Answer:
1. H = 29 cm
2. θ = 44°
Step-by-step explanation:
1. We can find the height of the triangle by considering the isosceles triangle as two right triangles. The height can be found by using Pitagoras:
[tex] L^{2} = H^{2} + B^{2} [/tex]
Where:
L: is the sides of the isosceles triangle = 42 cm
B: is the base = 30 cm
H: is the height =?
Then, the height is:
[tex] H = \sqrt{L^{2} - B^{2}} = \sqrt{(42 cm)^{2} - (30 cm)^{2}} = 29.4 cm = 29 cm [/tex]
2. The two equal angles (θ) can be found using the following trigonometric identity:
[tex] cos(\theta) = \frac{B}{L} [/tex]
[tex] \theta = cos^{-1}(\frac{30 cm}{42 cm}) = 44.4^{\circ} = 44^{\circ} [/tex]
Hence, the two equal angles are 44°.
I hope it helps you!
find ratio of 120 :80
120 : 80
= 12 : 8
= 6 : 4
= 3 : 2
This is the answer
Answer:
120/10=12
80/10=8
12/4=3
8/4=2
Nothing can further decide, then we have
3:2
Which polynomial represents the sum below (8x^2 + 5x + 3) + (-5x^6 - 2x^5 - 4x^2 - 2x)
Answer:
-5x^6 - 2x^5 + 4x^2 + 3x + 3
Step-by-step explanation:
Combine like terms from each of the polynomials.
(8x^2 + 5x + 3) + (-5x^6 - 2x^5 - 4x^2 - 2x)
(8x^2 - 4x^2) + (5x - 2x) + (3) + (-5x^6) + (-2x^5)
(4x^2) + (3x) + (3) + (-5x^6) + (-2x^5)
Then, order them by degree.
-5x^6 -2x^5 + 4x^2 + 3x + 3
Pythagorean theorem
please help
Answer:
c = square of a2+b2
i think its correct ome
Write an equivalent expression. 4x - x
Answer:
5x-2x
Step-by-step explanation:
4x-x = 3x
so,
5x-2x = 3x
The equivalent expression would be; 5x-2x
What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.
We are given that the expression as; 4x - x
We need to find an equivalent expression.
Therefore, solving further;
4x-x = 3x
Thus, we can also create one expression as;
5x-2x = 3x
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which set of number are right for this inequality x<14 plz help me i need help due in 20 min
A. 3,7,9,10,12
B. 15, 18 ,20, 21, 23
C. 17, 21, 24, 25, 31
D. 23, 27, 29, 30, 36
Answer:
it's A because all of those numbers are less than 14
Step-by-step explanation:
Sam says: 9.05kg is equal to 9500g. Is he right or wrong? Explain your answer.
Answer:
Step-by-step explanation:
Sam is wrong because 9,05 kg =9050g which is different to 9500g
Answer:
wrong 1 kilo in a gram is 1000 so u just going to add 1 zero on the back so 905+0= 9050 grams
HELP ME PLEASE I HAVE 1 MINUTE LEFT TO TRUN THIS IN
Answer:
1jdjsbsjsnsisn Shane Jana aus she sue euw
Answer:
Number of walnut trees: 4n+15
Divide using long division.
(x3 + 3x2 + x - 4) + (x - 1)
Answer:
2x+3x2 +x3 −5
Step-by-step explanation:
Hope this helps
Answer:
x^2 - 2x + 2
step-step explanation:
The 2 line segments form a ___ that helps us find the ___
Answer:
is this on shapes or multiple answer?
Step-by-step explanation:
like i was thinking 2 segments as parallel
If f(x)= 1/2x-10+3, which inequality can be used to find the domain of f(x)?
Answer:
x ≠ 5
Step-by-step explanation:
Assuming you mean f(x) = (1/(2x-10))+3
Please be careful with how ambigiuous your question can appear with the / sign.
The domain is the set of values that can be used as an input.
In this case the only input we have that could cause problem is if the denominator of the fraction is 0, because then we divide by 0 which is not allowed.
This gives us 2x-10 ≠ 0
2x ≠ 10
x ≠ 5
The domain of the function is given by the inequality ( 1/2 )x - 10 ≥ 0 and the value of x ≥ 20
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = [ √ ( 1/2 )x - 10 ] + 3
Now , the expression (1/2)x - 10 inside the square root must be greater than or equal to 0, as the square root of a negative number is not defined in the real number system.
(1/2)x - 10 ≥ 0
To solve this inequality, we can isolate x:
(1/2)x ≥ 10
x ≥ 20
Hence , the domain of the function f(x) is x ≥ 20.
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The complete question is attached below :
If f(x)= 1/2x-10+3, which inequality can be used to find the domain of f(x)?
Today is the birthday of Rahul and he is 3 times
as old as Nirmala. In 13 years, Rahul will be one
year less than twice as old as Nirmala will be
then. The age of Rahul today is:
a. 30 years
c. 49 years
b. 36 years
d. 30 years
Answer:
b. 36 years
Step-by-step explanation:
Today
Nirmala = x years
Rahul = 3x years
In 13 years
Nirmala = 3x + 13 years
Rahul = 2(x+13) - 1
3x + 13 = 2(x+13) - 1
3x + 13 = 2x + 26 - 1
3x + 13 = 2x + 25
3x - 2x = 25 - 13
x = 12
Nirmala = x years
= 12 years
Rahul = 3x years
= 3(12)
= 36 years
The age of Rahul today is 36 years
Sujan bought 16 pens for Rs256. how much would he have to pay for one pen he buys next time?
Step-by-step explanation:
.......................
Answer:
Rs 16
Step-by-step explanation:
Amount of money paid for 16 pens = Rs 256
Amount of money paid for 1 pen =
[tex] \frac{256}{16} = \frac{128}{8} \\ = \frac{64}{4} = \frac{32}{2} \\ = \frac{16}{1} \\ [/tex]
Therefore, amount paid for one pen is Rs 16
4y=5x-1 3x-2y=1 solve each system using substitution
Answer:
(1,1)
x=1 y=1
Step-by-step explanation:
When you solve by substitution, you have to isolate each equation Hope this helps.
how to find (a) and (b)?
Answer:
A) Gradient = -3
B) 3y - x = 7
Step-by-step explanation:
The curve has the equation;
y = x³ - 6x² + 9x + 1
We are given the pints it passes through as;
A(2,3) and P(3, 1)
A) to find the gradient, we will find the derivative of the given equation.
Thus;
Gradient = y' = 3x² - 12x + 9
At point A, x = 2. Thus;
Gradient = 3(2²) - 12(2) + 9
Gradient = 12 - 24 + 9
Gradient = -3
B) since the gradient of the tangent = -3, it means the gradient of the normal will be; -1/-3 = 1/3
Thus, equation of the normal to the curve at point A will be;
(y - 3) = ⅓(x - 2)
Multiply both sides by 3 to get;
3y - 9 = x - 2
3y - x = 9 - 2
3y - x = 7
find the value of a and b if 1/5+√7= a+b√7
Answer:
[tex]a=\dfrac{1}{5}[/tex] and b = 1
Step-by-step explanation:
Given that,
[tex]\dfrac{1}{5}+\sqrt7=a+b\sqrt7[/tex]
We need to find the value of a and b.
We should compare both sides of the above equation i.e.
[tex]a=\dfrac{1}{5}[/tex]
and
b = 1
Hence, the values of a and b are 1/5 and 1 respectively.
- Peter's bike bill is automatically
deducting $78 from his bank
account every month. If his bank
account balance is at $234, how
many months will it take for Pete to
run out of money?
PLEASE
A rectangle has sides 10 and 8. Find the length of the Diagonal
Answer:
Step-by-step explanation:
Remark
The diagonal is found by using the Pythagorean Theorem: a^2 + b^2 = c^2. This only works for certain figures. The rectangle is one of them.
Givens
a = 10
b = 8
c = ? This is the length of the diagonal.
Solution
a^2 + b^2 = c^2
10^2 + 8^ = c^2
100 + 64 = c^2
c^2 = 164
√c^2 = √164
c = 12.806
For the rational function f(x)=(-13x-27)/(x^(2)-4x-12), F(x)=2
What is 75% converted to a decimal? mal?
Answer:
75% = 0.75
Step-by-step explanation:
75% ÷ 100 = 0.75
Answer:
.75
Step-by-step explanation:
75.% you move the the point 2 spaces to the front and get .75
4. A regular hexagon is shown below. Find the value of x. (11x + 21)
Answer:
We need the picture
Step-by-step explanation:
Please help ASAP. Thanks so much.
Answer:
D. 1/9
Step-by-step explanation:
The x-coordinate is -1/3
hideki is draining a 45 gallon aquarium at a rate of 15 gallons per minute what is the initial value of the linear function that represents the situation ?
Answer:
45.
Step-by-step explanation:
Since Hideki is draining a 45 gallon aquarium at a rate of 15 gallons per minute, to determine what is the initial value of the linear function that represents the situation, the following calculation must be performed:
45 (starting number) - 15(number of gallons per minute) X(minutes) = Y
Therefore, the equation would be 45 - 15X = Y, with which the initial value of the linear function that represents the situation is 45.
The dollar value v (t) of a certain car model that is t years old is given by the following exponential function.
v (t) = 19,900(0.86)^t
Find the initial value of the car and the value after 11 years.
Round your answers to the nearest dollar as necessary.
Answer:
v(0) = 19,900, v(11) = 3,787.36
Step-by-step explanation:
v(0) = 19,900 (0.86)^0 = 19,900 * 1 = 19,000
v(11) = 19,900 (0.86)^11 = 19,900 * 0.190319 = 3,787.36
Find the circumference of the circle below. Use 3.14 pi. Round your answer to the nearest tenth.
12.1
12.6
25.1
50.2
PLEASE EXPLAIN HOW YOU GOT YOUR ANSWER!!!
Step-by-step explanation:
radius = 4 inches π = 3.14circumference = 2π × radius = 2 × 3.14 × 4 = 25.1 inches _________________________FOLLOW MEAnswer:25.1
Step-by-step explanation:
if x+y=5, then what does y-5 equal?
Answer:
-x
Step-by-step explanation:
rearrange the terms by adding or subtracting the same thing from both sides:
[tex]x+y=5\\y = 5 - x\\y - 5 = -x[/tex]
One number added to twice another number is 30. The sum of the numbers is 19.
Write and solve a system of equations to represent this situation.
What is the value of the smaller number?
What is the value of the larger number?
I don't understand :(
Answer:
The smaller number is 8
The bigger number is 11
Step-by-step explanation:
let the first number be A
let the second number be B
A + 2B = 30..... equation 1
A + B = 19...... equation 2
Subtract equation 2 from 1.
A + 2B = 30
- A + B = 19
-------------------
0 + B = 11
B = 11
Substitute B = 11 into equation 2
A + B = 19
A + 11 = 19
collect like terms
A = 19-11
A = 8.
A= 8 and B = 11
what are the equal factors to 10 to the second power
Answer:
100 i think
Step-by-step explanation:
Answer:
inequality 1 has a solution of 5
Step-by-step explanation:
Select the correct answer.
Use this tax table to find how much tax you need to pay on a taxable income of $40,000.
The tax is:
If taxable
income is over-
But not
over-
SO
$7,825
$31,850
$77,100
$7.825 10 percent of the
amount over SO
$31,850 $782.50 plus 15 percent
of the amount over
7,825
$77,100 $4,386.25 plus 25
percent of the amount
over 31,850
$160,850 $15,698.75 plus 28
percent of the amount
over 77.100
$349.700 $39,148.75 plus 33
percent of the amount
over 160,850
no limit S101,469.25 plus 35
percent of the amount
over 349.700
S160,850
S349,700
OA
$6,423.75
OB
$8.150.50
OC. $12.536.25
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if Rohans weight is t+6 kg and is 7 kg less than Rahul whose weight is 54 kg. What is the value of t
Answer:
T = 41
Step-by-step explanation:
Rohan's weight = t+6
Rahul's Weight = t+6+7 = 54
t = 54 - 6 - 7
t = 41
There are 5,000 books in the town's library. Of these,4,400 are fiction. To find the percent of the books that are fiction, first set up the percent equation. Then find the percent. Setup the percent equation. Choose the correct answer below. A. m B. m C. m Your answer is not correct.D. m This is the correct answer. nothing% of the books are fiction
Answer:
4,400=m•5,000 and 88%