Seattle, wa and san francisco, ca lie on the same longitudinal line. san francisco is at 38° latitude and seattle is at 47° latitude. if the earth is a sphere of radius 4000 miles, use arc length to find the distance between the cities. [use π = 3.14, and round to the nearest mile.]
Answers
Step 1.
Calculate measure of angle α:
[tex]47^o-38^o=9^o[/tex]
Step 2.
Calculate what fraction of the angle 360° is the angle α:
[tex]\dfrac{9^o}{360^o}=\dfrac{1}{40}[/tex]
Step 3.
Calculate the circumference of the Earth (circle):
[tex]C=2\pi r\to C=2\pi\cdot4000=8000\pi\ mi[/tex]
Step 4.
The length of arc is equal 1/40 of the circumference:
[tex]\dfrac{1}{40}C=\dfrac{1}{40}\cdot8000\pi=200\pi\ mi[/tex]
[tex]\pi\approx3.14\to\dfrac{1}{40}C\approx200\cdot3.14=628\ mi[/tex]
Answer: A) 628 miles
The distance between Seattle, WA, and San Francisco, CA, calculated using their latitudinal difference on a sphere with a radius of 4000 miles, is approximately 628 miles.
The question is asking for the distance between Seattle, WA and San Francisco, CA based on their respective latitudes and assuming they are on the same longitudinal line. To find the arc length and thus the distance between the two cities, you can use the formula for arc length on a sphere: [tex]\(Arc \ length = (\Delta Latitude \times \pi/180) \times \ Radius \ of\ Earth\)[/tex]. Here, [tex](\Delta Latitude\)[/tex] is the difference in latitude between the cities, which is [tex]\(47^\circ - 38^\circ = 9^\circ\)[/tex]. The radius of Earth is given as 4000 miles. Plugging these values into the formula, you get:
[tex]\(Arc \ length = (9 \times \pi/180) \times 4000\)[/tex]
[tex]\(Arc \ length = (9 \times 3.14/180) \times 4000\)\\\(Arc \ length = (0.157) \times 4000\)\\\(Arc \ length = 628 \ miles\)[/tex]
Therefore, the distance between Seattle and San Francisco, based on latitude and assuming they are directly north and south of each other, is approximately 628 miles.
Related Questions
In parallelogram ABCD , diagonals AC ? ? ? ? ? and BD ? ? ? ? ? intersect at point E, AE= x 2 ?16 , and CE=6x . What is AC ? Enter your answer in the box.
Answers
Answer:
Length of AC = 48 units.
Step-by-step explanation:
Given in parallelogram ABCD , diagonals AC and B intersects at a point E.
Length of AE = [tex]x^2-16[/tex] units and CE = 6x.
We have to find the length of AC.
According to the property of parallelogram:
Diagonals are intersecting each other at their midpoint.
Since, E is the midpoint AC ;
so, AE = CE
[tex]x^2-16[/tex] =6x
or we can write this as;
[tex]x^2-6x-16[/tex]=0
[tex]x^2-8x+2x-16[/tex]=0
[tex]x(x-8)+2(x-8)[/tex]=0
[tex](x-8)(x+2)[/tex] = 0
Zero product property states that if ab = 0 , then either a=0 or b =0.
By zero product property, we have;
(x-8) = 0 and (x+2) = 0
x = 8 and x = -2
Since, length x cannot be negative so we ignore x = -2.
then;
x = 8
AC = [tex]x^2-16[/tex] = [tex]8^2 -16 = 64- 16 =48[/tex] units.
Therefore, the length of AC = 48 units.
Answer:
I just took the test and got the answer AC=96.
Kelly buys a sweater for $16.79 and a pair of pants for $28.49. She pays with a $50 dollar bill. How much change should kelly get in return?
Answers
To get this answer, start by adding 16.79 and 28.49. The answer you should get is 45.28. Next, subtract 45.28 from 50 and your total should be 6.72. Hope this helped!
A parabola has x-int of (-8,0) and (4,0) and a minimum value of -9 in intercept form
Answers
Answer:
The function is 1/4x^2 + x - 8
Step-by-step explanation:
In Factor form the function is
a(x + 8)(x - 4) where a is a constant to be found.
= a( x^2 + 4x - 32) Note the coefficient of x is positive because the function has a minimum value.
The line of symmetry is x = (-8+4)/2 = -2.
So the minimum value will be the value of f(x) when x = -2, so we have the equation
a(-2+8)(-2-4) = -9
-36a = -9
a = 1/4.
Sweet t saved 20% of the total cost of the green-eyed fleas new album let three be fleas on the earth .If the regular price is $30 how much did sweet t save?
Answers
Answer:
$6 Sweet t saved on green-eyed fleas new album .
Step-by-step explanation:
As given
Sweet t saved 20% of the total cost of the green-eyed fleas new album .
.If the regular price is $30.
20% is written in the decimal form.
[tex]= \frac{20}{100}[/tex]
= 0.20
Thus
Sweet t saved on green-eyed fleas new album = 0.20 × 30
= $6
Therefore $6 Sweet t saved on green-eyed fleas new album .
Jayla buys and sells vintage clothing. She bought 2 blouses for $25 each and later sold them for $38 each. She bought 3 skirts for $15 each and later sold them for $26 each. She bought 5 pairs of pants for $30 each and later sold them for $65 each. Jayla's expenses for purchasing each items were: Her revenue: Total profit:
Answers
Answer:
Expenses for purchasing is $245 ,Revenue $479 and Total profit $ 234
Step-by-step explanation:
Cost of two blouses = 2× 25 = $50
Revenue from blouses = 2× 38 = $76
Profit of blouses = 76- 50 = $26
Similarly cost of 3 skirts = 3×15 = $45
Revenue from Skirts = 3×26 =$78
Profit from skirts = 78-45 =$33
Now cost price of pants = 5×30 =$150
Revenue from Pants = 5×65 =$325
Profit from pants = 325-150 = $175
So Jayla's expenses for purchasing = 50+45+150
= $245
Revenue = 76+78+325
= $479
Total Profit = 479 -245
= $234
Jayla's total expenses were $245, she made $479 in revenue through sales, making her resultant profit $234. This is calculated by subtracting the total expenses from the total revenue.
Explanation:The subject of this problem deals with the concepts of expenses, revenues, and profit in a small business setting. Jayla spent $50 on the blouses (2 x $25), $45 on the skirts (3 x $15), and $150 on the pants (5 x $30), adding up to a total expense of $245. She sold these items for total revenues of $76 for the blouses (2 x $38), $78 for the skirts (3 x $26), and $325 for the pants (5 x $65), giving her a total revenue of $479. The total profit can be calculated by subtracting the total expenses from the total revenue, and therefore, Jayla made a profit of $234 ($479 - $245).
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The function h=-16t^2 +1700 gives you the height h, of an object in feet, at t seconds. How long will it take the object to hit the ground ?Round to the nearest hundresth of a second?
Answers
Answer:
The object will hit the ground after 10.308 seconds.
Step-by-step explanation:
h(t) = -16t² + 1700
If you graphed this function, the object would be shown hitting the ground when it crosses the x-axis, in other words, when h = 0. So, to find the answer, just set h(t) equal to 0 and solve.
-16t² + 1700 = 0 Plug this into a calculator if you have one.
t = -10.308 and t = 10.308
Since time can't be negative, your answer will be the positive value, 10.308.
The object, described by the equation h(t) = -16t^2 + 1700, will hit the ground after around 10.308 seconds. This is determined by setting h(t) to 0, yielding a valid, positive solution.
The provided equation h(t) = -16t^2 + 1700 describes the height (h) of an object as a function of time (t), taking into account gravitational acceleration. To determine when the object hits the ground, set h(t) to 0 and solve for t:
-16t^2 + 1700 = 0
Solving this equation using the quadratic formula or factoring yields two solutions: t = -10.308 and t = 10.308. However, time cannot be negative in this context, so the only valid solution is t = 10.308.
Consequently, the object will hit the ground after approximately 10.308 seconds. This conclusion is reached by identifying the point where the height function intersects the x-axis, representing ground level. The positive value for t ensures a meaningful interpretation in the temporal context, indicating the time elapsed until the object reaches the ground.
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3) Julian's shadow is 6 feet long. At the same time a 31 foot tall building casts a shadow that is 28 feet long. What proportion could be used to find Julian's
Answers
You are given the height of the building and the length of the shadow the building gives, so you can set that up as a proportion of Height of building over the length of the shadow so 31/28.
Now you can set the same proportion for Julian, using X for her height, so you would have x/6.
To solve for her height, set the two proportions equal and solve for x:
31/28 = x/6
Cross multiply:
31 * 6 = 28 *x
186 = 28x
Divide both sides by 28:
x = 186 / 28
x = 6.64 feet tall
To find Julian's height using the proportion between the building's height and shadow length and Julian's shadow length, we set up a proportion as follows: 31 feet (building height) / 28 feet (building's shadow) = Julian's height / 6 feet (Julian's shadow). Solving for Julian's height, we determine it is approximately 6.64 feet.
The question pertains to similar triangles and proportionality in shadows cast by objects. Using the concept of similar triangles, we can set up a proportion to find Julian's height. The shadows and the objects (Julian and the building) form two sets of similar triangles because the angles of the sunshine are the same for both objects, and thus their corresponding sides are proportional.
To set up the proportion, we use the building's shadow and height relation and compare it to Julian's shadow and unknown height. So, we write:
Building's height / Building's shadow length = Julian's height / Julian's shadow length
31 feet / 28 feet = Julian's height / 6 feet
To generate an accurate answer, we solve for Julian's height as follows:
Julian's height = (31 feet / 28 feet) \ 6 feet = (31 / 28) \ 6
Julian's height = 6.64 feet (approximately)
This proportional relationship can be used to find unknown heights or lengths of shadows when a reference object is used, provided the angle of light is the same.
Will all problems adding positive radicals have a rational solution?
Answers
Answer:
No
Step-by-step explanation:
Let us consider two positive radicals first,
[tex]\sqrt{3} , \sqrt{5}[/tex]
We know that [tex]\sqrt{3}[/tex] is an irrational number and [tex]\sqrt{5}[/tex] is also an irrational number.
So the sum of two positive radicals does not always have a rational solution.
There are examples when the some of adding positive radicals can get us a rational solution. For example,
[tex]\sqrt{4}+\sqrt{4} =4[/tex]
So if the radicand is a perfect square then the solution is rational.
You are in charge of buying the hamburgers and chicken for a party. The hamburgers cost $2 per pound and the chicken is $3 per pound, You have $60 to spend.
Answers
You can buy 15 hamburgers, and 10 chickens if you spend $30 on each.
$30 divided by $2 = 15 Hamburgers
$30 divides by $3 = 10 Chickens
30 + 30 = 60
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Alison and Justins father donated $3 every lap they swam in a swim-a-thon.Alison swam 21 laps and justin swam 15 laps.Use the distributive property tp find out the amount of money their father donated/
Answers
Answer:
The total amount of money Alison and Justins father donated be $108 .
Step-by-step explanation:
Distributive property.
Let a, b and c be any real numbers.
Thus
a.( b + c ) = a.b + a.c
This is distributive property.
As given
Alison and Justins father donated $3 every lap they swam in a swim-a-thon.
Alison swam 21 laps and justin swam 15 laps.
Total amount of money Alison and Justins father donated = Cost of each lap (Number of laps of Alison father + Number of laps of Justins father )
As
Cost of each lap = $3
Number of laps of Alison father = 21 laps
Number of laps of Justins father = 15 laps
Putting in the above
Total amount of money Alison and Justins father donated = 3(21 + 15)
= 3 × 21 + 3 × 15
= 63 + 45
= $ 108
Therefore the total amount of money Alison and Justins father donated be $108 .
By which rule are these triangles congruent?
A) AAS
B) ASA
C) SAS
D) SSS
Answers
Answer:
Option B is correct.
By ASA rule are these triangles are congruent
Step-by-step explanation:
In triangle JMK and triangle JMN
[tex]\angle KJM \cong \angle NJK[/tex] [Angle] [Given]
[tex]JM \cong JM[/tex] [Common Side]
[tex]\angle JMK \cong \angle JMN [/tex] [Angle]
ASA(Angle-Side-Angle) theorem states that if two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then these triangles are congruent.
then, by ASA theorem;
[tex]\triangle JMK \cong \triangle JMN[/tex]
Therefore, by ASA rule are these triangles are congruent.
The rules AAS, ASA, SAS, SSS are a set of criteria that can determine if two triangles are congruent. They need accurate measurements of angles and sides of the triangles to be applied. Without these specifics, it's hard to identify which rule applies.
Explanation:In order to answer which rule makes the triangles congruent, we would need more specific information about these triangles, such as the measures of their angles and sides. However, let me explain what each of these rules represents:
AAS (Angle-Angle-Side): Two triangles are congruent if two pairs of corresponding angles and a non-included side are congruent.ASA (Angle-Side-Angle): If two pairs of corresponding angles and the included side are congruent, the triangles are congruent.SAS (Side-Angle-Side): Two triangles are congruent if two pairs of corresponding sides and the included angle are congruent.SSS (Side-Side-Side): If all three pairs of corresponding sides in two triangles are congruent, the triangles are congruent.Without specific information about your triangles, it's difficult to conclusively establish which rule applies.
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A spinner divided into four equal parts, A, B, C, and D, is spun, then is followed by a roll of a standard six-sided die.
1. How many total outcomes are possible?
2. How many outcomes have an ‘A’ and an odd number?
3. What is the probability of getting an ‘A’? Getting an odd number? Getting an ‘A’ and an odd number?
P(A)= P(odd)= P(A and odd)=
4. What is the probability of getting an odd number, given an ‘A’ has already been spun?
P(odd│A)=
5. Since P(odd│A)=P(odd), are the events independent or not independent?
6. What is the probability of getting an ‘A’ or an odd number?
P(A or odd)=
Answers
Answer:
1. 24 outcomes
2. 3
3. A= 1/4
Odd = 1/2 (reduced from 12/24 chances)
A/Odd = 1/8
4. 50% the letter chosen doesn't affect the outcome of the roll of the dice
5. i believe they are independent
6. 1/8
Hope that helps!
Answer:
3/4
Step-by-step explanation:
Which of the following is a trinomial with a constant term?
A. x3 + 12x2 + x
B. y - 426
C. -x + 42
D. x + 7y + 6
E. x7 - 6
F. y13
Answers
Choice A is a trinomial, but it doesn't have a constant term
Choice D is the only other trinomial. This has a constant term, which is 6. The constant is the term without any variables attached to it.
Answer: Choice D
Answer: D. [tex]x+7y+6[/tex]
Step-by-step explanation:
We know that a trinomial is a polynomial with three terms.
From all the given options, only option A. [tex]x^3+12x^2+x[/tex] and option D. [tex]x+7y+6[/tex] are trinomials having three terms .
But option A [tex]x^3+12x^2+x[/tex] does not have any constant term .
On the other hand option D. [tex]x+7y+6[/tex] has a constant term of 6.
Therefore, the option D. [tex]x+7y+6[/tex] represents a trinomial with a constant term.
Justin's rice ball recipe uses 100100 grams of rice to make 11 rice ball. Justin has 700700 grams of rice. How many rice balls can Justin make with 700700 grams of rice?
Answers
Tiffany used to live 15 kilometers away from the school, but after she moved she now lives 9.9 kilometers away. She is _____ percent closer to the school.
Answers
Answer:
Tiffany is 34% closer to the school.
Step-by-step explanation:
Given the statement: Tiffany used to live 15 kilometers away from the school, but after she moved she now lives 9.9 kilometers away.
She lived away from the school = 15 km
as, she moved 9.9 km away.
Now, the distance closer to school from where she lived = 15 -9.9 = 5.1 km
To, find how much percent she is closer to school.
Percent states that a number or ratio expressed as a fraction of 100.
[tex]percent = \frac{5.1}{15} \times 100[/tex] = [tex]\frac{51 \times 100}{150} = \frac{51 \times 10}{15}[/tex]
Simplify:
percent closer to school = 34%
Therefore, she is 34% closer to the school.
Which expression is equivalent to the given expression after using the distributive property? 9(x+3)+15x
Answers
The correct answer is option a.[tex]\(9 \cdot x + 9 \cdot 3 + 15x\)[/tex].
The correct option is (a).
To use the distributive property to simplify the expression (9(x+3) + 15x), we need to distribute the terms outside the parentheses to each term inside the parentheses.
The given expression is [tex]\(9(x+3) + 15x\)[/tex].
1. Distribute 9 to (x) and (3):
[tex]\[ 9(x+3) = 9 \times x + 9 \times 3 \][/tex]
2. Distribute 15 to (x):
[tex]\[ 15x \][/tex]
So, after using the distributive property, the expression becomes:
[tex]\[ 9 \cdot x + 9 \cdot 3 + 15x \][/tex]
Now, let's compare this with the options:
a. [tex]\(9 \cdot x + 9 \cdot 3 + 15x\)[/tex] - This matches our result.
b. [tex]\(9(x+3+15)x\)[/tex] - This option seems incorrect as it doesn't distribute 9 to each term inside the parentheses correctly.
c. [tex]\(9:x+3+15x\)[/tex] - This option doesn't seem to use the distributive property correctly.
d. [tex]\(9x+9 \cdot 3+9 \cdot 15x\)[/tex] - This option distributes 9 correctly but includes an extra term (9x) that doesn't appear in the original expression.
Therefore, the correct answer is option a.[tex]\(9 \cdot x + 9 \cdot 3 + 15x\)[/tex].
Which expression is equivalent to the given expression after using the distributive property? 9(x+3)+15x
a.9· x+9· 3+15x
b.9(x+3+15)x
c.9: x+3+15x
d.9 x+9· 3+9· 15x
Answer:
24x + 15
Step-by-step explanation:
9(x+3)+15x
Use the distributive property.
9*x +9*3 + 15x
9x + 15 + 15x
Combine the like terms.
24x + 15
Samuel is 10 years old. He mowed the neighbors lawn on Saturday and earned $40. It took him 4 hours to mow the lawn and 2 hours to clean his room. How much money did Samuel earn an hour?
Answers
Answer:
He got paid 10$ an hour. It does not say he gets paid for cleaning his room.
Step-by-step explanation:
10 x 4 = 40$
Samuel earned $6.67 per hour.
Explanation:To calculate how much money Samuel earned per hour, we need to find the total number of hours he spent both mowing the lawn and cleaning his room.
Samuel spent 4 hours mowing the lawn and 2 hours cleaning his room, for a total of 6 hours.
He earned $40 for this time period.
To find how much he earned per hour, we divide the total amount earned by the total number of hours:
$40 divided by 6 hours = $6.67 per hour.
Therefore, Samuel earned $6.67 per hour.
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Please Help!! Urgent ( Zoom in to see it better)
Answers
1. You are trying to isolate "F" in the equation
[tex]C=\frac{5}{9}(F-32)[/tex] Multiply 9/5 on both sides
[tex](\frac{9}{5})C=(\frac{9}{5}) \frac{5}{9} (F-32)[/tex]
[tex]\frac{9}{5}C=F-32[/tex] Add 32 on both sides
[tex]\frac{9}{5}C+32=F-32+32[/tex]
[tex]\frac{9}{5}C+32=F[/tex]
THIS IS WRONG
2. You are trying to isolate "y" in the equation
[tex]m=\frac{x+y+z}{3}[/tex] Multiply 3 on both sides
3m = x + y + z Subtract x and z on both sides
3m - x - z = y
THIS IS CORRECT
3. Isolate "r"
[tex]s=\frac{r}{r-1}[/tex] Multiply (r - 1) on both sides
s(r - 1) = r Distribute s into (r - 1)
sr - s = r Subtract sr on both sides
-s = r - sr Factor out r from (r - sr)
-s = r(1 - s) Divide (1 - s) on both sides
[tex]\frac{-s}{1-s}=r[/tex]
THIS IS WRONG
4. Isolate "b"
[tex]A=\frac{1}{2}(a+b)[/tex] Multiply 2 on both sides
2A = a + b Subtract a on both sides
2A - a = b
THIS IS CORRECT
5. Isolate "y"
[tex]m=\frac{x+y}{2}[/tex] Multiply 2 on both sides
2m = x + y Subtract x on both sides
2m - x = y
THIS IS WRONG
The 2nd and 4th one is right
Answer:
. You are trying to isolate "F" in the equation
Multiply 9/5 on both sides
Add 32 on both sides
THIS IS WRONG
2. You are trying to isolate "y" in the equation
Multiply 3 on both sides
3m = x + y + z Subtract x and z on both sides
3m - x - z = y
THIS IS CORRECT
3. Isolate "r"
Multiply (r - 1) on both sides
s(r - 1) = r Distribute s into (r - 1)
sr - s = r Subtract sr on both sides
-s = r - sr Factor out r from (r - sr)
-s = r(1 - s) Divide (1 - s) on both sides
THIS IS WRONG
4. Isolate "b"
Multiply 2 on both sides
2A = a + b Subtract a on both sides
2A - a = b
THIS IS CORRECT
5. Isolate "y"
Multiply 2 on both sides
2m = x + y Subtract x on both sides
2m - x = y
THIS IS WRONG
The 2nd and 4th one is right
Step-by-step explanation:
A large farm has 75 acres of wheat and 62.5 acres with a new job . The farm crew can harvest the wheat from 12 acres and the corn from 10 acres per day. In how many days will all the fields be harvested
Answers
Answer:
All the fields will be harvested in 6.25 days
Step-by-step explanation:
because 75 ÷ 12 and 62.5 ÷ 12 is 6.25
PLEASE HELP A store has sales of $500 in their first month. If sales increase at a rate of $10 each month, they can be modeled by this equation:an=500+(k-1)10 Use summation notation to model and evaluate the sales for the first ten years. Explain your steps.
Answers
Answer: 131,400$
Step-by-step explanation:
The sale for first month is $500.
The sale increases by $10 each month, as modelled by the equation:
a_k=500+(k-1)10
where, k = 1 (first month)
k = 2 (second month)
.... and so on.
we have to calculate the sale for the first 10 years, that means for 10*12 = 120 months (1 year = 12 months)
Total sales = ∑ a_k
∑ a_k = ∑ (500+(k-1)10)
= 500k + ∑ (10k - 10)
= 500k + 10∑k - 10k
= 490k + 10∑k
= 490k + 10 {k*(k+1)/2}
= 490k + 5{k*(k+1)}
= 490k + 5k^2 + 5k
= 5k^2 + 495k
∴∑ a_k = 5k^2 + 495k
For calculating the total sales of 10 years, we will put the value of k = 120 (120th month after the first month)
= 5*(120*120) + 495*120
= 72,000 + 59, 400
= 131,400$
Answer:
Distribute 10 to (k – 1) and simplify.
Rewrite the summation as the sum of two individual summations.
Evaluate each summation using properties or formulas from the lesson.
The lower index is 1, so any properties can be used. The upper index is 10*12=120.
The values of the summations are 58,800 + 72,600. So, the total sales is $131,400.
Step-by-step explanation:
Nala is escaping from the dragon's lair! She is running toward the entrance of the lair at a speed of 9.29.2 meters per second. The entrance is 180180 meters away. The distance dd between Nala and the entrance of the lair is a function of tt, the time in seconds since Nala began running. Write the function's formula.
Answers
Answer: Our function will be
[tex]d=180-9.2t[/tex]
Step-by-step explanation:
Since we have given that
Distance of the entrance = 180 meters
Speed of Nala who is running towards the entrance of the lair = 9.2
As we know the "Distance-Speed formula":
[tex]Time=\frac{Distance}{Speed}\\\\t=\frac{180}{9.2}\\\\t=19.565\\\\t=19.57\ seconds[/tex]
So, our required function will be
[tex]d=180-9.2t[/tex]
As we increase the time distance get reduced from 180 which is the distance of the entrance .
Hence, our function will be
[tex]d=180-9.2t[/tex]
Given that pentagon, ABCDE pentagon FGHIJ find the measure of <1
a. 99
b. 100
c. 121
d. cant be determined
Answers
The measure of the angle 1 cannot be determined
How to find the measure of the angle 1From the question, we have the following parameters that can be used in our computation:
The pentagons ABCDE and FGHIJ
Given that pentagon ABCDE ≅ pentagon FGHIJ
We can see that there is no occurrence of the angle 1 in both figure
This means that the measure of the angle 1 cannot be determined
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PLEASE HELPPPPPPPPPP!!!!!!!!!
Answers
Answer:
11a^2b^8
Step-by-step explanation:
Rule 1: The coefficient (121 in this case) has it's square root taken to derive the side.
Rule 2: If a variable with a power is part of the area of a square, then just divide the power by two
The square root of 121 = 11
The square root of a^4 = a^(4/2) = a^2
The square root of b^16 = b^(16/2) = b^8
I need help ASAP PLEASE SOMEONE 100 POINTS IF CORRECT
Answers
Answer:
Step-by-step explanation:
84-90=90-96=96-102=102-108=-6
its a sequence where A(1)=84 n A(n+1)-A(n)=6
A(n)=84+(n-1)*6; n=1,2,3,4,5
Answer:
f(x) = 84 + 6x where x=0, 1, 2, 3, 4, ...
Step-by-step explanation:
Given 84, 90, 96, 102, 108, ...
the numbers are a sequence with 84 as the initial value and in increment of 6s. So the function can be written as:
f(x) = 84 + 6x where x=0, 1, 2, 3, 4, ...
Jack can run a mile in 9, 1/3 minutes. How long will it take for him to run 3, 1/2 miles? What is the answer
Answers
Answer:
32, 2/3 minutes.
Step-by-step explanation:
Divide the original mile time by two to get what half a mile would be. Multiply the original mile time by 3, since he is running 3 miles. Add 4 and 2/3, half of a mile time, to that and you're left with 32 minutes and 40 seconds.
the perimeter of a rectangle of a rectangular field is 76 ft. The length is 12 ft longer than the width. Find the fields dimensions
Answers
Answer:
The length is 25 and the width is 13. (25,13)
Step-by-step explanation:
the formula for perimeter is l+l+w+w=76 or 2l+2w=76
and since we know that the length is 12 more than the width, we can create an equation. w+12=l (-l+w=-12)
solve with elimination method:
2l+2w=76
2(-l+w=-12)
2l+2w=76
-2l+2w=-24
4w=52
w=13
Now that we know w=13, add 12 to the width and you get your width (25)
You can check this with the formula 2l+2w=76
2(25)+2(13)=76
50+26=76
and
w+12=l
13+12=25
Hope this helps!
The dimensions of the field will be 13 ft and 25ft.
The perimeter of a rectangle is given as: = 2l + 2w
Length = w + 12Width = wTherefore, the perimeter will be:
2(w + 12) + 2w = 76
2w + 24 + 2w = 76
4w = 76 - 24.
4w = 52
w = 52/4.
w = 13
Width = 13 ft
Length will be: = w + 12 = 13 + 12 = 25
Therefore, the dimensions of the field will be 13 ft and 25ft.
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PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
Subract and simplify.
Answers
Answer: C
Step-by-step explanation:
[tex]\dfrac{x+1}{x-5} - \dfrac{x-2}{x+3}[/tex]
= [tex]\dfrac{x+1}{x-5}(\dfrac{x+3}{x+3}) - \dfrac{x-2}{x+3}(\dfrac{x-5}{x-5})[/tex]
= [tex]\dfrac{x^{2}+4x+3}{(x-5)(x+3)} - \dfrac{x^{2}-7x+10}{(x-5)(x+3)}[/tex]
= [tex]\dfrac{x^{2}+4x+3-(x^{2}-7x+10)}{(x-5)(x+3)}[/tex]
= [tex]\dfrac{11x-7}{(x-5)(x+3)}[/tex]
Determine whether the polynomial is a difference of squares and if it is, factor it.
y2 – 225
is a difference of squares: (y – 15)(y + 15)
is a difference of squares: (y – 15)2
is not a difference of squares
is a difference of squares: (y + 15)2
Answers
Answer:
The correct answer option is: it is a difference of squares: (y – 15)(y + 15)
Step-by-step explanation:
We are given a polynomial and we are to determine if it is a difference of squares.
Let us recall the algebraic formulas which include:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
[tex](a-b)^2=a^2-2ab+b^2[/tex]
[tex](a+b)(a-b)=a^2-b^2[/tex]
So if we look closely, we can conclude that the given polynomial observes the third formula of the perfect squares.
Hence, we can say that it is a difference of squares: (y – 15)(y + 15)
[tex]y^2-225 = (y-15)(y+15)[/tex]
Use your knowledge of insulators and conductors to explain why
cooking pots are usually made of metal with some sort of plastic
handle
Answers
Cooking pots are made of metal because metals are good conductors of heat. Plastic is an insulator that is slow at conducting heat. That is why an insulator is used so that we don't burn ourselves.
The cooking pots are good conductor of electricity and sort of plastic
handle are insulator for safety purpose.
Conductors are materials that permit electrons to flow freely from particle to particle. Conductors allow for charge transfer through the free movement of electrons. Conductors are good conduction of electricity.Insulators are materials that does not allow the free flow of electrons from atom to atom and molecule to molecule.Insulator are bad conductor of electricity.Learn more:
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Answers
Answer:
B.) 72
Step-by-step explanation:
Because when there is one cup there are 8 fluid ounces, when there are 9 cups there are 9 times more fluid ounces.
Hello :3
To get your answer we would need to multiply.
So, if there's 8 fl. oz. in 1 cup then we need to multiply 8 by 4.
8 x 4 = 32
Your answer would be 32 fl. oz.
Hope This Helps!
Cupkake~