Let the width be w and the length be l
Since the width is 5ft less than the length,
then
w=l-5
The area of the rectangle is 126 square feet
Then
l times w = 126
therefore
l(l-5) = 126
[tex]\begin{gathered} \Rightarrow l^2-5l=126 \\ \Rightarrow l^2-5l-126=0 \end{gathered}[/tex]Factorising the equation, we have:
[tex]\begin{gathered} l^2+9l-14l-126=0 \\ \Rightarrow(l+9)(l-14)=0 \\ \Rightarrow l=-9\text{ or 14} \end{gathered}[/tex]Since l cannot be negative
then the only correct option is l=14
Since w = l - 5
then
w = 14 - 5 = 9
Therefore the length is 14ft and the width is 9ft
To get around a small pond, a local electrical utility must lay two sections of underground cable that are 371 m and 440 m long. The two sections meet at an angle of 145°. How much extra cable is needed due to going around the pond?
If the cable could went through the pond there would be only one straight section conecting the two points. If we draw this new section in the picture we'll form a triangle:
In order to find how much extra cable is needed because of the pond we must find the length of the imaginary cable that connects the points through the dot, for this length we are going to use x.
The cosine rule will help as find it. Let's assume that we have a triangle with an angle A which has an opposite side with a length a and the lengths of the other two sides are b and c. Then the cosine rule states the following:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]We can apply this to our triangle. The 145° angle that we know is A, its opposite side a is x and the remaining sides b and c are the two cable sections of 371 m and 440 m. Then we get:
[tex]\begin{gathered} x^2=371^2+440^2-2\cdot371\cdot440\cdot\cos145^{\circ} \\ x^2=598677.7594 \end{gathered}[/tex]Then we apply a square root to both sides of this equation:
[tex]\begin{gathered} \sqrt{x^2}=\sqrt{598677.7594} \\ x=773.74 \end{gathered}[/tex]So without the pond the length of the cable would have been of 773.74 m. In order to find the amount of extra cable needed we must take the total length of both sections and substract 773.74 m from it. Then we get:
[tex]371+440-773.74=37.26[/tex]AnswerThen the answer is 37.26m.
clarify each of the following triangles by their angles in sides
SOLUTION
From the diagram below,
Triangle A is right isosceles, since two angles are equal, two sides are equal, and there is a right-angle (90 degrees angle) present.
Triangle B is obtuse scalene, since none of the sides are equal, and one of the angles is greater than 90 degrees.
Triangle C is acute scalene, since none of the sides are equal, and all the angles are less than 90 degrees.
Triangle D is acute isosceles, since two angles and two sides are equal, and all the angles are less than 90 degrees.
What is the missing exponent?w^3 x w^? = w^-6
Let the missing exponent be a,
[tex]w^3\times w^a=w^{-6}[/tex]From the law of indices stated below which satisfies the above equation,
[tex]\begin{gathered} x^a\times x^b=x^{a+b} \\ \text{relating the equation to the formula,} \\ w^3\times w^a=w^{-6} \\ w^{3+a}_{}=w^{-6} \\ \text{solving the exponents,} \\ 3+a=-6 \\ \text{Collect like terms} \\ a=-6-3 \\ a=-9 \end{gathered}[/tex]Hence, the missing exponent a is -9.
Can you help me answer a, b and c please?
Answer
a)
[tex]B=B_{0}(1+\frac{a}{12})^{t}[/tex]b)
[tex]B=B_{0}(1+\frac{25}{3}a)^{t}[/tex]c)
[tex]B=B_0(1+\frac{25}{3}a)^{12y}[/tex]Explanation
We're given the function:
[tex]B=B_0(1+r)^t[/tex]To represent the equation with the data given in the problem, we need to solve the three parts of this problem.
The part a ask us to write the expression in terms of annual percentage rate (APR) in decimal. If we call "a" the APR in decimal, then the monthly rate is the APR divided in 12:
[tex]r=\frac{a}{12}[/tex]Now we can rewrite the balance equation in terms of the initial investment, the number of months and the APR:
[tex]B=B_0(1+\frac{a}{12})^t[/tex]In part b, we need to write the balance equation using the APR as percentage. The APR as decimal is equal to the APR in percentage divided by 100. If we call A the APR in percentage:
[tex]a=\frac{A}{100}[/tex]Now we replace this value in the balance equation we got in part a:
[tex]B=B_0(1+\frac{100a}{12})^t[/tex]Then simplify:
[tex]B=B_0(1+\frac{25}{3}a)^t[/tex]That's the answer to b.
In part c, we need to write the balance equation with the time in years. Since 1 year has 12 months, if we call the number of months t, and the number of years y:
[tex]t=12y[/tex]Then:
[tex]B=B_0(1+\frac{25}{3}a)^{12y}[/tex]And this is the answer to c.
a cylindrical container with an 8 in. diameter and an 2 in. height is completely filled with water. all of its contents are poured into another cylindrical container that is 32 in. tall. if the water completely fills the second container, the second container's diameter is ___ in.
Volume of a cylinder: π r^2 h
Where:
r = radius
h= height
Calculate the volume of the first cylindrical container:
radius = diameter/2
Volume = π (8/2)^2 (2) = 100.5 in3
Second container
Volume = 100.5
heigth = 32 in
100.5 = π r^2 32
Solve for r
100.5/ (π 32 ) = r^2
1 = r^2
√1 = r
r=1
Diameter = 2 r = 2 (1) = 2 in
What is the slope of the linear function given the following table?
х у-3. 6 -2. 51/3-1. 42/30. 43. 2Help please !
Let's use two points of the table:
[tex]\begin{gathered} (x1,y1)=(-1,3) \\ (x2,y2)=(0,1) \end{gathered}[/tex]Let's find the slope using the following formula:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{1-3}{0-(-1)}=-\frac{2}{1}=-2[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-3=-2(x+1) \\ y-3=-2x-2 \\ y=-2x+1 \end{gathered}[/tex]-------------------------------------------------
For the 2nd table:
[tex]\begin{gathered} (x1,y1)=(-3,6) \\ (x2,y2)=(0,4) \end{gathered}[/tex]Let's find the slope:
[tex]m=\frac{4-6}{0-(-3)}=-\frac{2}{3}[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-6=-\frac{2}{3}(x+3) \\ y-6=-\frac{2}{3}x-2 \\ y=-\frac{2}{3}x+4 \end{gathered}[/tex]Find the next term of the geometric sequence 3/2, 3/4, 3/8 , ...
Given:
Geometric sequence:
[tex]\frac{3}{2},\frac{3}{4},\frac{3}{8},.....[/tex]Find-: Next term of the geometric.
Sol:
Common ratio of a geometric sequence.
[tex]r=\frac{a_n}{a_{n-1}}[/tex]A common ratio is:
[tex]\begin{gathered} r=\frac{\frac{3}{4}}{\frac{3}{2}} \\ r=\frac{3}{4}\times\frac{2}{3} \\ r=\frac{1}{2} \end{gathered}[/tex]The next term is:
[tex]a_n=ra_{n-1}[/tex][tex]\begin{gathered} =\frac{1}{2}\times\frac{3}{8} \\ =\frac{3}{16} \end{gathered}[/tex]3The number of hours that the employees at the local Fry's grocery store worked last week is normallydistributed with a mean of 28 hours and a standard deviation of 4. What percentage of employees workedbetween 24 and 36 hours?Answer:
We can solve this question by using the fact that a normal distribution is symmetric and using the empirical rules. The empirical rules are
• 68% of the data falls within one standard deviation of the mean.
• 95% of the data falls within two standard deviations of the mean.
• 99.7% of the data falls within three standard deviations of the mean.
In our problem, the mean is 28 and the standard deviation is equal to 4. Our interval is 24(one standard deviation below the mean) and 36(2 standard deviations above the mean)
[tex](24,36)=(28-4,28+8)=(28-\sigma,28+2\sigma)[/tex]Our area is the area that falls within one standard deviation of the mean plus the area between one standard deviation and two on the positive side. The first area is 68% of the data, and the second area we can calculate using the fact that a bell curve is symmetric. Since 68% of data falls within one standard deviation and 95% of the data falls within two standard deviations of the mean, the difference between them represents the data that falls between one standard deviation and two standard deviation.
[tex]95-68=27[/tex]Since the distribution is symmetric, the data that falls between one standard deviation and two standard deviation on the positive side is half of this value.
[tex]\frac{27}{2}=13.5[/tex]Now, we just add this value to 68% and we're going to have our answer.
[tex]68+13.5=81.5[/tex]The percentage of employees worked between 24 and 36 hours is 81.5%.
Natalie bought a tank for her pet fish. She is measuring how much water will fill the tank.Which measurement will best help Natalie determine how much water will fill the tank?O Natalie should measure the area of the fish tank in square units.O Natalie should measure the area of the fish tank in cubic units.O Natalie should measure the volume of the fish tank in square units.O Natalie should measure the volume of the fish tank in cubic units.
Answer:
Natalie should measure the volume of the fish tank in cubic units.
Explanation:
The measure of the area is in square units and the measure of the volume is in cubic units.
The area gives you the measure of a plane surface and the volume gives you how much space a solid occupies
So, the measurement that will best help Natalie is the volume of the fish tank in cubic units.
Solve the following system of equations by graphing. y = –1∕2x – 2 y = –3∕2x + 2
We can see the solution in the graph as follows:
PLEASE HELP DUE SOON ONLY Q6 I have the work for the rest.
Given:
Diameter=40 feet
so radius=20 feet(d=2r)
Height of 2nd tank= 130 feet
Required:
Volume of sphere
Volume of cylinder
Explanation:
First of all we are going to calculate volume of sphere=
[tex]\begin{gathered} \frac{4}{3}\pi r^3 \\ =\frac{4}{3}\times3.14\times20\times20\times20 \\ =33,493.33feet^3 \end{gathered}[/tex]Then we are going to calculate volume of cylinder=
[tex]\begin{gathered} =\pi r^2h \\ =3.14\times20\times20\times130 \\ 163,280feet^3 \end{gathered}[/tex]and the vertically cross- section of tank 2 is a rectangle.
Required answer:
volume of sphere is 33,493.33
volume of cylinder=163,280
and the shape is rectangle.
Hi can someone please help me out on this drag and drop assignment? I’ll appreciate the help :)
Answer:
Step-by-step explanation:
1.
circumference of circular fence = 2πr
π = 3.14
r = radius
radius of circular fence, r= 10 feet
putting the values in the formula,
circumference = 2× 3.14 × 10
= 62.8 feet
therefore the fencing brad need will be 62.8 feet
2.
Area of the circular hot tub = πr²
π= 3.14
r = radius
as given in the question,
diameter = 80 inches
we know diameter is equal to half radius so r = 40 inches
putting the values in the formula,
area = 3.14 × 40× 40
= 5,024 inches
hence the area of the hot tub is equal to 5,025 inches
3.
Area of the circular wall clock = πr²
π= 3.14
r = radius
as per the question ,
area of 5 inches wall clock = 3.14× 5×5 = 78.5 inches
and area of 6 inches wall clock = 3.14 ×6×6 = 113.04 inches
To find the how much wall space will 6 inches wall clock takes we have to subtract both areas,
area of 6 inches wall clock - area of 5 inches wall clock = 113.04 - 78.5
= 34.54 inches
6 inches wall clock will take 34.54 inches of area more.
4.
In one rotation tire will cover whole area so to find the diameter we have to put area of circle equals to area of tire
Area of the circle = πr²
π= 3.14
r = radius
as per the question ,
area of the tire =116.18 inches
πr² = 116.18
r=6.08 inches
diameter = 2 × r= 12.16 inches
read more about circle:
https://brainly.com/question/2870743
Suppose you found a CD that pays 2.1% interest compounded monthly for 6 years. If you deposit $12,000 now, how much will you have in the account in 6 years? (Rounded to the nearest cent.) What was the interest earned? Now suppose that you would like to have $20,000 in the account in 6 years. How much would you need to deposit now?
The interest earned is the difference between the initial amount that was deposited in the bank and the amount that is in the account after six years.
[tex]\begin{gathered} A\text{ = 12000\lparen1+}\frac{2.1\%}{12})^{6*12} \\ This\text{ is from the compound interest formula.} \\ A\text{ = 13609.89} \end{gathered}[/tex]Amount in the account: $13609.89
The interest earned is therefore: 13609.89 - 12000 = $1609.89
[tex]\begin{gathered} 20000\text{ = P\lparen1+}\frac{2.1\%}{12})^6*12 \\ 17634.24\text{ = P} \end{gathered}[/tex]To earn $20000 in six years he should invest $17634.24.
1. Determine the domain and range of the quadratic function shown in the graph and represent the domainand range using inequalities.
Domain: [ -5 , 4.5 )
Range: ( -7 , 6 ]
Using inequalities:
[tex]\text{Domain: }\lbrace-5\leq x<4.5\}[/tex][tex]\text{Range: }\mleft\lbrace-7Find the slope of the line in simplest form
Answer:
[tex]\boxed{\sf \sf Slope(m)=-\cfrac{5}{4}}[/tex]
Step-by-step explanation:
To find the slope between two points we'll use the slope formula:-
[tex]\boxed{\bf \mathrm{Slope}=\cfrac{y_2-y_1}{x_2-x_1}}[/tex]
Given points:-
(-3, 1)(1, -4)[tex]\sf \left(x_1,\:y_1\right)=\left(-3,\:1\right)[/tex]
[tex]\sf \left(x_2,\:y_2\right)=\left(1,\:-4\right)[/tex]
[tex]\sf m=\cfrac{-4-1}{1-\left(-3\right)}[/tex]
[tex]\sf m=-\cfrac{5}{4}[/tex]
Therefore, the slope of the line is -5/4!
____________________
Hope this helps!
Have a great day!
find the missing side. triangle trig
Answer:
see below; round to the correct number of digits (I couldn't see this part)
Step-by-step explanation:
cos(28°) = x / 14
x = 14cos(28°) ⇒ calculator
x ≈ 12.3612663
Answer:
x ≈ 12.36
Step-by-step explanation:
using the cosine ratio in the right triangle
cos28° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{14}[/tex] ( multiply both sides by 14 )
14 × cos28° = x , that is
x≈ 12.36 ( to 2 dec. places )
Determine whether triangle DEF with vertices D(6, -6), E(39, -12), and F(24, 18) isscalene (no congruent sides), isosceles (two congruent sides), or equilateral (threecongruent sides).
We have three given points. We need to graph them, and then find the distances between them.
We need to remember that we can classify the triangles according to their sides:
1. A triangle with three congruent sides is an equilateral triangle.
2. A triangle with two congruent sides is an isosceles triangle.
3. A triangle with no congruent sides is a scalene triangle.
Additionally, we know that a segment is congruent to other when it has the same size as the other.
Then we can graph the three points as follows:
Now, we need to find the distances between the sides of the triangle using the distance formula as follows:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]This is the distance formula for points (x1, y1) and (x2, y2).
Finding the distance between points D and EThe coordinates for the two points are D(6, -6) and E(39,-12), and we can label them as follows:
• (x1, y1) = (6, -6) and (x2, y2) = (39, -12)
Then we have:
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ d=\sqrt{(39-6)^2+(-12-(-6))^2} \\ \\ d=\sqrt{(33)^2+(-12+6)^2} \\ \\ d=\sqrt{33^2+(-6)^2}=\sqrt{1089+36}=\sqrt{1125} \\ \\ d_{DE}=\sqrt{1125}\approx33.5410196625 \end{gathered}[/tex]Therefore, the distance between points D and E is √1125.
And we need to repeat the same steps to find the other distances.
Finding the distance between points E and FWe can proceed similarly as before:
The coordinates of the points are E(39, -12) and F(24, 18)
• (x1, y1) = (39, -12)
,• (x2, y2) = (24, 18)
Then we have:
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ d=\sqrt{(24-39)^2+(18-(-12))^2} \\ \\ d=\sqrt{(-15)^2+(18+12)^2}=\sqrt{(-15)^2+(30)^2}=\sqrt{225+900} \\ \\ d_{EF}=\sqrt{1125}\approx33.5410196625 \end{gathered}[/tex]Then the distance between points E and F is √1125.
Finding the distance between F and D
The coordinates of the points are F(24, 18) and D(6, -6)
• (x1, y1) = (24, 18) and (x2, y2) = (6, -6)
Then we have:
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ d=\sqrt{(6-24)^2+(-6-18)^2}=\sqrt{(-18)^2+(-24)^2}=\sqrt{324+576} \\ \\ d=\sqrt{900}=30 \\ \\ d_{FD}=30 \end{gathered}[/tex]Now, we have the following measures for each of the sides of the triangle:
[tex]\begin{gathered} \begin{equation*} d_{DE}=\sqrt{1125}\approx33.5410196625 \end{equation*} \\ \\ d_{EF}=\sqrt{1125}\approx33.5410196625 \\ \\ d_{FD}=30 \end{gathered}[/tex]Therefore, in summary, according to the results, we have two sides that are congruent (they have the same size). Therefore, the triangle DEF is an isosceles triangle.
an object is thrown down from the top of a building. A height function for the object is given by the equation h=16(8+ t ) (5 - t) where T is the number of seconds elapsed since the object was thrown and H is the height of the object above the ground ( in feet). explain how to reason about the structure of the equation to determine when the object will hit the ground
The height is a function of the time, given by the following equation:
h(t) = 16(8+t)(5-t)
The object hits the ground when h(t) = 0. So
16(8 + t)(5 - t) = 0
This means that:
8 + t = 0 or 5 - t = 0
8 + t = 0
t = -8
We cannot have negative values for t.
5 - t = 0
-t = -5 *(-1)
t = 5
The object hits the ground when t = 5, which was easy to find since the equation was already factored by it's roots.
What is the area of this trapezoid? 13 ft Enter your answer in the box. 16 ft ft2 31 ft
The area of a trapezoid is given as
[tex]A=\frac{1}{2}(a+b)h[/tex]From the given trapezoid
[tex]a=13ft,b=31ft,h=16ft[/tex]Substitute the values of a, b, and h into the equation
This gives
[tex]A=\frac{1}{2}(13+31)\times16[/tex]Calculate the value of A
[tex]\begin{gathered} A=\frac{1}{2}(44)\times16 \\ A=44\times8 \\ A=352 \end{gathered}[/tex]Therefore the area of the trapezoid is
[tex]352ft^2[/tex]Answer:
Your answer would be 352ft²
Step-by-step explanation:
I took the test and got 100%
write a part to part and a part to whole ratio for each problem situation of the 31 students surveyed 19 prefer white bread and the remaining students prefer wheat bread
Total number of students = 31
19 prefer white bread
31 - 19 prefer wheat bread ==> 31- 19 = 12 prefer wheat bread
Relations:
Part to part:
Relation between the number of students that prefer wheat bread to the number of students that prefer white bread:
Ratio: 12/19
Part to part:
Relation between the number of students that prefer white bread to the number of students that prefer white bread:
Ratio: 19/12
Part to whole:
Relation between the number of students that prefer wheat bread to the total number of students:
Ratio: 12/31
Part to whole:
Relation between the number of students that prefer white bread to the total number of students:
Ratio: 19/31
A loan of $43,000 is made at 5.25% interest, compounded annually. After how many years will the amount due reach $64,000 or more? (Use the calculator provided if necessary.)Write the smallest possible whole number answer.
Answer:
8 years
Explanation:
For a compound interest loan compounded annually, the amount due after t years is calculated using the formula:
[tex]A(t)=P(1+r)^t\text{ where }\begin{cases}P={Loan\;Amount} \\ {r=Annual\;Interest\;Rate}\end{cases}[/tex]We want to find when the amount due will reach $64,000 or more.
[tex]43000(1+0.0525)^t\geq64,000[/tex]The equation is solved for t:
[tex]\begin{gathered} \text{ Divide both sides by }43000 \\ \frac{43,000(1+0.0525)^t}{43000}\geqslant\frac{64,000}{43000} \\ (1.0525)^t\geq\frac{64}{43} \\ \text{Take the log of both sides:} \\ \log(1.0525)^t\geqslant\log(\frac{64}{43}) \\ \text{By the power law of logarithm:} \\ \implies t\operatorname{\log}(1.0525)\geq\operatorname{\log}(\frac{64}{43}) \\ \text{ Divide both sides by }\operatorname{\log}(1.0525) \\ t\geq\frac{\operatorname{\log}(\frac{64}{43})}{\operatorname{\log}(1.0525)} \\ t\geq7.77 \end{gathered}[/tex]The number of years when the amount due will reach $64,000 or more is 8 years.
Use the Factor Theorem to find all real zeros for the given polynomial function and one factor. (Enter your answers as a comma-separated list.)f(x) = 4x3 − 19x2 + 29x − 14; x − 1
Given:
The polynomial and one factor
[tex]f(x)=4x^3-19x^2+29x-14[/tex]Required:
Use the Factor Theorem to find all real zeros for the given polynomial function and one factor.
Explanation:
We have one factor, we will us that
[tex]\begin{gathered} =\frac{4x^3-19x^2+29x-14}{x-1} \\ \text{ It can be written as } \\ =(x-1)(4x^2-15x+14) \\ \text{ So, roots are} \\ =1,2,\frac{7}{4} \end{gathered}[/tex]Answer:
answered the question.
A high school has 52 players on the football team. The summary of the players weight is given in the box plot approximately what is the percentage of players weighing less than or equal to 194 pounds
Explanation
We are given the box plot below:
We are required to determine the percentage of players weighing less than or equal to 194 pounds.
We know that a box plot interprets as follows:
Therefore, we have:
[tex]Q_1=194[/tex]Also, we know that:
[tex]Q_1=\frac{1}{4}\text{ }of\text{ }100\%=25\%[/tex]Hence, the percentage of players weighing less than or equal to 194 pounds is:
[tex]\begin{equation*} 25\% \end{equation*}[/tex]Solve the systems using subsitution for 1 and 2Solve the system using elimination for question 3
3x+y=2 (a)
6x+2y= 11 (b)
Solve equation (a) for y :
3x+y = 2
y= 2-3x
Replace the y value on (b)
6x+2(2-3x) =11
6x+4-6x=11
4=11
the system has no solution.
#32 At 10am, a green car leaves a house at a rate of 60 mph. At the same time, a blue carleaves the same house at a rate of 50 mph in the opposite direction. At what time will the carsbe 330 miles apart?#3b. Two bicyclists ride in the same direction. The first bicyclist rides at a speed of 8 mph.One hour later, the second bicyclist leaves and rides at a speed of 12 mph. How long will thesecond bicyclist have traveled when they catch up to the first bicyclist?
Which of these expressions represents the product of an irrational number and a rational number being irrational?
ANSWER
Option B
EXPLANATION
We want to find which of the expressions is in the form:
Irrational number * Rational number = Irrational Number
An irrational number is a number that cannot be expressed as a ratio or fraction of two integers, such as pi or roots.
Options A and C cannot be correct because they each have two irrational numbers multiplying one another.
Simplifying Option D, we have:
[tex]\begin{gathered} 3\cdot\text{ }\sqrt[]{9} \\ \Rightarrow\text{ 3 }\cdot\text{ 3} \\ =\text{ 9 } \end{gathered}[/tex]The correct option is B, because:
[tex]\begin{gathered} \frac{1}{4}\cdot\text{ }\sqrt[]{44} \\ \frac{1}{4}\cdot\text{ }\sqrt[]{4\cdot\text{ 11}} \\ \frac{1}{4}\cdot\text{ 2 }\cdot\text{ }\sqrt[]{11} \\ \frac{1}{2}\sqrt[]{11} \end{gathered}[/tex]That is an irrational number that is a product of a rational number and an irrational number.
Therefore, the answer is Option B.
The map above is a road map of Learner County. Each centimeter on the map represents 30 miles. About how far is it from the town of Presley to Mt. Sametone on the road shown in red?A. 270 milesB. 180 milesC. 360 milesD. 390 miles
Scaling
Each centimeter on the map represents 30 miles in Learner County.
The town of Presley and Mt. Samerone are separated by a horizontal distance of 8 centimeters,
If we only consider the horizontal component of the distance, then both points are separated by 8 * 30 = 240 miles.
Since there is not an option for this number, we choose the closest, considering they are including a smaller vertical distance in the calculations, thus the answer is:
A. 270 miles
Answer:
A. 270 miles
Step-by-step explanation:
simplifyx^-1 X (y^-8 X z^5)^3------------------------------x^-4 X y^-3 X z^6
Given:
[tex]\frac{x^{-1}\left(y^{-8}z^5\right)^3}{x^{-4}y^{-3}z^6}[/tex]Simplify:
[tex]\frac{x^{-1}y^{-24}z^{15}}{x^{-4}y^{-3}z^6}[/tex]And:
[tex]x^{-1-(-4)}y^{-24-(-3)}z^{15-6}=x^3y^{-21}z^9[/tex]Re order:
[tex]\frac{x^3z^9}{y^{21}}[/tex]Answer:
[tex]\frac{x^{3}z^{9}}{y^{21}}[/tex]If tan theta = 4/3 and pi
Given that tan theta = 4/3 and theta lies in the third quadrant.
[tex]\pi<\theta<\frac{3\pi}{2}[/tex]Divide the compound inequality by 2.
[tex]\frac{\pi}{2}<\frac{\theta}{2}<\frac{3\pi}{4}[/tex]This means theta/2 lies in the second quadrant. So, cos theta/2 and sec theta/2 are negative.
Use trigonometric identities to find sec theta.
[tex]\begin{gathered} \sec \theta=\sqrt[]{1+\tan ^2\theta} \\ =\sqrt[]{1+(\frac{4}{3})^2} \\ =\sqrt[]{1+\frac{16}{9}} \\ =\sqrt[]{\frac{25}{9}} \\ =-\frac{5}{3} \end{gathered}[/tex]we know that cosine is the inverse of secant. So, cos theta = -3/5.
now, using the half-angle formula, we have to find cos theta/2,
[tex]\begin{gathered} \cos (\frac{\theta}{2})=-\sqrt[]{\frac{1+\cos x}{2}} \\ =-\sqrt[]{\frac{1-\frac{3}{5}}{2}} \\ =-\sqrt[]{\frac{\frac{2}{3}}{2}} \\ =-\sqrt[]{\frac{1}{3}} \end{gathered}[/tex]Find the GCF : (7x^2y ,x^2y^2,21x^4y^2)
The given expressions are
[tex]7x^2y,x^2y^2,21x^4y^2[/tex]We have to find the greatest common factor of the coefficients and variables.
The Greatest Common Factor between coefficients is 7 because that's the highest factor that's common.
The Greatest Common Factor between variables is
[tex]x^2y[/tex]Hence, the GCF is[tex]7x^2y[/tex]