theres 2 fill in the blank boxes and 3 drop down menus, below i will list the options in the drop down menus.box 1 - apply quotient identities, apply Pythagorean identities, apply double-number identities, apply even-odd identities.box 2 - apply cofunction identities, use the definition of subtraction, apply even-odd identities, Write as one expresssion combine like terms.box 3 - apply cofunction identities, apply double-number identities, apply Pythagorean identities, apply even-odd identities.
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Solution
Box 1 : Apply Quotient Identities
[tex]cotx-tanx=\frac{cosx}{sinx}-\frac{sinx}{cosx}[/tex]The answer for the first box is
[tex]\begin{equation*} \frac{cosx}{sinx}-\frac{sinx}{cosx} \end{equation*}[/tex]Box 2: Write as one expression
[tex]\begin{gathered} cotx-tanx=\frac{cosx}{s\imaginaryI nx}-\frac{s\imaginaryI nx}{cosx} \\ cotx-tanx=\frac{cosx(cosx)-sinx(sinx)}{sinxcosx} \\ cotx-tanx=\frac{cos^2x-sin^2x}{sinxcosx} \end{gathered}[/tex]The answer for the second box is
[tex]\frac{cos^{2}x-s\imaginaryI n^{2}x}{s\imaginaryI nxcosx}[/tex]Before the box 3, please note the identity
Note: Trigonometry I dentities
[tex]\begin{gathered} cos^2x-s\mathrm{i}n^2x=cos2x \\ 2sinxcosx=sin2x \end{gathered}[/tex]Box 3: Apply Double - Number Identities
[tex]\begin{gathered} cotx-tanx=\frac{cos^{2}x-s\imaginaryI n^{2}x}{s\imaginaryI nxcosx} \\ Applying\text{ the above trigonometry identities} \\ cotx-tanx=\frac{cos2x}{sinxcosx} \\ cotx-tanx=\frac{cos2x}{sinxcosx}\times\frac{2}{2} \\ cotx-tanx=\frac{2cos2x}{2sinxcosx} \\ cotx-tanx=\frac{2cos2x}{sin2x} \end{gathered}[/tex]Related Questions
Complete the steps to find the value of x .
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I need help with my statistics homework " -compute the range ,sample variance,and sample standard deviation cost."
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We need to find the range, sample variance, and sample standard deviation cost.
The range is already given: $247. It can be found by subtracting the least from the greatest value:
[tex]466-219=247[/tex]Now, in order to find the sample variance and the sample standard deviation, we first need to find the mean of the sample:
[tex]\text{ mean }=\text{ }\frac{415+466+400+219}{4}=\frac{1500}{4}=375[/tex]Now, we can find the sample variance s² using the formula:
[tex]s²=\frac{\sum_{i\mathop{=}1}^n(x_i-\text{ mean})²}{n-1}[/tex]where n is the number of values (n = 4) and the xi are the values of the sample.
We obtain:
[tex]\begin{gathered} s²=\frac{(415-375)²+(466-375)²+(400-375)²+(219-375)²}{4-1} \\ \\ s²=\frac{40²+91²+25²+(-156)²}{3} \\ \\ s²=\frac{1600+8281+625+24336}{3} \\ \\ s²=\frac{34842}{3} \\ \\ s²=11614 \end{gathered}[/tex]Now, the sample standard deviation s is the square root of the sample variance:
[tex]\begin{gathered} s=\sqrt{11614} \\ \\ s\cong107.8 \\ \\ s\cong108 \end{gathered}[/tex]Therefore, rounding to the nearest whole numbers, the answers are:
Answer
range: $247
s² = 11614 dollars²
s ≅ $108
A car can travel 43/1/2 miles on 1/1/4 gallons of gas. What is the unit rate for miler per gallon
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The unit rate for the car is 34.8 miles per gallon.
How to get the unit rate for mile per gallon?
The unit rate will be given by the quotient between the distance traveled and the gallons of gas consumed to travel that distance.
Here we know that the car travels 43 and 1/2 miles on 1 and 1/4 gallons of gas, then the quotient is:
U = (43 + 1/2)/(1 + 1/4) mi/gal = (43.5)/(1.25) mi/gal = 34.8mi/gal
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2. Axely says that 8is equivalent to –.125repeating. Without solving, evaluate her claim in thespace below.
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we are asked about the claim that the fraction -12 / 8 is equivalent to the decimal expression -0.125... (repeating)
Without evaluating the expression, we can say that the clain is INCORRECT, since just the quotient 12/8 should give a number LARGER than "1" (one) in magnitude (the number 12 is larger than the number 8 in the denominator. We can also say that such division cannot ever give a repeating decimal at infinity, since divisions of integer numbers by 8 or 4 never render a repeating decimal, but a finite number of decimals.
Solve the equation3 x² - 12x +1 =0 by completing the
square.
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By completing squares, we wll get that the solutions of the quadratic equation are:
x = 6 ± √35
How to complete squares?Here we have the quadratic equation:
x² - 12x + 1 = 0
We can rewrite this as:
x² - 2*6x + 1 = 0
So we can add and subtract 6² to get:
x² - 2*6x + 1 + 6² - 6² = 0
Now we rearrange the terms:
(x² - 2*6x + 6²) + 1 - 6² = 0
Now we can complete squares.
(x - 6)² + 1 - 36 = 0
(x - 6)² = 35
Now we solve for x:
x = 6 ± √35
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Question 6 (1 point)Below are four scenarios where counting is involved. Select those scenarios in whichPERMUTATIONS are involved. There may be more than one permutation.How many possible ways can a group of 10 runners finish first, second andthird?How many ways can 2 females and 1male be selected for a conference from alarger group of 5 females and males?How many 3 letter arrangements of the word OLDWAYS are there?How many 5-card hands from a standard deck of cards would result in allspades?Previous PageNext PagePage 6 of 12
Answers
Step 1: Definition
Arranging people, digits, numbers, alphabets, letters, and colors are examples of permutations. Selection of menu, food, clothes, subjects, the team are examples of combinations.
Step 2:
How many possible ways can a group of 10 runners finish first, second and third?
PERMUTATION because it involved arrangement
Step 3:
How many ways can 2 females and 1 male be selected for a conference from a larger group of 5 females and males?
NOT PERMUTATION because it involved selection, hence it is a combination.
Step 4:
How many 3 letter arrangements of the word OLDWAYS are there?
PERMUTATION because it involved arrangement
Step 5:
How many 5-card hands from a standard deck of cards would result in all spades?
NOT PERMUTATION because it involved selection, hence it is a combination.
There is sales tax of $9.00 on an item t that costs $ 120.00 before tax. The sales tax on a different item is $ 19.05. How much does the second item cost before tax?
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SOLUTION:
Step 1:
In this question, we are given that:
There is sales tax of $9.00 on an item that costs $ 120.00 before tax.
The sales tax on a different item is $ 19.05.
We are meant to find how much the second item cost before tax.
Step 2:
Assuming that there is an equal percentage of tax,
and let the second item cost before tax be y,
then we have that:
[tex]\frac{9}{120}\text{ = }\frac{19.05}{y}[/tex]Cross-multiply, we have that:
[tex]\begin{gathered} 9\text{ x y = 19.05 x 120} \\ 9y\text{ = 2286} \\ \end{gathered}[/tex]Divide both sides by 9, we have that:
[tex]\begin{gathered} y\text{ = }\frac{2286}{9} \\ y\text{ = 254} \end{gathered}[/tex]CONCLUSION:
The cost of the second item before tax = $ 254
Give the slope and the y-intercept of the line y=– 8x+7. Make sure the y-intercept is written as a coordinate.
Answers
Solution
We have the following function given:
y =-8x+7
If we compare this with the general formula for a slope given by:
y= mx+b
We can see that the slope m is:
m =-8
And the y-intercept would be: (0,7)
LM is a perpendicular bisector of NP. The length of LN is 12w + 7, and rhe length of LP is 15w - 5. What is the length of LN?(every capital letter has a line over it and i cant add that. Ex. There would be a line over LP. Because its a line. But i dont know to do that so im adding this!)
Answers
LN = LP
So, we can say:
12w + 7 = 15w - 5
Solving for w,
7 + 5 = 15w - 12w
12 = 3w
w = 12/3
w = 4
Length of LN is 12w + 7
plug in w = 4 to get:
12 (4) + 7
48 + 7 = 55
Length of LN is 55
Solve for x. Then find m
(8x+4)°
(10x-6)°
Both lines are intersecting and the two equations are vertical pairs
Answers
Answer:
x = 5
m∠QRT = 44
Step-by-step explanation:
8x + 4 = 10x - 6
-10x -10x
------------------------
-2x + 4 = -6
-4 -4
---------------------
-2x = -10
÷-2 ÷-2
--------------------
x = 5
m∠QRT
8x + 4
8(5) + 4
40 + 4 = 44
I hope this helps!
From the image, [tex](8x + 4 )° = (10x - 6)°[/tex]
Reason: Vertically opposite angles are equal.
Now, we solve for x
[tex]8x + 4 = 10x - 6[/tex]
collect like terms
[tex] 4 + 6 = 10x - 8x[/tex]
[tex]→ 10 = 2x[/tex]
Divide both sides by the coefficient of x to find the value of x
[tex] x = 5[/tex]
Now, substitute for the value of x in the expression for m∠QRT to find the degree
[tex](8x + 4 )° → (8(5) + 4)°[/tex]
Therefore: m∠QRT = 44°
I hope this helpsWrite an equation of a line in SLOPE INTERCEPT FORM that goes through (-5,-3) and is parallel to the line y = x +5.
Answers
Since the slope of the line y=x+5 is m=1, then if the other line is parallel to y=x+5, then it must have the same slope, this is, m'=1.
Now we can use the point-slope formula to get the equation of the line:
[tex]\begin{gathered} m^{\prime}=1 \\ (x_0,y_0)=(-5,-3) \\ y-y_0=m(x-x_0) \\ \Rightarrow y-(-3)=1\cdot(x-(-5))=x+5 \\ \Rightarrow y+3=x+5 \\ \Rightarrow y=x+5-3=x+2 \\ y=x+2 \end{gathered}[/tex]therefore, the equation of the line in slope intercept form that goes through (-5,-3) and is parallel to the line y=x+5 is y=x+2
Your parents will retire in 25 years. They currently have $230,000 saved, and they think they will need $1,850,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Round your answer to two decimal places.
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6.62% is annual interest rate must they earn to reach their goal.
What exactly does "interest rate" mean?
An interest rate informs you of how much borrowing will cost you and how much saving will pay off. Therefore, the interest rate is the amount you pay for borrowing money and is expressed as a percentage of the entire loan amount if you are a borrower.N = 25
PV = - $230,000
FV = $1,850,000
PMT = 0
CPT Rate
Applying excel formula:
=RATE(25,0,-230,000,1,850,000)
= 6.62%
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Solve for t. If there are multiple solutions, enter them as a
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we have the equation
[tex]\frac{12}{t}+\frac{18}{(t-2)}=\frac{9}{2}[/tex]Solve for t
step 1
Multiply both sides by 2t(t-2) to remove fractions
[tex]\frac{12\cdot2t(t-2)}{t}+\frac{18\cdot2t(t-2)}{(t-2)}=\frac{9\cdot2t(t-2)}{2}[/tex]simplify
[tex]12\cdot2(t-2)+18\cdot2t=9\cdot t(t-2)[/tex][tex]24t-48+36t=9t^2-18t[/tex][tex]\begin{gathered} 60t-48=9t^2-18t \\ 9t^2-18t-60t+48=0 \\ 9t^2-78t+48=0 \end{gathered}[/tex]Solve the quadratic equation
Using the formula
a=9
b=-78
c=48
substitute
[tex]t=\frac{-(-78)\pm\sqrt[]{-78^2-4(9)(48)}}{2(9)}[/tex][tex]t=\frac{78\pm66}{18}[/tex]The solutions for t are
t=8 and t=2/3
therefore
the answer is
t=2/3,8
Find the axis of symmetry, vertex and which direction the graph opens, and the y-int for each quadratic function
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Solution
Part a
The axis of symmetry
Part b
The vertex
Vertex (2,3)
Part c
The graph opens downward
Part D
The y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x=0.
The y-intercept
[tex](0,-5)[/tex]Another
The y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x=0.
[tex]\begin{gathered} y=-2x^2+8x-5 \\ y=-2(0)+8(0)-5 \\ y=0+0-5 \\ y=-5 \end{gathered}[/tex]x=0 y=-5
[tex](0,-5)[/tex]PLEASE READ BEFORE ANSWERING: ITS ALL ONE QUESTION HENCE "QUESTION 6" THEY ARE NOT INDIVIDUALLY DIFFERENT QUESTIONS.
Answers
First, lets note that the given functions are polynomials of degree 2. Since the domain of a polynomial is the entire set of real numbers, the domain for all cases is:
[tex](-\infty,\infty)[/tex]Now, lets find the range for all cases. In this regard, we will use the first derivative criteria in order to obtain the minimum (or maximim) point.
case 1)
In the first case, we have
[tex]\begin{gathered} 1)\text{ }\frac{d}{dx}f(x)=6x+6=0 \\ which\text{ gives} \\ x=-1 \end{gathered}[/tex]which corresponds to the point (-1,-8). Then the minimum y-value is -8 because the leading coefficient is positive, which means that the curve opens upwards. So the range is
[tex]\lbrack-8,\infty)[/tex]On the other hand, the horizontal intercept (or x-intercept) is the value of the variable x when the function value is zero, that is,
[tex]3x^2+6x-5=0[/tex]which gives
[tex]\begin{gathered} x_1=-1+\frac{2\sqrt{6}}{3} \\ and \\ x_2=-1-\frac{2\sqrt{6}}{3} \end{gathered}[/tex]Case 2)
In this case, the first derivative criteria give us
[tex]\begin{gathered} \frac{d}{dx}g(x)=2x+2=0 \\ then \\ x=-1 \end{gathered}[/tex]Since the leading coefficient is positive, the curve opens upwards so the point (-1,5) is the minimum values. Then, the range is
[tex]\lbrack5,\infty)[/tex][tex]\lbrack5,\infty)[/tex]and the horizontal intercepts do not exists.
Case 3)
In this case, the first derivative criteris gives
[tex]\begin{gathered} \frac{d}{dx}f(x)=-2x=0 \\ then \\ x=0 \end{gathered}[/tex]Since the leading coeffcient is negative the curve opens downwards and the maximum point is (0,9). So the range is
[tex](-\infty,9\rbrack[/tex]and the horizontal intercepts occur at
[tex]\begin{gathered} -x^2+9=0 \\ then \\ x=\pm3 \end{gathered}[/tex]Case 4)
In this case, the first derivative yields
[tex]\begin{gathered} \frac{d}{dx}p(t)=6t-12=0 \\ so \\ t=2 \end{gathered}[/tex]since the leading coefficient is postive the curve opens upwards and the point (2,-12) is the minimum point. Then the range is
[tex]\lbrack-12,\infty)[/tex]and the horizontal intercetps ocurr when
[tex]\begin{gathered} 3x^2-12x=0 \\ which\text{ gives} \\ x=4 \\ and \\ x=0 \end{gathered}[/tex]Case 5)
In this case, the leading coefficient is positive so the curve opens upwards and the minimum point ocurrs at x=0. Therefore, the range is
[tex]\lbrack0,\infty)[/tex]and thehorizontal intercept is ('0,0).
In summary, by rounding to the nearest tenth, the answers are:
Find seco, coso, and coto, where is the angle shown in the figure.Give exact values, not decimal approximations.
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step 1
Find out the value of cosθ
cosθ=8/17 ------> by CAH
step 2
Find out the value of secθ
secθ=1/cosθ
secθ=17/8
step 3
Find out the length of the vertical leg in the given right triangle
Applying the Pythagorean Theorem
17^2=8^2+y^2
y^2=17^2-8^2
y^2=225
y=15
step 4
Find out the value f cotθ
cotθ=8/15 -----> adjacent side divided by the opposite side
therefore
secθ=17/8cosθ=8/17cotθ=8/15Which linear inequality is represented by the graph?1. y≤ 2x+42. y≤ x+33. y²x+34. y≥ 2x+3
Answers
Given a graph represented a linear inequality.
First, we will find the equation of the shown line.
As shown, the line passes through the points (0, 3) and (2, 4)
the general equation of the line in the slope-intercept form will be:
[tex]y=mx+b[/tex]Where (m) is the slope and (b) is the y-intercept
b = y-intercept = 3
We will find the slope as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-3}{2-0}=\frac{1}{2}[/tex]So, the equation of the line will be:
[tex]y=\frac{1}{2}x+3[/tex]As shown, the point (0, 0) lying in the area of the solution
So, the linear inequality will be as follows:
[tex]y\leq\frac{1}{2}x+3[/tex]7. The cylinder shown has a radius of 3inches. The height is three times the radiusFind the volume of the cylinder. Round yoursolution to the nearest tenth.
Answers
Answer:
250 cubic inches
Explanation:
Given that:
Radius of the cylinder, = 3 in.
Height of the cylinder = 3r
= 3(3)
=9 in.
The formula to find the volume of a cylinder is
[tex]V=\pi r^2h[/tex]Plug the given values into the formula.
[tex]\begin{gathered} V=\pi3^29 \\ =81\pi \\ =254.469 \end{gathered}[/tex]Rounding to nearest tenth gives 250 cubic inches, which is the required volume of the cylinder.
marie invested 10000 in a savings account that pays 2 interest quartarly 4 times a yesr. how much money will she have in her account in 7 years?
Answers
Okey, here we have the following:
Capital: 10000
Interest: 2%
Time: 7 Years= 7*4=28 quarters of year
Using the compound interest formula, we get:
[tex]C_f=10000(1+\frac{0.02}{4})^{4\cdot7}=1000(1+\frac{0.02}{4})^{28}[/tex]Working we get:
[tex]C_f\approx11.498.73[/tex]She will have aproximately $11,498.73 in her account after 7 years.
The dimensions and the weight of several solids are given. Use the density information to determine what element is the solid made up of.
Answers
Given:
Dimensions and weight of a solid is given.
Height (h) of a cylinder (in cm) =
[tex]h=5[/tex]Radius (r) of a cylinder (in cm) =
[tex]r=5[/tex]Mass (m) of solid (in grams)=
[tex]m=3090.5[/tex]Density of several elements is given.
Cobalt=8.86, Copper=8.96, Gold=19.3, Iron=7.87, Lead 11.3, Platinum=21.5, Silver=10.5, Nickel=8.90.
Required:
What element is the solid made up of.
Answer:
Let us find the volume (V) of cylinder (in cubic cm).
[tex]\begin{gathered} V=\pi\times r^2\times h \\ V=3.14\times\left(5\right)^2\times5 \\ V=3.14\times25\times5 \\ V=392.5 \end{gathered}[/tex]Using formula of density (D), we get,
[tex]\begin{gathered} D=\frac{m}{V} \\ D=\frac{3090.5}{392.5} \\ D=7.87 \end{gathered}[/tex]Hence, the density of the solid is 7.87 grams per cubic cm.
From the given information of density of several elements, we see that the solid is made up of Iron.
Final Answer:
The solid is made up of Iron.
What is an equation of the line that passes through the points (-3,3) and (3, — 7)?Put your answer in fully reduced form.
Answers
The equation of line passing through two points (x_1,y_1) and (x_2,y_2) is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Substitute the points in the equation to obtain the equation of line.
[tex]\begin{gathered} y-3=\frac{-7-3}{3-(-3)}(x-(-3)) \\ y-3=\frac{-10}{6}(x+6) \\ 3(y-3)=-5(x+6) \\ 3y-9+5x+30=0 \\ 3y+5x+21=0 \end{gathered}[/tex]So equation of line is 3y+5x+21=0.
Fragment Company leased a portion of its store to another company for eight months beginning on October 1, at a monthly rate of $1,250. Fragment collected the entire $10,000 cash on October 1 and recorded it as unearned revenue. Assuming adjusting entries are only made at year-end, the adjusting entry made on December 31 would be:
Answers
Given:
Credit to rent earned for
Amount of total rent = $10,000
Amount unearned = amount of total rent ( 3 month / 8 month)
[tex]\begin{gathered} \text{Amount unearned=10000}\times\frac{3}{8} \\ =3750 \end{gathered}[/tex]Unearned rent is : $3750
Pls help with the question in the picture. 20 Points and brainliest.
Answers
Answer:
∠ UTV = 66°
Step-by-step explanation:
the central angle USV is twice the angle on the circle ∠ UTV , subtended on the same arc UV , that is
10x + 82 = 2(10x + 16) ← divide both sides by 2
5x + 41 = 10x + 16 ( subtract 5x from both sides )
41 = 5x + 16 ( subtract 16 from both sides )
25 = 5x ( divide both sides by 5 )
5 = x
Then
∠ UTV = 10x + 16 = 10(5) + 16 = 50 + 16 = 66°
help meeeeeeeeeeee pleaseee
Answers
Equations (f∙g)(x) and (g∙f)(x) have the same product which is 5x² - 19x - 4.
What exactly are equations?In a mathematical equation, the equals sign is used to express that two expressions are equal.An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.Such as 3x + 5 = 15 as an example.There are many different types of equations, including linear, quadratic, cubic, and others.The three primary forms of linear equations are point-slope, standard, and slope-intercept.So, (f∙g)(x) and (g∙f)(x):
Where, f(x) = 5x + 1 and g(x) = x - 4:(f∙g)(x):
5x(x - 4) + 1(x - 4)5x² - 20x + x - 45x² - 19x - 4(g∙f)(x):
x(5x + 1) - 4(5x + 1)5x² + x - 20x - 45x² - 19x - 4Therefore, equations (f∙g)(x) and (g∙f)(x) have the same product which is 5x² - 19x - 4.
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A) What is the perimeter of the regular hexagon shown above?B) What is the area of the regular hexagon shown above?(see attached image)
Answers
Remember that
A regular hexagon can be divided into 6 equilateral triangles
the measure of each interior angle in a regular hexagon is 120 degrees
so
see the attached figure to better undesrtand the problem
each equilateral triangle has three equal sides
the length of each side is given and is 12 units
Part A) Perimeter
the perimeter is equal to
P=6(12)=72 units
Part B
Find the area
Find the height of each equilateral triangle
we have
tan(60)=h/6
Remember that
[tex]\tan (60^o)=\sqrt[]{3}[/tex]therefore
[tex]h=6\sqrt[]{3}[/tex]the area of the polygon is
[tex]A=6\cdot\lbrack\frac{1}{2}\cdot(6\sqrt[]{3})\cdot(12)\rbrack[/tex][tex]A=216\sqrt[]{3}[/tex]alternate way to find out the value of happlying Pythagorean Theorem
12^2=6^2+h^2
h^2=12^2-6^2
h^2=108
h=6√3 units
Use the given scale factor and the side lengths of the scale drawing to determine the side lengths of the real object. Scale factor. 4:1 10 in 10 in A C 12 in Scale drawing Object A. Side a is 6 inches long, side bis 6 inches long, and side cis 8 inches long. B. Side a is 14 inches long, side bis 14 inches long, and side cis 16 inches long. C. Side a is 40 inches long, side bis 40 inches long, and side c is 48 inches long D. Side a is 2.5 inches long, side bis 2.5 inches long, and side cis 3
Answers
As the scale factor is 4:1 it means that for each 4inches in scale drawing correspond to 1 inch in the object.
Then, to find the side lengths in the object you multiply the measure of each side in the scale drawing by 1/4:
[tex]\begin{gathered} 10in\cdot\frac{1}{4}=2.5in \\ \\ 10in\cdot\frac{1}{4}=2.5in \\ \\ 12in\cdot\frac{1}{4}=3in \end{gathered}[/tex]Then, side a is 2.5 inches, side b is 2.5in and side c is 3inchesPerform the indicated operation and write the answer in the form A+Bi
Answers
The Solution:
Given:
[tex](3+8i)(4-3i)[/tex]We are required to simplify the above expression in a+bi form.
Simplify by expanding:
[tex]\begin{gathered} (3+8i)(4-3i) \\ 3(4-3i)+8i(4-3i) \\ 12-9i+32i-24(-1) \end{gathered}[/tex]Collecting the like terms, we get:
[tex]\begin{gathered} 12-9i+32i+24 \\ 12+24-9i+32i \\ 36+23i \end{gathered}[/tex]Therefore, the correct answer is [option 3]
how do you find the x intercept for -(x-3)^2+12
Answers
This is the equation for the line.
Here the given equation is,
[tex]-(x-3)^2+12[/tex]We can calculate x intercept by substituting 0 for y, as there is no value of y,
the x intercept is none here. The graph is as follows,
A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 17.6 ft. give the area A of the window in square feet when the width is 4.1 ft. Give the answer to two decimals places.
Answers
To find the area of the window you need to find the area of rectangular part and the area of semicircle part.
To find the area of the rectangular part you need to find the height of the rectangle, use the perimeter to find it:
Perimeter of the given window is equal to: The circunference or perimeter of the semicircle (πr) and the perimeter of the rectangular part (w+2h)
[tex]P=\pi\cdot r+w+2h[/tex]The radius of the semicircle is equal to the half of the width:
[tex]\begin{gathered} r=\frac{4.1ft}{2}=2.05ft \\ \\ w=4.1ft \\ \\ P=17.6ft \\ \\ 17.6ft=\pi\cdot2.05ft+4.1ft+2h \end{gathered}[/tex]Use the equation above and find the value of h:
[tex]\begin{gathered} 17.6ft-\pi\cdot2.05ft-4.1ft=2h \\ 7.06ft=2h \\ \\ \frac{7.06ft}{2}=h \\ \\ 3.53ft=h \end{gathered}[/tex]Find the area of the rectangular part:
[tex]\begin{gathered} A_1=h\cdot w \\ A_1=3.53ft\cdot4.1ft \\ A_1=14.473ft^2 \end{gathered}[/tex]Find the area of the semicircle:
[tex]\begin{gathered} A_2=\frac{\pi\cdot r^2}{2} \\ \\ A_2=\frac{\pi\cdot(2.05ft)^2}{2} \\ \\ A_2=6.601ft^2 \end{gathered}[/tex]Sum the areas to get the area of the window:
[tex]\begin{gathered} A=A_1+A_2 \\ A=14.473ft^2+6.601ft^2 \\ A=21.074ft^2 \end{gathered}[/tex]Then the area of the window is 21.07 squared feetUse mental math to find all of the quotients equal to 50. Drag the correct division problems into the box.
4
,
500
÷
900
450
÷
90
45
,
000
÷
900
4
,
500
÷
90
450
÷
9
Quotients equal to 50
Answers
Answer: 45,000 ÷ 900=50
Step-by-step explanation: