A right triangle has a hypotenuse with a length 12 and a leg with
length 5. How long is the triangle's other leg?
Answer:
13
Step-by-step explanation:
pythagorean theorum
a^2+b^2=c^2
12^2+5^2=c^2
144+25=c^2
c^2=169
c=13
The length of the triangle's other leg is approximately 10.908.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
We can use the Pythagorean theorem to solve for the length of the other leg of the right triangle.
The Pythagorean theorem states that for any right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides (the legs).
That is, for a right triangle with legs a and b and hypotenuse c:
c² = a² + b²
In this case,
We know that the hypotenuse has a length of 12 and one of the legs has a length of 5.
Let's denote the length of the other leg as "x".
So we can set up the equation:
12² = 5² + x²
Simplifying, we get:
144 = 25 + x^2
Subtracting 25 from both sides, we get:
119 = x²
Taking the square root of both sides, we get:
x ≈ 10.908
Therefore,
The length of the triangle's other leg is approximately 10.908.
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Consider the rhombus ABCD with the side length AB of 14 cm and the measure of the angle B of 120 °. Through the vertex A goes a certain secant that intersects the extensions of the sides BC and CD in E, respectively F.
Calculate:
[tex] \frac{1}{ce} + \frac{1}{cf} [/tex]
Answer:
1/14
Step-by-step explanation:
In the given geometry, we have similar triangles:
ΔCEF ~ ΔBEA ~ ΔDAF
This lets us write the relations for corresponding sides ...
CF/CE = DF/DA
where DF = CF -CD
We can rearrange this relation to give the value we're looking for as follows.
__
Making the substutition for DF, and multiplying by CE, we have ...
CF = CE(CF -CD)/DA
Both DA and CD are sides of the rhombus, so are both 14 cm in length. Multiplying by DA and making the number substitution, we have ...
DA·CF = CE·CF -CE·CD
14·CF = CE·CF -14·CE . . . . substitute 14 for DA and CD
14(CF +CE) = CE·CF . . . . . add 14·CE
(CF +CE)/(CE·CF) = 1/14 . . . . divide by 14·CE·CF
1/CE +1/CF = 1/14 . . . . . . . . . simplify
45th term of an arithmetic sequence having a=3 and d=8 is:
Answer:
a45 = 320
Step-by-step explanation:
The 45th term of the Arithmetic Sequence will be 355.
We have a Arithmetic Sequence with a = 3 and d = 8.
We have to determine the 45th term of this sequence.
What is the formula to calculate the nth term of an Arithmetic Sequence ?The formula to calculate the nth term of an Arithmetic Sequence is -
a(n) = a + (n - 1)d
a - first term of A.P.
d - Common difference of A.P.
n - position of term
According to the question -
a = 3
d = 8
n = 45
Then, using the formula to calculate the nth term, we get -
a(n) = a + (n - 1)d
a(45) = 3 + (45 - 1)8
a(45) = 3 + 44 x 8
a(45) = 3 + 352
a(45) = 355
Hence, the 45th term of the Arithmetic Sequence will be 355.
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sheri caught twice as many fireflies as robert. jessica caught 10 more flies than robert all together they caught 150 flies. how many flies did jessica catch?
Answer:
45 fireflies
Step-by-step explanation:
Because,
Sheri caught 70 and Robert caught 35.
150-35-70= 35
35+10 is equal to 45.
Following the rules given is the right answer
The cost of 5 pounds of apples is $12.45. What will be the cost of 12 pounds of apples if the
cost varies directly with the number of pounds purchased.
Edit View Insert Format Tools Table
Answer: 29.88
Step-by-step explanation: if 5 pounds = $12.45,
then 12 pounds = x
Therefore, Cross-multiply
5 x = 12 (12.45)
5x=149.4
x=149.4/5
x=29.88
Answer:
Step-by-step explanation:
Equation
Cost = k*weight
Givens
weight = 5 pounds
Cost = 12.45
12 pounds
Find k
Cost = k*weight
cost = 12.45
weigh = 5 pounds Substitute these values into the equation
12.45 = k * 5 Divide by 5
12.45 /5 = k*5/5
2.49 = k
Solve for 12 pounds
k = 2.49weight = 12 poundsCost = 2.49 * 12
Cost = 29.88
Answer
Cost = 29.88
Finish the polynomial by adding one number to make it a perfect square
x^2+18x+
Answer:
81
Step-by-step explanation:
[tex] {x}^{2} + 18x + {(( \frac{1}{2})(18)) }^{2} [/tex]
[tex] {x}^{2} + 18x + {9}^{2} [/tex]
[tex] {x}^{2} + 18x + 81[/tex]
[tex] {(x + 9)}^{2} [/tex]
What is the equation of the line that passes through the point (3,7) and has a slope of 2/3
Answer:
[tex]Y=\frac{2}{3} x +5[/tex]
Hope This Helped! :) Please Mark Brainliest!
Which point would be a solution to the system of linear inequalities shown below?
Answer: (-4, -6)
Step-by-step explanation:
Solving by graphing
[] See attached
() The only point in the required range is point (-4, -6)
Solving by plugging-in
I will figure out what the correct option is by plug them into the first equation. Since only one of these options is true, I do not need to do the second equation.
[✗] Let's check point (4, 10)
() 10 < (1/4)4 - 4
10 < 1 - 4
10 < -3 is false, so this answer is incorrect
[✗] Let's check point (-4, 5)
() 5 < (1/4)-4 - 4
5 < -1 -4
5 < -5 is false, so this answer is incorrect
[✗] Let's check point (-4, -4)
() -4 < (1/4)-4 - 4
-4 < -1 -4
-4 < -5 is false, so this answer is incorrect
[✓] Let's check point (-4, -6)
() -6 < (1/4)-4 - 4
-6 < -1 - 4
-6 < -5 is true, so this answer is correct
a. Use the appropriate formula to find the value of the annuity
b. Find the interest
Rate
Periodic Deposit
$6000 at the end of each year
15.5% compounded annually
Time
10 years
The value of the $6000 annuity given annual compounding is $124,836.12.
What is the value of the annuity?
The value of the annuity can be determining using this formula: amount deposited x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
n = number of years r = interest rate$6000 x [(1.155^10) - 1/0.155] = $124,836.12
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what is 2pi*4^2 + 2pi*4*4
~giving brainliest!~
Answer:
[tex]64\pi[/tex]
Step-by-step explanation:
[tex]2\pi {(4)}^{2} + 2\pi \: 4 \ast4 \\ \\ = 2\pi \ast16 + 2\pi \ast16 \\ \\ = 32\pi + 32\pi \\ \\ = 64\pi[/tex]
Answer:
64π
Step-by-step explanation:
2π(4²) + 2π(4)(4) <== exponents first
2π(16) + 2π(16) <== multiply
32π + 32π <== add
64π <== final answer
Note: 4 * 4 can also be written as 4²
Hope this helps!
How much pound sterling can be obtained while exchanging NRs250000 paying 2% commission?
(Buying rate: 1 pound=NRs 148.96) (Selling rate: 1 pound=NRs 149.74)
10.A water tank has strps inside it. A monkeyis sitting on topmost floor(i.e.,the first step).The water level is at ninth step. (i) He jumps 3 steps down and then jumps back 2 strps up.In gow many jumps will he reach the water level? Ch-integers class-7
Answer:
7 steps.
Step-by-step explanation:
Since the monkey is sitting on the first step already you can subtract 9 by 1 to find the amount of steps left.
9-1 = 8 steps left
The monkey jumps 3 steps down
8-3= 5 steps
Then jumps 2 steps up
5 + 2 = 7 steps
The monkey has 7 more steps until he reaches the water level.
Vera has challenged Alexey to a round of Marker Mixup. Marker Mixup is a game where there is a bag of 5 red markers numbered 1 through 5, and another bag with 5 green markers numbered 6 through 10
Alexey will grab 1 marker from each bag, and if the 2 markers add up to more than 12 he will win If the sum is exactly 12, he will break even, and If the sum is less than 12, he will lose $6
What is Alexey's expected value of playing Marker Mixup?
Answer:
Step-by-step explanation:
The total possble combinations = 5 * 5 = 25 ways.
The number of ways to get exactly 12
= 2,10 3,9 4,8 5,7 = 4 ways.
The ways to get > 12
= 3,10 4,9 4,10 5,8 5,9 5,10 = 6 ways.
So the number of ways to get < 12 = 25 - 4 - 6 = 15 ways.
Expected value
= 4(0) + 6(x) + 15(-6)
I have written x as you have not said how much he gets if he wins.
Answer:
−$2.40
Step-by-step explanation:
correct on khan
Need help as soon as possible
Answer:
100cm
Step-by-step explanation:
divide the shape into smaller shapes then find the area of each and add them together
300,000+5,000+80+8· 1/100 +9· 1/10,000
Answer:
305,080.0809
Step-by-step explanation:
3 x 100,000 : digit 3 is in the hundred thousands place
5 x 1000 : digit 5 is in the thousands place
8 x 10 : digit 8 is in the tens place
8 x 1/100 : digit 8 is in the hundredths place which means it is the second number after the decimal
9 x 1/10,000 : digit 9 is in the ten thousandths place which means it is the fourth number after the decimal
we get the following number:
305080.0809
HELPPP PLSSSS THE PYTHAGOREAN THEOREM
Answer:
Step-by-step explanation:
a²+b² = c² c is always the longest line thats opposite to the 90 degree angle
for 1
15² + b² = 17²
b² = 17² - 15²
b = √(17² - 15²)
b= 8
‼️GET BRANLIEST HERE‼️
PLS AND TY IT IS DUE SOON :))
Answer:
b = 0.62
Step-by-step explanation:
Hello!
We can look at the y-values of the function to find our multiplier. A multiplier will determine if the graph decays or grows in an exponential function, and by how much.
When x is 0, we can see the y-value is around 3, but as x approaches 1, the y-value comes to around 2.
We can find the multiplier by dividing the current term by the previous term.
2 ÷ 32/30.6666...This number is closest to 0.62, so the approximation is 0.62.
2/3
0.6666..
Approximation is 0.62 (b)
Hope this helped! Stay healthy!♡
Emily walked 5 2/6 miles in the morning and another 3 3/5 miles in the afternoon What was the total distance she walked?
Answer:
The correct answer would be 8 14/15 miles.
Step-by-step explanation:
You have to get the fractions 5 2/6 and 3 3/5 to a common denominator (30) getting you the fractions 10/30 and 18/30. 10/30+18/30 is 28/30 which can simplify to 14/15. 5+3 = 8 getting you the answer of 8 14/15
How many centimetres are there in 1.6 metres?
Choose all statements that are true.
A 15% of 15 is 1.
B 5% of 50 is 10.
C 10% of 100 is 10.
D 2% of 100 is 5.
E 3% of 200 is 6.
Answer:
C, D, E
Step-by-step explanation:
15 * .15 = 2.25
50 * .05= 2.5
100 * .10= 10
100 * .05= 5
200 * .03= 6
solve for a ~
[tex]a {}^{2} - 5a + 6 = 0[/tex]
thankyou ~
Answer:
Hi there!
Given equation :-[tex]\:\mathsf{a^2\:-\:5a\:+\:6\:=\:0}[/tex]
Now=> By splitting the middle term
=> [tex]\:\mathsf{a^2\:-\:2a\:-\:3a\:+\:6\:=\:0}[/tex]
=> [tex]\:\mathsf{a(a\:-\:2)\:-\:3(a\:-\:2)\:=\:0}[/tex]
=> [tex]\:\mathsf{(a\:-\:2)\:-\:(a\:-\:3)\:=\:0}[/tex]
We get ,=> [tex]\:\sf{a\:=\:2\: and\: a\:=\:3}[/tex]
[tex]\:\mathsf{Hope\:this\:helps\:you!\::)}[/tex]
Thank you!
Answer:
[tex]a = 3 \: \: \: and \: \: a = 2[/tex]
Step-by-step explanation:
⬇
[tex]a^{2} - 3a - 2a + 6 = 0[/tex]
⬇
[tex]a \: (a - 3) \: \: (a - 2)[/tex]
⬇
[tex]{}\ a - 3 = 0 \\ a = 2{}[/tex]
Question is on the screenshot.
X/5= 7
X/2= 6.5
Find x
Answer:
1. Answer is 35
2. Answer is 13
Step-by-step explanation:
All you have to do is multiply 5 on both sides for number 1 and multiply by 2 on both sides for number 2.
1) Graph y = f(x) = 3(2)%. Adjust the equation to make the y-intercept (0, -3). Which response is not correct?
A) Replace 3 with -3.
B) Replace x with -x.
C) Add -6 to the right side.
D) Replace x with -x and subtract 6 from the right side.
Using the concept of y-intercept, it is found that the response that is not correct is given by:
B) Replace x with -x.
What is the y-intercept of a function?It is the value of the function when x = 0, hence it is the point (0, f(0)).
In this problem, the function is:
[tex]f(x) = 3(2)^x[/tex]
The y-intercept is given by:
[tex]f(0) = 3(2)^0 = 3[/tex]
If we just replace x with -x, we still have the same expression as above, hence the y-intercept does not change and option B is the answer to this question.
More can be learned about y-intercepts at https://brainly.com/question/24737967
help me help me help me
Answer:
read step by step
Step-by-step explanation:
6 is +4.
19, 23, 27, 31
7 is all perfect square numbers
25, 36, 49, 64
8 is x2.
32, 64, 128, 256
9 is each number multiplied by the next. ex: 1x2=2, 2x3+6, 3x4=12
so the next few would be 30, 42, 56, 72
This recipe makes 10 flapjacks.
How much of each ingredient is needed to make 35 flapjacks by following this recipe?
Recipe: Makes 10 flapjacks
140 g margarine
120 g sugar
100 ml syrup
240 g oats
50 g raisins
Answer:
Multiply each measure of ingredients by 3.5
Step-by-step explanation:
This recipe makes 10 flapjacks. We want to be able to make 35 flapjacks.
Divide 35 by 10 to find the ratio of these 2 numbers.
35 / 10 = 3.5
Now we can multiply the measures by this number to find out how much of each ingredient we need.
140 * 3.5 = 490
120 * 3.5 = 420
100 * 3.5 = 350
240 * 3.5 = 840
50 * 3.5 = 175
Answer:
Recipe: Makes 35 flapjacks
490 g Margarine
420 g sugar
350 ml syrup
840 g oats
200 g raisins
Using proportions to solve for missing sides.
RST~YSZ, find YZ.
Answer:
YZ = 28
Step-by-step explanation:
A proportion involving the known and unknown sides is ...
TR/ST = ZY/SZ
__
This proportion uses SZ, which is not shown on the diagram. The length of SZ can be found from ...
SZ +ZT = ST . . . . . . . segment sum theorem
SZ + 5 = 40 . . . . with given values
SZ = 35 . . . . . subtract 5
__
So, the proportion with values filled in is ...
(3x -7)/40 = (2x +2)/35
7(3x -7) = 8(2x +2) . . . . . . . multiply by 280
21x -49 = 16x +16 . . . . . . . eliminate parentheses
5x = 65 . . . . . . . . . . add 49 -16x
x = 13 . . . . . . . . divide by 5
YZ = 2x +2 = 2(13) +2
YZ = 28
_____
Additional comment
RT = 3x -7 = 3(13) -7 = 32
Express (x+9)^2 as a trinomial in standard form.
Answer:
x^2 + 18x + 81
Step-by-step explanation:
(x+9) (x+9)
then distributive property
[tex](x+9)^2\\\\=x^2 + 2\cdot 9 \cdot x + 9^2\\\\=x^2 +18x+81[/tex]
Solve the system of linear equations. separate the x- and y- values with a coma. -5x+6y=33 -18x+4y=-22
Order the integers from greatest to
least: 4, -3, 0, 8, -5.
A 5, 3, 0, 4,8
B 3.-5, 0. 4.8
8, 4.0, 3, 5
D 0, -3, 4, 5,8
Answer:
8, 4, 0, -3, -5
(greatest to least order)
-Answer: C-
Step-by-step explanation:
8 is positive so its greatest
-5 is negative but it is farthest away from 0 so it is least
