Use the diagram to answer the question. 15 ft 120 ft2 10 ft A rectangular yard contains a 120-square-foot garden. If seeds are scattered uniformly over the yard, what is the probability that a seed lands in the garden?
Answers
area of the rectangle
[tex]\begin{gathered} \text{area}=\text{length}\times width \\ \text{area}=15\times10=150 \end{gathered}[/tex]area of rectangle is 150 sq ft, therefore the probability that a seed lands in the garden is
[tex]\frac{area\text{ garden}}{area\text{ rectangle}}=\frac{120}{150}=\frac{4}{5}[/tex]answer: 4/5
Related Questions
Simplify completely: cos/1−sin
Answers
There are basic six ratios in trigonometry that help in establishing a relationship between the ratio of sides of a right triangle with the angle. If θ is the angle in a right-angled triangle, formed between the base and hypotenuse, then
sin θ = Perpendicular/Hypotenuse
cos θ = Base/Hypotenuse
tan θ = Perpendicular/Base
The value of the other three functions: cot, sec, and cosec depend on tan, cos, and sin respectively as given below.
cot θ = 1/tan θ = Base/Perpendicular
sec θ = 1/cos θ = Hypotenuse/Base
cosec θ = 1/sin θ = Hypotenuse/Perpendicular
Given:
cos x/ 1- sin x
Using Trigonometric identities
1-sin²x = cos²x
So, on rationalizing
= (cos x) /(1-sinx) x (1+sinx)/(1+sinx)
= (cos x) (1+sinx) /(1²-sin²x)
= (cos x) (1+sinx) /(1-sin²x)
= (cos x)(1+sinx)/(cos²x)
= (1+sinx)/(cos x)
=1/ cos x + sin x / cos x
=sec x + tan x
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The diagonal of a rectangular filed 135m long is 157m. What is the Width of the field?
Answers
To solve this exercise let's make a sketch of the rectangular field first:
The length, width, and diagonal of the rectangular field form a right triangle, to determine the width of the rectangle you can apply the Pythagorean theorem.
This theorem states that the square of the hypotenuse is equal to the sum of the square of the legs of the triangle.
[tex]a^2+b^2=c^2[/tex]The diagonal is the hypotenuse of the triangle, the length is one of the legs "a" and the width is the other leg "b".
Write the theorem for b:
[tex]\begin{gathered} a^2-a^2+b^2=c^2-a^2 \\ b^2=c^2-a^2 \\ \sqrt[]{b^2}=\sqrt[]{c^2-a^2} \\ b=\sqrt[]{c^2-a^2} \end{gathered}[/tex]Replace the expression with c=157 and a=135
[tex]\begin{gathered} b=\sqrt[]{157^2-135^2} \\ b=\sqrt[]{24649-18225} \\ b=\sqrt[]{6424} \\ b=80.149\approx80.15 \end{gathered}[/tex]The width of the field is 80.15 meters.
Pls help I’m close finishing this assignment
A. No, Alexandra made a mistake going from the given expression to Step 1. Alexandra should have added 18 and 3 before evaluating the exponent. The order of operations says to perform operations inside parentheses before you evaluate exponents.
B. No, Alexandra made a mistake going from Step 1 to Step 2. Alexandra should have divided 9 by 9 before adding. The order of operations says to divide before you add.
C. Yes, Alexandra's work is correct.
Answers
The expression illustrates that C. Yes, Alexandra's work is correct.
What is an expression?The expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The expression is given as:
= (18 + 3²) ÷ 3²
= (18 + 9) ÷ 9
= 27 ÷ 9
= 3
In this case, the work is correct.
Therefore, the correct option is C.
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12y=28x+609y=21x+45A.) no solution B.) many solutions C.) one solution
Answers
Step 1: Name the equation
12y = 28x + 60 ....... equation 1
9y = 21x + 45 ........... equation 2
Step 2: Eliminate one of the variables (either x or y ) in the two equations
To do this,
(12y = 28x + 60) multiply by 9
=> 108y = 252x + 540 ........ equation 3
(9y = 21x + 45 ) multiply by 12
=> 108y =252x + 540....... equation 4
step 4
equate equations 3 and 4
252x + 540 = 252x + 540
step 5 :solve the equation
252 x -252x = 540
0 = 0
Hence, the Equations has no solution
option A i
If Volume = 216 cm^3, what is the length of one edge of Julie's jewelry box?
Answers
The volume of a cube = Side³
The length of one edge of Julie's Jewelry box is 6 cm.
What is a cube?A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices, and 12 edges.
The volume of a cube = Side³
We have,
The volume of the Jewelry box = 216 cm³
The length of one edge of the box = L
The volume of a cube is given as:
V = L³
216 = L³
[ 6 x 6 x 6 = 216 ]
L = ∛216
L = ∛6³
L = 6
Thus,
The length of one edge of Julie's Jewelry box is 6 cm.
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Three horse share five bales of hay equally. Five cows share eight bales of hay equally.
How much hay does each horse and each cow get?
Which animal gets more, a horse of a cow? How much more hay do they get?
Answers
How much hay does each horse and each cow get?
(a)The hay shared by 3 horses = 5 bales
So, the hay shared by 1 horse = x
Rewriting the statements ,
3 h = 5 b --(1)
1 h = x -(2)
By applying cross multiplication method to (1) and (2)
3 (x) = 5
x = 5/3
The hay shared by 1 horse = 5/3
(b)The hay shared by 5 cows = 8 bales
So, the hay shared by 1 cow = y
Rewriting the statements ,
5 c = 8 b --(3)
1 c = y -(4)
By applying cross multiplication method to (3) and (4)
5 (y) = 8
x = 8/5
The hay shared by 1 cow = 8/5
Which animal gets more, a horse of a cow?
Comparing the fractions,
The hay shared by 1 horse = 5/3 = 1.7
The hay shared by 1 cow = 8/5 = 1.6
1.7 > 1.6
So, a horse gets more than a cow
How much more hay do they get?
Considering the difference of fractions,
Amount of more hay consumed = Hay shared by a horse - hay shared by a cow.
[tex]=\frac{5}{3} -\frac{8}{5} \\\\=\frac{25-24}{15} \\\\=\frac{1}{15}[/tex]
The horse share [tex]\frac{1}{15}[/tex] more hay than cows
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1) Our baseball team last year had 10 boys. This year there are 15 boys. Find the percent of
change including whether it is an increase and decrease.
Answers
Answer: Hi, the answer would be 150% or in decimal form 1.5 this is an increase. There fore your answere is 1.5 which makes it an increase.
Say a certain manufacturing industry has 63.1 thousand jobs in 2008, but is expected to decline at arate of 1.7 thousand jobs per year from 2008 to 2018. Assuming this holds true, what will be this induchange from 2008 to 2018?a. 70%b. -27%C. -17%d. -75%
Answers
The inicial number of jobs is 63.1 thousand, and each year this number will decrease by 1.7 thousand.
So the change from 2008 to 2018, that is, 10 years, will be:
[tex]10\cdot(-1.7)=-17[/tex]To find the change in percentage, we need to divide the change (-17) by the inicial amount of jobs (63.1), then we have that:
[tex]\frac{-17}{63.1}=-0.27=-27\text{\%}[/tex]So the change in this period is -27%, therefore the answer is B.
what is 2×700 please tell me
Answers
2 multiply by 700 is 1400
An easier trick to multipy numbers with zeros is;
Remove the zeros first, multiply the numbers, then add back the zeros
That is;
2 x 7 = 14
Then add back the zeros
That is;
1400
2x700=1,400
In the diagram below, AB || DEF, AE and BD intersect at C, m2B = 43°, and mZCEF = 152°.
Answers
From the picture, we have the necessary information:
The supplementary angles.
The parallels being intersected by two secant lines. And alternate interior angles are congruent under this condition.
The other angle of the triangle is then:
As a result, the angles vertical angles, therefore
< BAC = 28 (it confirms the alternate interior angle Therefore, we can write all the angles in the following drawing:
Write a paragraph proof of your conclusion in part A. To begin your proof, draw radii OA and OC.
Answers
In the given figure we have that
AC=AD -----> by the radius of the circle
Δ ACO -------> is a right triangle
Δ ADO -------> is a right triangle
Applying the Pythagorean Theorem in both triangles
AC^2=CO^2+AO^2
AD^2=DO^2+AO^2
Remember that
AC=AD ----> radius of the circle
so
CO=DO
Δ ACO≅Δ ADO -----> by SSS
therefore
is proved that the radius that bisects the chord is a perpendicular bisector
What is the exact value of tan 7pi/12? Thank you!
Answers
Remember that
[tex]tan(\frac{7\pi}{12})=tan(105^o)=-tan(75^o)=-tan(45^o+30^o)[/tex]and
[tex]tan(A+B)=\frac{tanA+tanB}{1-tanA*tanB}[/tex]therefore
[tex]tan(45^o+30^o)=\frac{tan45^o+tan30^o}{1-tan45^o*tan30^o}[/tex]substitute given values
[tex]tan(45^o+30^o)=\frac{1+\frac{\sqrt{3}}{3}}{1-(1)(\frac{\sqrt{3}}{3})}=\frac{\frac{3+\sqrt{3}}{3}}{\frac{3-\sqrt{3}}{3}}=\frac{3+\sqrt{3}}{3-\sqrt{3}}*\frac{3+\sqrt{3}}{3+\sqrt{3}}=\frac{9+6\sqrt{3}+3}{6}=\frac{12+6\sqrt{3}}{6}=2+\sqrt{3}[/tex]therefore
The answer is
[tex]tan(\frac{7\pi}{12})=-(2+\sqrt{3})[/tex]The answer is the second option
Which graph represents this equation?y = 3:2 - 61ОА.+X-4No26-24-6B.24N- 2C.
Answers
To determine which one is the graph of the equation:
[tex]y=\frac{3}{2}x^2-6x[/tex]We can finc the x-intercepts of the equations, we know that this happens when y=0, then we have:
[tex]\frac{3}{2}x^2-6x=0[/tex]Solving for x we have:
[tex]\begin{gathered} \frac{3}{2}x^2-6x=0 \\ x(\frac{3}{2}x-6)=0 \\ \text{then} \\ x=0 \\ or \\ \frac{3}{2}x-6=0 \\ \frac{3}{2}x=6 \\ x=\frac{2}{3}\cdot6 \\ x=4 \end{gathered}[/tex]This means that the the graph have to cross the x axis in the values x=0 and x=4.
Looking at the options we notice that the only graph that do this is option B, therefore the gaprh of the equation is shown on B.
Which of the following is the correct mathematical expression for:
Halve a number and then increase it by five
Answers
Answer:
1/2 x + 5
Step-by-step explanation:
Haf of x = 1/2 x
then add 5 : 1/2 x + 5
Four people ordered total bill for soup and four people ordered stew is $31 .If only 2 people had ordered soup and one person ordered stew ,the bill would have been $12.25 .How much is each order of soup and stew ?
Answers
Let price of 1 soup be "x" and 1 stew be "y".
4 soup and 4 stew is $31, thus we can write:
[tex]4x+4y=31[/tex]Also, given
2 soup and 1 stew costs $12.25, thus we can write:
[tex]2x+y=12.25[/tex]Let' solve this for y and substitute it back to Equation 1. Then we will solve for x. The process is shown below:
[tex]y=12.25-2x[/tex]Substituting,
[tex]\begin{gathered} 4x+4y=31 \\ 4x+4(12.25-2x)=31 \\ 4x+49-8x=31 \\ 49-31=8x-4x \\ 18=4x \\ x=\frac{18}{4} \\ x=4.5 \end{gathered}[/tex]Finding y:
[tex]\begin{gathered} y=12.25-2x \\ y=12.25-2(4.5) \\ y=3.25 \end{gathered}[/tex]Thus,
Answer:
Each order of Soup = $4.50
Each order of Stew = $3.25
Solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. 7t+5−−−−−√=7 Enter the exact answers.
Answers
The given equation is
[tex]\sqrt[]{7t+5}=7[/tex]Square both sides to cancel the square root
[tex]\begin{gathered} (\sqrt[]{7t+5})^2=(7)^2 \\ 7t+5=49 \end{gathered}[/tex]Subtract 5 from both sides
[tex]\begin{gathered} 7t+5-5=49-5 \\ 7t=44 \end{gathered}[/tex]Divide both sides by 7
[tex]\begin{gathered} \frac{7t}{7}=\frac{44}{7} \\ t=\frac{44}{7} \\ t=6\frac{2}{7} \end{gathered}[/tex]The solution is t = 44/7 OR t = 6 2/7 (mixed number)
Build Understanding ACTIVITY When two lines are cut by a third line, the third line is called a transversal. The intersections of the lines form eight angles, including five special types of angle pairs. When the two lines cut by a transversal are parallel, as shown, the angles in any of the special pairs will be either congruent or supplementary. 1/2 3/4 5/6 7/8 1 The term alternate means that two angles are on opposite sides of the transversal. A. Alternate interior angles are angles on opposite sides of the transversal inside the parallel lines. Measure a pair of alternate interior angles with a protractor. Name the angles you found. Are they congruent or supplementary?
Answers
Answer
First of, let us explain what congruent and supplementary mean.
Congruent angles are equal to each other.
Supplementary angles add up to give 180 degrees.
A) Alternate interior angles are congruent. Examples of alternate interior angles from the image include
- angles 3 and 6.
- angles 4 and 5.
B) Alternate exterior angles are congruent. Examples of alternate exterior angles from this image include
- angles 1 and 8.
- angles 2 and 7.
C) Same-side interior angles are supplemetary. Examples of same-side interior angles from the image include
- angles 3 and 5.
- angles 4 and 6.
D) Same-side corresponding angles are also supplementary. Examples of same-side exterior angles from the image include
- angles 1 and 7.
- angles 2 and 8.
E) Corresponding angles for two parallel lines are congruent. Examples of corresponding angles from the image include
- angles 1 and 5.
- angles 2 and 6.
- angles 3 and 7.
- angles 4 and 8.
Hope this Helps!!!
for the first week of January,Patricia Morgan worked 46 hours. Patricia earns $9.70 an hour. her employer pays overtime for all hours worked in excess of 40 hours per week and pays 1.5 times the hourly rate for overtime hours. calculate the following for the first week of January ( round your responses to the nearest cent if necessary) regular pay amount, overtime pay, gross pay
Answers
Answer
Regular pay = $388
Overtime pay = $87.3
Gross pay = $388 + $87.3
= $475.3
Explanation
During the first week of January, Patricia Morgan worked 46 hours at a rate of $9.70 per hour for regular hours.
For overtime, the pay is 1.5 times the normal rate. That is, 1.5 × $9.70 = $14.55
So, working for 46 hours, that is, 40 hours regular pay rate, and 6 hours overtime pay rate.
Regular pay = 40 × $9.70 = $388
Overtime pay = 6 × $14.55 = $87.3
Gross pay = Regular pay + Overtime pay
= $388 + $87.3
= $475.3
Hope this Helps!!!
Answer the questions below.
Answers
(a) Daily high temperature
The daily high temperature does not depend on the number of ticket sales.(b) Amount of sleep
The amount of medication influences the amount of sleep.(c) Input U
The independent variable is the input.Find 75% of 150. Round to the nearest tenth if necessary.
Answers
Find 75% of 150
First, let's convert 75% to decimal by dividing by 100:
[tex]\frac{75}{100}=0.75[/tex]Now, we will multiply 0.75 with 150 to find out answer:
[tex]\begin{gathered} 0.75\times150 \\ =112.5 \end{gathered}[/tex]Answer112.5I believe that it would be 112.5.
__________________________________________
Convert 75% to a decimal by dividing it by 100:
[tex]\frac{75}{100} = 0.75[/tex]
Next, multiply 0.75 to 150:
[tex]0.75[/tex] × [tex]150 = 112.5[/tex] ← Final Solution
Hope this helps!
i only need the answer THANK YOU!
Answers
The trigonometry expression is cos Ф = 3√5/7 , sec Ф = 7/3√5, cosec Ф = 7/2, tan Ф = 2/3√5, cot Ф = 3√5/ 2
sin Ф = perpendicular(p) / hypotenuse(h)
= 2/7
base(b) = √(h²-p²)
=[tex]\sqrt{7^{2} - 2^{2} }[/tex]
= √45
= 3√5
cosФ = b/h
= 3√5/7
sec Ф = h/b
= 7/3√5
cosec Ф = h/ p
= 7/2
tan Ф = p/b
= 2/3√5
cot Ф = b/p
=3√5/ 2
Therefore cos Ф = 3√5/7, sec Ф = 7/3√5, cosec Ф = 7/2, tan Ф = 2/3√5, cot Ф = 3√5/ 2.
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Assume the random variable X is normally distributed with mean μ = 50 and standard deviation o=7. Find the 78th percentile
Answers
The 78th Percentile is 55.402
What is Percentile?
A Percentile (or centile) is a statistic measure that indicates the value below which a given percentage of observations in a group fall. The 20th percentile, for example, is the value (or score) below which 20% of the observations can be found.
The terms Percentile and Percentile rank are frequently used in the reporting of norm-referenced test scores. For example, a score in the 86th percentile, where 86 is the percentile rank, corresponds to a value below which 86% of the observations can be found. In contrast, a score in the 86th percentile indicates that it is at or below the value at which 86% of the observations can be found.
We know that,
μ = 50,
and σ = 7,
First, we need to find the z-score associated to this percentile.
We need to find the value [tex]Z_{p}[/tex] that solves the equation below.
[tex]Pr(Z < Z_{p}) = 0.78[/tex]
The value of [tex]Z_{p}[/tex] that solves the equation above cannot be made directly, it is solved either by looking at a standard normal distribution table or by approximation.
Based on this, we find that that the solution is [tex]Z_{p}[/tex] 0.772, because from the normal table we see that
Pr(Z<0.772)=0.78
Therefore, the percentile we are looking for is computed using the following formula:
[tex]P_{78}[/tex] = μ+ [tex]Z_{p}[/tex] × σ
= 50+0.772×7
= 55.405
Therefore, it is concluded that the corresponding 78-th percentile is found to be [tex]P_{78}[/tex] is 55.405.
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Answer the image below
Answers
The value of the function f'(g(x)) is -10
What is a function?
an expression or rule or law that describes a relationship between one variable and another variable. i.e. between independent variable and dependent variable is known as function.
We are given f(-6)=-3, f'(-6)=-5, g(2)=-6, g'(2)=2
We are asked to find F'(2) where F(x)= f(g(x))
We will use the algebra of function to solve the given problem and find the required value
We have
[tex]F(x)=f(g(x))\\F'(x)= f'(g(x))*g'(x)[/tex]
Substituting x=2 in the above equation we get
[tex]F'(2)=f'(g(2))*g'(2)\\F'(2)=f'(-6)*2\\F'(2)=-5*2\\F'(2)=-10[/tex]
Hence the value of F'(2)= -10 as asked
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In right triangle ABC, CD¯¯¯¯¯ is the altitude to hypotenuse AB¯¯¯¯¯. If AB = 28.3¯ and DB = 12, find CD.
Answers
The side of the right triangle CD is 25.63 units
How to find side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees.
Base on the angles, the side of a right triangle can be named as follows:
opposite sidehypotenuse sideadjacent sideTherefore, the side CD of the right triangle can be found as follows:
using Pythagoras theorem,
c² = a² + b²
Hence,
CD = √28.3² - 12²
CD = √800.89 - 144
CD = √656.89
CD = 25.6298653918
Therefore,
CD = 25.63 units
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The area of the front yard for question number 1 is 60x^2 + 12x - 21 The grass area of the backyard for question number 2 is 81x^2 - 212x + 68
Answers
Given,
The area of the front yard is 60x^2 + 12x - 21 .
The grass area of the backyard is 81x^2 - 212x + 68.
The total are is the sum of the front yard and the back yard.
So, to obtain the total area adding the area of the front yard and back yard.
[tex]\begin{gathered} \text{Total area= area of front yard+area of back yard} \\ =60x^2+12x-21+81x^2-212x+68 \\ =60x^2+81x^2+12x-212x-21+68 \\ =x^2(60+81)+x(12-212)-21+68 \\ =141x^2-200x+47 \end{gathered}[/tex]Hence, the total area is 141x^2-200x+47.
1
Suppose Vanessa can clean her bedroom in 30
minutes. Steven can clean the same room in only
15 minutes. If they work together, how long
will it take them to clean the bedroom ?
Answers
How long will it take them to clean the bedroom? 10 minutes
How to calculate the time of the work done together?
Given:
Vanessa (A)= 30 minutes
Steven (B) = 15 minutes
The total time taken if both work together is given by,
[tex]A+B=\frac{AB}{A+B} \\\\=\frac{30*15}{30+15}\\\\=\frac{450}{45}\\\\= 10[/tex]
So, it would take 10 minutes to clean the bedroom, if they work together
What is the time - work concept ?
Time and work is concerned with the amount of time it takes a person or a group of people to complete a task and the effectiveness of the work performed by each of them. The rate of work and the amount of time required are inversely proportional. Time taken = 1 / The rate of work.To learn more about time and work , refer:
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How do I turn the contents of the passage into an equation?Her phone bill, the cost of diapers, and the subscriptions and pizza for her son. I guess I have to give her an amount to start with, so I’ll go with she started with $100.What if the subscriptions and pizza were 65. The diapers were 30. And her phone bill is 150. Can you show how much she paid toward the diapers and phone bill?
Answers
Let G be the cost os monthly game subscriptions, P the cost of a wekly phone bill, D = $30 the cost of a package of 42 diapers, F the cost of pizza on fridays and W the amount she receives each workday.
Then, for a initial amount I = $100, the money M she still have after the events in the text is given by:
[tex]\begin{gathered} M=(W+I)-(G+P+D+F) \\ M=(W+100)-(G+P+30+F) \\ M=W+70-G-P-F \end{gathered}[/tex]If F + G = $65 and P = $150, we have:
[tex]\begin{gathered} M=W+70-65-150 \\ M=W-145 \end{gathered}[/tex]If we are considering only how much she payed for the diapers and the phone bill, we have:
[tex]D+P=30+150=\text{ \$}180[/tex]x + y = 5 17x + 4y = 46 ) Find the solution to the system of equations. Write it as an ordered pair below.
Answers
we have
x + y = 5 -----> equation A
17x + 4y = 46 ------> equation B
Solve the system by substitution
step 1
isolate the variable x in equation A
x=5-y ------> equation C
step 2
substitute equation C in equation B
17(5-y)+4y=46
solve for y
85-17y+4y=46
17y-4y=85-46
13y=39
y=3
Find the value of x
x=5-y
x=5-3=2
thereforethe solution is the ordered pair (2,3)Use the vertex (0,3) and a point on the graph (2,7) to find the general form of the equation of the quadratic function.
Answers
The line which is passing through the point on the graph (2,7) and with vertex (0,3) having equation is [tex]x^{2}[/tex] -y +3 = 0
The polynomial equations of degree two in one variable of type f(x) = ax^2 + bx + c = 0 and with a, b, c are R and a [tex]\neq[/tex] 0, are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f(x).
The general equation of the quadratic equation if (h, k) is the vertex and (x, y) is a point on the curve is given by
y = [tex]a(x-h)^{2} + k[/tex] ......eqn 1
In the situation where a must be determined at position (h, k) and (x, y)
In the above question, it is given that,
vertex is (h,k) = (0,3) and the point on the graph is (x,y) = (2,7)
Now we'll put the points in the general equation of the quadratic equation to get the desired equation
y = [tex]a(x-h)^{2} + k[/tex]
y = [tex]a(x-0)^{2}[/tex] + 3 .....eqn 1
Now putting the value of (x,y)
7 = [tex]a(2-0)^{2}[/tex] + 3
7 = 4a + 3
4a = 4
a = 1
putting the value of a in the equation 1, we get
y = [tex]1(x-0)^{2}[/tex] + 3
y = [tex]x^{2}[/tex] + 3
[tex]x^{2}[/tex] -y +3 = 0
Hence, the equation of the line passing through a point on the graph (2,7) with the vertex (0,3) is [tex]x^{2}[/tex] -y +3 = 0
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Find the 11th term of the sequence: 32805, 10935, 3645...
Answers
first term a=32805
common ration: r=10935/32805=1/3
11th term:
[tex]\begin{gathered} a_{11}=32805(\frac{1}{3})^{11-1} \\ a_{11}=32805(\frac{1}{3})^{10} \\ a_{11}=32805(\frac{1}{59049}) \\ a_{11}=0.555 \end{gathered}[/tex]So the 11th term is 0.555