Answer:
2
Step-by-step explanation:
a2 = a1×3
a3 = a2×3 = a1×3×3
=>
an = an-1 × 3 =
[tex]a1 \times {3}^{n - 1} [/tex]
a5 = 162 = a1×3⁴ = a1×81
a1 = 162/81 = 2
Find the length of side xx in simplest radical form with a rational denominator.
Explanation:
For any 30-60-90 triangle, the hypotenuse is always twice as long compared to the short leg. The short leg is always opposite the 30 degree angle.
The length of x is 6.
What is a right-angled triangle?
'A triangle in which one of the interior angles is 90° is called a right-angled triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the perpendicular and the base.'
According to the given problem,
Perpendicular = 3
Hypotenuse = x
We know,
sin∅ = [tex]\frac{perpendicular}{hypotenuse}[/tex]
∅ = 30°
⇒ sin30 = [tex]\frac{3}{x}[/tex]
⇒ [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{x}[/tex] [ sin30 = [tex]\frac{1}{2}[/tex] ]
⇒ x = 3 * 2
⇒ x= 6
Hypotenuse = 6
Applying Pythagoras theorem:
⇒ Hypotenuse² = Perpendicular² + Base²
⇒ 6² = 3² + Base²
⇒ 6² - 3² = Base²
⇒ Base² = 25
⇒ Base = √25
⇒ Base = 5
Hence, we can conclude the value of x to be 6.
Learn more about right-angled triangle here:
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Benjamin writes an expression for the sum of 1 cubed, 2 cubed, and 3 cubed -- What is the value of the expression? options---
18, 36, 38, or 20-- ANSWER FAST!!!
Answer:
36
Step-by-step explanation:
1^3 + 2^3 + 3^3= 1+8+27
9+27= 36
look at the image for the question and the answers
Answer: The answer is your bad, you shouldnt be "answering" questions with " sorry i need points"
Alice bought a (k) kg of pork and (i) kg of chicken. how many kg of meat did alice buy??
Write the solutions and explanation with algebraic expression
Answer:
(k)kg+(l)kg=kg
Step-by-step explanation:
I just looked at letters. it's definitely wrong but I typed something so I could get points and get my answers. idc tbh but good luck ig
PLEAS ANSWER ASAP If you like peanut butter and chocolate, then you will love Reese's.
What is the contrapositive of the statement?
Find the area.
A hexagon with side length 6m.
Answer:
93.53m.
Step-by-step explanation:
.
Martin can travel 174 miles in 3 hours. At this rate, how far can he travel in 7 hours.
Answer:
406
Step-by-step explanation:
all you have to do is divide 174 by 3 and multiply 58 by 7
At maximum speed, an airplane travels
1680 miles against the wind in 5 hours.
Flying with the wind. the plane can
travel the same distance in 4 hours.
What is the speed of the plane with no wind?
Answer:
The speed of the plane with no wind is 378 miles per hour.
Step-by-step explanation:
Since at maximum speed, an airplane travels 1680 miles against the wind in 5 hours, and flying with the wind. the plane can travel the same distance in 4 hours, to determine what is the speed of the plane with no wind, the following calculation must be performed:
Against the wind = 1680/5 = 336
With the wind = 1680/4 = 420
420 - ((420 - 336) / 2) = X
420 - 42 = X
378 = X
Therefore, the speed of the plane with no wind is 378 miles per hour.
Find the probability of exactly three successes in six trials of a binomial experiment in which the the probability of is 50%.
Start by doing the binomial expansion of (x+y)^6 where x represents success. This is
(x^6y^0) + 6(x^5y^1) +15(x^4y^2) +20(x^3y^3) +15(x^2y^4) +6(x^1y^5) +(x^0y^6)
We are interested in the x^3y^3 term which represents exactly 3 sucesses. Since the probalbility of sucess and failure are both .5 we should be able to figure this out just using the coefficients of the terms which is
20/64 = .3125 which is 31.25%
The probability of exactly three successes in six trials of a binomial experiment in which the the probability of is 50% is 31.25%.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
Here,
Probability =(³₆×(50%)³×(1-50%)⁶⁻³
= 20×(1/2)³×(1/2)³
= 20× 1/64
= 20/64
= 5/16
= 0.3125
= 0.3125×100
= 31.25%
Therefore, the probability of exactly three successes in six trials of a binomial experiment in which the the probability of is 50% is 31.25%.
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h(x) = x2 + 3. Is frl a function and why/why not?
No, the inverse function does not pass the horizontal line test.
No, the inverse function does not pass the vertical line test.
Yes, the inverse function has one y-value for every x-value.
Yes, the inverse function has one x-value for every y-value.
is good answer the x value and y value
Answer:
No, the inverse function does not pass the horizontal line test.
Step-by-step explanation:
A boy spent 20% of his money on books and 20% of the remainder on food.If he had $2000 left, how much money did he have at first?
Answer:
[tex]\$3,125[/tex]
Step-by-step explanation:
Let [tex]s[/tex] represent the amount of money he initially started with.
After he spent 20% on books, he will have [tex]100\%-20\%=80\%[/tex] of his initial money left. We can represent this as [tex]0.8s[/tex].
Following that, the boy spends 20% of the remainder of his money on food. Similarly, he will have [tex]100\%-20\%=80\%[/tex] of the remainder of money he had left after he purchased the books. Therefore, he ends up with [tex]0.8(0.8s)=0.64s[/tex] of his money left.
Since we're given that he had $2,000 after all these transactions, we have the following equation:
[tex]0.64s=\$2,000[/tex]
Divide both sides by 0.64 to isolate and solve for [tex]s[/tex]:
[tex]s=\frac{2,000}{0.64}=\boxed{\$3,125}[/tex]
Therefore, the boy had $3,125 to begin with.
Answer:
2800
Step-by-step explanation:
20%+20%=40%
40/100x2000=2800
which statement proves that polygon ABCD is not a rectangle
Answer:
ummm u did not add the statements to the question
Step-by-step explanation:
but a polygon ABCD might not be a rectangle if:
opposite sides of polygon ABCD are not of equal lengthsall angles of the polygon may not be right angles (90°)opposite sides may not be parallelPLEASE HELP !!!
Annabelle went to the store to buy some apples. The price per pound of the apples is $3.75 per pound and she has a coupon for $3.25 off the final amount. With the coupon, how much would Annabelle have to pay to buy 3 pounds of apples? Also, write an expression for the cost to buy pp pounds of apples, assuming at least one pound is purchased.
final cost of 3 pounds: ______
final cost of p pounds: ______
Answer:
final cost of 3 pounds: 8 dollars
final cost of p pounds: 3.75p - 3.25 dollars
Step-by-step explanation:
Each pound costs $3.75, so 3 pounds cost 3*3.75 = 11.25 dollars. Subtract off the $3.25 to get the final cost to be 11.25-3.25 = 8 dollars. This takes care of the first part.
For the second part, the expression for the final cost is 3.75p - 3.25; where the 3.75p is the cost before the coupon is applied. If you plugged p = 3 into that expression, you should get 8 as a result. The variable p is some positive whole number. It's a place holder for the number of pounds of apples.
What Is the factored form of the polynomial
x^2-12x+27
Step-by-step explanation:
The Answer is (x-9) (x-3) Factor 12 and 27 out.
Answer:
[tex]x^{2} -12x+27=[/tex]
[tex](x-3)and\:(x-9)[/tex]
-----------------------
hope it helps...
have a great day!!
Grace earned £32,000 last year. She worked for 35 hours a week for 50 weeks. Calculate her pay per hour. Give your answer to 2 decimal places.
Answer:
18.29
Step-by-step explanation:
32000 ÷ 35 ÷ 50 = 18.2857143
Factor completely x2 + 16
Answer:
not a factorable number i think
Step-by-step explanation:
Find the length of AC. Round to the nearest hundredth if necessary.
Answer:
13.86
Step-by-step explanation:
In ∆ ABC ,
cos 30° = AC/BC√3/2 = AC/ 16 AC = 16 * √3/2 AC = 8√3 AC = 8 * 1.732AC = 13.86There are 2 boys for every 3 girls in Mrs. Sorrentino's class. If there are 30 students in the class, what percentage are boys?
A:20
B:25
C:30
D:33
E:40
Find the product of the Mixed numbers.
2 2/3 x 1 1/2
what statemets are correct? Check all that apply.
1. write the mixed numbers as improper fractions
2. multiply the numerators to get 24.
3. multiply the denominators to get 6.
4. write the improper fractions as a mixed number
5. The product is 4.
6. The product is 2 2/5
Answer:
1., 2., 3., 5.
Step-by-step explanation:
2 2/3 x 1 1/2 =
= (2 * 3 + 2)/3 * (1 * 2 + 1)/2
= 8/3 * 3/2
= 24/6
= 4
Answer:
Write the mixed numbers as improper fractions.
Multiply the numerators to get 24.
Multiply the denominators to get 6.
Write the improper fraction as a mixed number.
The product is 4.
Step-by-step explanation:
the other person is wrong
I purposely got this question wrong so I can see the right answers
these are the correct answers
(edge)
Someone help me please!!!
Helppppp and explain pls and thankyouuu
Answer: B
Step-by-step explanation:
multiply all the the sales by 11% and you will get the answers in option b
ex: 1300*0.11=143
can someone help me w/ this question plz?
Answer:
16 birds
8 mammals if you need to know.
Step-by-step explanation:
We can set this system of equations up by plugging the 2m from the second equation into where it says r in the first equation. The reason why we do this is because
The 2m is equal to r, so we can replace the r in the first equation with 2m, since they are equal.
Divide both
We can confirm this because
uh
(I like the enter key lol.)
It's the return key on some keyboards in other countries.
Oh yeah.
We can confirm the values.
If there are 16 birds, there is probably going to be a total of 32 legs.
With 8 mammals, it is something like 8 x 4, which is 32
32 + 32 = 64, which is the total.
Find the value of the variable that results in congruent triangles.
A. 80
B. 10
C. 50
D. 30
Answer:
x = 10
Step-by-step explanation:
Mathematically, the sum of the interior angles of a triangle is 180
Thus, we have it that;
55 + 45 + (5x + 30) = 180
100 + 5x + 30 = 180
5x = 180-30-100
5x = 50
x = 50/5
x = 10
what is the binary 11110-10101
How many 2/3 are in 4 use the tape diagram
does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?
Given equation of the Circle is ,
[tex]\sf\implies x^2 + y^2 = 25 [/tex]
And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,
[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]
Here we can say that ,
• Radius = 5 units
• Centre = (0,0)
Finding distance between the two points :-
[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]
Here we can see that the distance of point from centre is less than the radius.
Hence the point lies within the circle .
inside the circle
Step-by-step explanation:
we want to verify whether (-4,2) lies inside or outside or on the circle to do so recall that,
if [tex]\displaystyle (x-h)^2+(y-k)^2>r^2[/tex] then the given point lies outside the circleif [tex]\displaystyle (x-h)^2+(y-k)^2<r^2[/tex] then the given point lies inside the circleif [tex]\displaystyle (x-h)^2+(y-k)^2=r^2[/tex] then the given point lies on the circlestep-1: define h,k and r
the equation of circle given by
[tex] \displaystyle {(x - h)}^{2} + (y - k) ^2= {r}^{2} [/tex]
therefore from the question we obtain:
[tex] \displaystyle h= 0[/tex][tex] \displaystyle k= 0[/tex][tex] {r}^{2} = 25[/tex]step-2: verify
In this case we can consider the second formula
the given points (-4,2) means that x is -4 and y is 2 and we have already figured out h,k and r² therefore just substitute the value of x,y,h,k and r² to the second formula
[tex] \displaystyle {( - 4 - 0)}^{2} + (2 - 0 {)}^{2} \stackrel {?}{ < } 25[/tex]
simplify parentheses:
[tex] \displaystyle {( - 4 )}^{2} + (2 {)}^{2} \stackrel {?}{ < } 25[/tex]
simplify square:
[tex] \displaystyle 16 + 4\stackrel {?}{ < } 25[/tex]
simplify addition:
[tex] \displaystyle 20\stackrel { \checkmark}{ < } 25[/tex]
hence,
the point (-4, 2) lies inside the circle
A store buys items at a wholesale price of $45 each. If the store marks up the price, and no discounts are given, which could be possible retail prices?
Answer:
$49 and $65 are the choices you should check. These prices are greater than $45.
Step-by-step explanation:
It is given that the store buys items at a wholesale price of $45 each. If the store marks up the price, and no discounts are given, then that would mean that the store sells the store has to sell at a price greater than the buying price which is $45.
Out of the given options, only two options have a selling price which is greater than $45. These are the last and the second last options. Thus the fourth and the fifth options are applicable and hence they are to be checked.
hshsjshshsjsksjjsbsbbs bc hd
Answer:
its b b b
Step-by-step explanation:
use the order of operations -5 + 3(7.2 - 3.2)
Answer:
-5 + 3(7.2 - 3.2) equals 7.
Step-by-step explanation:
The order of operations states the order in which different mathematical operations should be done first, you can use the mnemonic PEMDAS to remember the order to complete each operation. PEMDAS states that the order must be followed as Parenthesis, Exponents, Multiplication/Division, and Addition/Subtraction. In the expression -5 + 3(7.2 - 3.2), the three mathematical operations being used are subtraction, multiplication, and parenthesis, so based on PEMDAS, the order to complete them is parenthesis, multiplication, and subtraction. -5 + 3(7.2 - 3.2) = -5 + 3(4) = -5 + 12 = 7, so that is your final answer.
[tex]\displaystyle\bf -5+3(7.2-3.2)=7\\\\1)\:7.2-3.2=4\\\\2)\:4\cdot3=12\\\\3)\:12-5=7[/tex]
A ream contains 500 sheets of paper. How many sheets in 2 reams?
