The width of a rectangle is 3/4 its length.
[tex]w=\frac{3}{4}l[/tex]The perimeter of the rectangle is 420 ft.
Recall that the perimeter of a rectangle is given by
[tex]P=2(w+l)[/tex]Let us substitute the value of the given perimeter and the width
[tex]\begin{gathered} P=2(w+l) \\ 420=2(\frac{3}{4}l+l) \end{gathered}[/tex]Now simplify and solve for length
[tex]\begin{gathered} 420=2(\frac{3}{4}l+l) \\ 420=\frac{3}{2}l+2l \\ 420=3.5l \\ l=\frac{420}{3.5} \\ l=120\: ft \end{gathered}[/tex]Therefore, the length of the rectangle is 120 feet.
Solve for the hypotenuse and then determine the ratios below (show all work)
hypotenuse=29
[tex]\sin x=\frac{20}{29}[/tex][tex]\cos y=\frac{20}{29}[/tex]
Explanation
Step 1
a) hypotenuse
to find the hypotenuse we can use the Pythagorean theorem ,it statse that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)
so
[tex]\begin{gathered} 21^2+20^2\text{= hypotenuse}^2 \\ 441+400=\text{ hypotenuse}^2 \\ 841=\text{hypotenuse}^2 \\ taking\text{ the square root in both sides} \\ \sqrt{841}=\sqrt{(hypotenuse)^2} \\ 29=hypotenuse \end{gathered}[/tex]so
hypotenuse=29
Step 2
now, sin x
the sin of an angle is the ratio of the opposite side ( the one in front of the angel) to the hypotenuse
[tex]\sin\theta=\frac{opposite\text{ side}}{hypotenuse}[/tex]hence, replace
[tex]\sin x=\frac{20}{29}[/tex]Step 3
finally, cos of y
the cos of an angle is the ratio of the adjancent side( the side the makes the angle) to the hypotenuse
[tex]cos\theta=\frac{adjacent\text{ side}}{hypotenuse}[/tex]so,replace
[tex]\cos y=\frac{20}{29}[/tex]I hope this helps you
Ethan and Evan are twins. They each deposit $3,000 into separate bank accounts.Their accounts each accrue interest annually as shown in the tables below.
Part A.
Ethan's account can be model as a linear equation since it is increasing at a constant rate of the form:
[tex]y=240x+3000[/tex]And Evan's account can be model as a exponential equation of the form:
[tex]y=3000(1.08)^x[/tex]Part B:
Evaluate the 1st and 2nd equation for x = 5:
[tex]\begin{gathered} y=240(5)+3000=4200 \\ y=3000(1.08)^5=4407.98 \\ so\colon \\ \frac{4407.98}{4200}=1.05 \end{gathered}[/tex]It would be 1.05 higher
I inserted a picture of the question, please give a VERY SHORT explanation
To multiply two polynomials we have to multiply each term in one polynomial by each term in the other polynomial, and then add the similar terms, as follows:
Philip departed from town A with coordinates (1,6) towards town B with coordinates (7 ,6). At the same time Bruce headed from town B to town A. What are the coordinates of Point C where they will meet if the ration of Phillip's to Bruce's rates is 7:5 respectively ?
if there was no ratio they were in the middle (4,6)
but in this case we must multiply by the ratio
so
[tex]4\times\frac{7}{5}=\frac{28}{5}\approx5.6[/tex]so the C point is
[tex](5.6,6)[/tex]
Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD
15.70(d-3)=2.30
3d-15.70=2.30
15.70d-3=2.30
3(d-15.70)=2.30
Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD:
15.70(d-3)=2.30
3d - 15.70 = 2.30
15.70d-3=2.30
3(d-15.70)=2.30
used to figure for exercises two through nine period determine whether each pair of lines are parallel or perpendicular. right yes or no
2. q and v are parallel. YES
3. r and s are parallel. NO
4. r and t are parallel. NO
5. s and u are parallel. YES
6. q and s are perpendicular. NO
7. q and v are perpendicular. NO
8. r and s are perpendicular. YES
9. t and v are perpendicular. YES
what is the least common denominator for the two fractions 2 / 5 3 / 2
The multiples of the denominator of 2/5 is,
5,10,15,20,25....
The multiples of the denominator of 3/2 is,
2,4,6,8,10.....
Thus, the required least common denominator is 10.
Ashlee was born on 09/08/1981. How many eight digit codes could she make using the digits in her birthday
Ashlee could make 2520 eight digit codes using the digits in her birthday .
In the question
it is given that
the birthdate of Ashlee is 09/08/1981.
So, the number of digits are 0,0,1,1,8,8,9,9 .
number of digits = 8
So, 8 digits can be arranged in 8! ways
8! = 8*7*6*5*4*3*2*1 = 40320
Repeating digits are
0 repeated 2 times = 2! = 2
1 repeated 2 times = 2! = 2
8 repeated 2 times = 2! = 2
9 repeated 2 times = 2! =2
So, the number of 8 digits codes is = 8!/(2!*2!*2!*2!)
= 8!/(2*2*2*2)
= 40320/16
= 2520
Therefore , Ashlee could make 2520 eight digit codes using the digits in her birthday .
The given question is incomplete , the complete question is
Ashlee was born on 09/08/1981. How many eight digit codes could she make using the digits in her birthday ?
Learn more about Arrangement here
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4. A stone nudged off the Royal Gorge Bridge near Cañon City, Colorado, falls 1053 feet before hitting water. Because its speed increases as it falls, the distance ittravels each second increases. During the first second, it drops 16 feet. During the next second, it drops an additional 48 feet. During the third second, it drops another80 feet. The distances traveled each second form an arithmetic sequence:16, 48, 80,...Part 1: How far does the stone fall during the 5th second? Find and use the explicitformula.a. What is the first term of the sequence?b. What is d, the common difference?c. Write the explicit formula in function notation. Use f(n) = f(1) + (n - 1)d, wheref(1) represents the first term.d. Use the explicit formula to find the distance the stone travels in the 5th second.Part II: The table below shows the values in the sequence you already know. Use the explicit formula or the common difference to complete the table for the first 7 seconds. Time (s) 1 2 3 4 5 6 7 Distance (ft) 16 48 80 | | 144 | | | | Part ||| : Use the table from part 2 to answer the questions a. The values in the table form a(n)___ sequence and the term numbers are shownb. The term values are shown in the in the____row, and the term numbers are shown in the ___ row. c. This sequence is associated with a(n)___function d. The domain of the function is the set of time values:___
The formula for determining the nth term of an arithmetic sequence is expressed as
f(n) = f(1) + (n - 1)d
Where
f(1) represents the first term
d represents the common difference
n represents the number of terms
From the information given,
f(1) = 16
d = 48 - 16 = 80 - 48 = 32
a) The first term of the sequence is 16
b) the common difference is 32
c) The explicit is
f(n) = 16 + 32(n - 1)
d) To find the distance the stone travels in the 5th second, it means that n = 5
Thus
f(5) = 16 + 32(5 - 1)
f(5) = 16 + 32 * 4
f(5) = 144
the distance the stone travels in the 5th second is 144 feet
The probability that John recieves junk mail is 11 percent. If he receives 94 pieces of mail in a week, about how many of them can he expect to be junk mail.a. 5 b. 15 c. 10 d.20
10 (option C)
Explanation:The probability of getting a junk mail = 11%
Number of mails received = 94
Amount that will be junk mail = The probability of getting a junk mail × Number of mails received
Amount that will be junk mail = 11% × 94
= 0.11 × 94 = 10.34
Since we can't have decimal number of mails, we would approximate to the nearest whole number
10.34 to the nearest whole number is 10
Hence, 10 junk mails are expected
Riley has $955 in a savings account that earns 15% interest, compounded annually.To the nearest cent, how much interest will she earn in 2 years?
In order to calculate the interest generated in 2 years, we can use the formula below:
[tex]I=P((1+r)^t-1)[/tex]Where I is the interest generated after t years, P is the principal (initial amount) and r is the interest rate.
So, for P = 955, r = 0.15 and t = 2, we have:
[tex]\begin{gathered} I=955((1+0.15)^2-1) \\ I=955(1.15^2-1) \\ I=955(1.3225-1) \\ I=955\cdot0.3225 \\ I=307.99 \end{gathered}[/tex]Therefore the interest generated is $307.99.
...........................
Solution
We have the following:
5!= 5*4*3*2= 20*3*2= 60*2= 120
Can u guys simplify this?
(2x^-3y^5)^2*(x^7y^-11)
Select the three expressions that are equivalent to 410
Answer:
A, C, E
Step-by-step explanation:
4^10 = 1048576
A: (4^5)^2 = 1048576
C: 4^20 / 4^10 = 1048576
E: (4^2 x 4^3)^2 = 1048576
every week, Hector works 20 hours and earns $210.00. he eans a constant amount per hour. write an equation that can be used to determine the number of hours, h, Hector works given the number of weeks, w.
From the question, we're told that Hector earns $210.00 for working 2hours every week. Let's go ahead and determine
Soue se compound inequality and give your answer in intentel notation- 10 AND-80-72-1
S= (-4, 1 ]
1) Solving that compounded inequality
4x +6 > -10 and -8x+7 ≥ -1
2) Let's start by 4x +6 > -10
4x +6 > -10 Subtracting 6 from both sides
4x > -10-6
4x > -16 Dividing both sides by 4
x > -4
And with -8x+7 ≥ -1
-8x+7 ≥ -1 Subtract 7 from both sides
-8x ≥ -1 -7
-8x ≥ -8 Multiply by -1
8x ≤ 8
x ≤ 1
3) Graphing the solution interval:
So the solution is the interval S= (-4, 1 ] not including x= -4 and including the value x = 1
3x + 9 ≤ 30answer the solution
A creative writing class compiled a list of their favorite superheroes. They listed each superhero's superpower and personality flaw. Fly Read minds Forgetful 6 11 Lazy 5 7 What is the probability that a randomly selected superhero is forgetful and can fly? Simplify any fractions.
The probability is given the following formula:
Probability = Favorable / total outcomes
In this case, there number of students that selected a forgetfull sperheroe that can fly is 6, the total number of outcomes is 6 + 11 + 5 + 7 = 29, then we get:
Probability = 6 / 29
Then, the probability of selecting a forgetful superheroe that can fly is 6/29
Question 7, pre calc, include the answer in bold please. I have bad WiFi so please finish question if I get disconnected so I can see it, thanks
Given the following function
[tex]f(x)=x^4-x^3+7x^2-9x-18[/tex]We want to find its roots. Since we already know that (x + 1) and (x - 2) are factors of this polynomial, we can divide our polynomial by those factors and factorize the result to get the other roots.
Let's start by dividing by the first factor
[tex]\frac{x^4-x^3+7x^2-9x-18}{x+1}[/tex]To divide a polynomial by other, we start by dividing the leading term of the dividend by the leading term of the divisor(this will be the first term of our result)
[tex]\frac{x^4}{x}=x^3[/tex]Then, we ultiply it by the divisor
[tex]x^3(x+1)=x^4+x^3[/tex]Subtracting this result from the dividend, we have
[tex](x^4-x^3+7x^2-9x-18)-(x^4+x^3)=-2x^3+7x^2-9x-18[/tex]This means that our division is
[tex]\frac{x^4-x^3+7x^2-9x-18}{x+1}=x^3+\frac{-2x^3+7x^2-9x-18}{x+1}[/tex]Repeating the whole process of division with the second term, we have
[tex]\begin{gathered} x^3+\frac{-2x^3+7x^2-9x-18}{x+1}=x^3-2x^2+\frac{9x^2-9x-18}{x+1} \\ \Rightarrow\frac{x^4-x^3+7x^2-9x-18}{x+1}=x^3-2x^2+9x-18 \end{gathered}[/tex]From this result, we can rewrite our function as
[tex]x^4-x^3+7x^2-9x-18=(x+1)(x^3-2x^2+9x-18)[/tex]Repeating this same process with the other know factor, the other division we have to solve is
[tex]\frac{(x^3-2x^2+9x-18)}{x-2}=x^2+9[/tex]Then, our function is
[tex]f(x)=(x^4-x^3+7x^2-9x-18)=(x+1)(x-2)(x^2+9)[/tex]Then, to find the roots we need to solve the following equation
[tex](x+1)(x-2)(x^2+9)=0[/tex]Since we have a product of 3 terms, the result will be zero if and only if one of the terms is zero. This means that the roots can be found by assuming each one is zero. The solutions for this equation are the same solutions for the following system
[tex]\begin{cases}x+1=0 \\ x-2=0 \\ x^2+9=0\end{cases}\Rightarrow\begin{cases}x=-1 \\ x=2 \\ x=\pm\sqrt[]{-9}=\pm3i\end{cases}[/tex]And those are the roots for our function. x = -1, 2, +-3i.
Find the value of m and n that prove the two triangles are congruent by the HL theorem.
If both triangles are congruent by the HL theorem, then their hypotenuses are equal and at least one of the corresponding legs is equal too.
Hypothenuses:
[tex]13=4m+1[/tex]From this expression, you can calculate the value of m
[tex]\begin{gathered} 13=4m+1 \\ 13-1=4m \\ 12=4m \\ \frac{12}{4}=\frac{4m}{4} \\ 3=m \end{gathered}[/tex]Legs:
[tex]2m+n=8m-2n[/tex]Replace the expression with the calculated value of m
[tex]\begin{gathered} 2\cdot3+n=8\cdot3-2n \\ 6+n=24-2n \end{gathered}[/tex]Now pass the n-related term to the left side of the equation and the numbers to the right side:
[tex]\begin{gathered} 6-6+n=24-6-2n \\ n=18-2n \\ n+2n=18-2n+2n \\ 3n=18 \end{gathered}[/tex]And divide both sides of the expression by 3
[tex]\begin{gathered} \frac{3n}{3}=\frac{18}{3} \\ n=6 \end{gathered}[/tex]So, for m=3 and n=6 the triangles are congruent by HL
Which of the following is a factor of the polynomial Step By Step Explanation Please
Use the quadratic formula.
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where a = 3, b = -31, and c = -60.
[tex]x=\frac{-(-31)\pm\sqrt[]{(-31)^2-4(3)(-60)}}{2(3)}[/tex]Solve to find both solutions.
[tex]x=\frac{31\pm\sqrt[]{961+720}}{6}=\frac{31\pm\sqrt[]{1681}}{6}=\frac{31\pm41}{6}[/tex]Rewrite the expression as two.
[tex]\begin{gathered} x_1=\frac{31+41}{6}=\frac{72}{6}=12 \\ x_2=\frac{31-41}{6}=\frac{-10}{6}=-\frac{5}{3} \end{gathered}[/tex]Once we have the solutions, we express them as factors. To do that, we have to move the constant to the right side of each equation.
[tex]\begin{gathered} x=12\to(x-12) \\ x=-\frac{5}{3}\to(3x+5)_{} \end{gathered}[/tex]As can observe, the factor of the polynomial is (x-12).
Therefore, the answer is d.What are the first two steps to graph y=4/5x + 3?
The function y=4/5x + 3 represents a linear equation.
Let's find some points.
Where x=1, then:
[tex]y=\frac{4}{5}x+3[/tex][tex]y=\frac{4}{5}(1)+3[/tex][tex]y=\frac{19}{5}[/tex]We find the point (1,19/5).
Where 19/5 = 3.8
Now, lest find the x-intercept and y-intercept.
To find the x-intercept, set y=0
[tex]0=\frac{4}{5}x+3[/tex]Solve for x:
[tex]-3=\frac{4}{5}x[/tex][tex]5\cdot-3=4x[/tex][tex]-15=4x[/tex]where
[tex]x=-\frac{15}{4}=-3.75[/tex]So, the x-intercept is the point (-15/4, 0)
To find the y-intercept, set x=0. Then:
[tex]y=\frac{4}{5}x+3[/tex][tex]y=\frac{4}{5}(0)+3[/tex][tex]y=3[/tex]So, the y-intercept is the point (0,3)
Use this information to graph the line.
Hence, the graph for y=4/5x + 3 is given by:
Find the average rate of change of the following function from t = 1 to t=2.5h(t) = 148 – 16t
The average rate of change of the function from t=1 to t=2.5 is given by:
[tex]\frac{h(2.5)-h(1)}{2.5-1}=\frac{h(2.5)-h(1)}{1.5}[/tex]It is given that:
[tex]\begin{gathered} h(t)=148-16t \\ h(2.5)=148-16\times2.5=108 \\ h(1)=148-6=142 \end{gathered}[/tex]Substitute the values to get:
[tex]\frac{h(2.5)-h(1)}{1.5}=\frac{108-142}{1.5}=\frac{-68}{3}\approx-22.6667[/tex]Hence the rate of change is -22.6667.
A circle has a circumference of 10 inches. Find its approximate radius, diameter and area
Answer:
Radius = 1.59 in
Diameter = 3.18 in
Area = 7.94 in²
Explanation:
The circumference of a circle can be calculated as:
[tex]C=2\pi r[/tex]Where r is the radius of the circle and π is approximately 3.14. So, replacing C by 10 in and solving for r, we get:
[tex]\begin{gathered} 10\text{ in = 2}\pi r \\ \frac{10\text{ in}}{2\pi}=\frac{2\pi r}{2\pi} \\ 1.59\text{ in = r} \end{gathered}[/tex]Then, the radius is 1.59 in.
Now, the diameter is twice the radius, so the diameter is equal to:
Diameter = 2 x r = 2 x 1.59 in = 3.18 in
On the other hand, the area can be calculated as:
[tex]A=\pi\cdot r^2[/tex]So, replacing r = 1.59 in, we get:
[tex]\begin{gathered} A=3.14\times(1.59)^2 \\ A=3.14\times2.53 \\ A=7.94in^2 \end{gathered}[/tex]Therefore, the answer are:
Radius = 1.59 in
Diameter = 3.18 in
Area = 7.94 in²
20% of blank = 100 I suck at math
Answer:
20% means divide by 5 so 100 * 5 = 500
Step-by-step explanation:
because 20% of 500 is 100
Hello!
Original Question: 20% of blank = 100
⇒ 20% = [tex]\dfrac{20}{100} =0.2[/tex]
⇒ 0.2 of blank ⇒ 0.2 * blank = 100
Let's solve:
[tex]0.2 *\text{blank}=100\\\\blank = \dfrac{100}{0.2} = 500[/tex]
Thus blank is 500!
Answer: 500
Hope that helps!
9 - 6 - 19 c) y - 12 OC p = b) y 24 c) = 9
x=70, y= -50 and x=80
1) Let's solve each equation, plugging in the given value for x
y=5x -300
a) y=50
y=5x -300 Plug y=50
50=5x -300 Add 300 to both sides
50+300=5x
350 = 5x Divide both sides by 5
x=70
b) x = 50
y=5x -300 Plug x=50
y=5(50) -300 Distribute the factor
y= 250 -300
y= -50
c) y=100
y=5x -300 Plug y=100
100 = 5x -300 Add 300 to both sides
400 = 5x
x =80
Hence, the answer is
x=70, y= -50 and x=80
Today's high temperature is 72°F. If yesterday's high temperature was 87"F, what was the change in high temperatures?
To find the change in temperature we have to do a subtraction:
Highest temperature-lowest temperature-
87-72= 15F
The change in high temperatures was 15 F .
What is the area of the figure? Please if you don’t understand ask me to move onto the next tutor as many people have gotten these questions wrong thank you and please double check and take your time!
Determine the area of the figure.
[tex]\begin{gathered} A=3\cdot8+12\cdot9+\frac{1}{2}\cdot4\cdot6 \\ =24+108+12 \\ =144 \end{gathered}[/tex]So answer is 144 yards square.
Use the fact that 521•73=38, 033.Enter the exact product of 5.21•7.3
Answer: 38.033
5.21 x 7.3
= 38.033
ill take a pic of it
The line passes through the points given.
Select any two points from the table, (-4,2) and (-3,5).
The slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Hence the slope is:
[tex]\begin{gathered} m=\frac{5-2}{-3-(-4)} \\ m=\frac{3}{1} \\ m=3 \end{gathered}[/tex]The slope is 3.
