= h'/L/2
= 2h'/L
So, h' = LtanФ'/2
= Ltan60°/2
= L/2 × √3
= √3L/2
Ratio of the height of the towersSo, the ratio of the height of the towers is n = h/h'
= L/2 ÷ √3L/2
= 1/√3
= 1/1.732
= 0.577
≅ 0.58
So, the ratio of the height of the towers is 0.58:1
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Identify a transformation of the function ƒ(x) = x2 by observing the equation of the function g(x) = (x – 6)2.
f(x) moves 6 unit towards right side along X-axis and forms the function g(x).
Given that, the original function is
[tex]f(x)=x^2[/tex]
and now the function is
[tex]g(x) =(x-6)^2[/tex]
When f(x)=0 then we can get by calculating that,
[tex]x^2=0[/tex]
x=0
So, the f(x) function satisfied by point (0,0).
Now when g(x)=0 then by calculating that we get,
[tex](x-6)^2=0[/tex]
x-6 = 0
x = 6
So g(x) function satisfied by (6,0).
In geometrical words we can say that if we transform from f(x) to g(x) then (0,0) tranformed to (6,0).
That suggests that the function moves 6 unit right along X axis, which is towards positive X axis.
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5. In 2011, Manitoba progressive income tax rates were 10.8% on the first $31,000, 12.75% on the next $36,000, anc
17.4% on any additional income. If your gross taxable earnings for the year were $85,000, what percentage of your
earnings did you pay in taxes?
Step-by-step explanation:
0 <= income <= 31000 : 10.8%
31000 < income <= 31000+36000 = 67000 : 12.75%
67000 < income < anything above 67000 : 17.4%
the total income is
$85,000
the taxes paid are
10.8% of 31000 = $3348
12.75% of 67000 - 31000 = 12.75% of 36000 = $4590
17.4% of 85000 - 67000 = 17.4% of 18000 = $3132
so, out of $85000 you paid
3348
4590
3132
----------
$11,070
taxes
100% = 85000
1% = 100%/100 = 85000/100 = 850
how many % are 11070 ?
well, as many as how often 1% fits into that amount :
11070 / 850 = 13.02352941...% ≈ 13.02%