Answer:
(-√2 + 3)/7
Step-by-step explanation:
To rationalize the denominator, we need to multiply by the conjugate:
1/(3 + √2)*(3 - √2)/(3 - √2)
(3 - √2)/(9 - √4)
(3 - √2)/(9 - 2)
(-√2 + 3)/7
Write [tex]3x^{2} -x-3+x^{3}[/tex] in standard form. Identify the leading coefficient.
Answer:
Standard form: [tex]x^3+3x^2-x-3[/tex]
Leading coefficient: 1
Step-by-step explanation:
[tex]3x^2-x-3+x^3=\\x^3+3x^2-x-3[/tex]
The leading coefficient is 1 because the leading term is [tex]x^3[/tex].
The hypotenuse of a right triangle is 9[tex]\sqrt{2}[/tex] cm, and the shorter leg is 9 cm. Find the length of the other leg.
Answer:
9 cm
Step-by-step explanation:
If you were to imagine this right triangle, you would find it to be a 45 - 45 - 90 triangle. Perhaps the " shorter leg " piece of information was present to trick you, considering that the legs are congruent by converse to base angle theorem.
How is this triangle a 45 - 45 - 90? In such a triangle, the legs can be posed as x cm, as the base angles are congruent ( 45 and 45 ), thus the legs of the triangle are congruent as well. The hypotenuse would be x√2, and as we can see -
If legs = x, Hypotenuse = x√2 = 9√2
Thus, the length of the other leg is 9 centimeters ( 9 cm )
Hope that helps!
If the slope of the line joining the points (2k, -2) and (1, - k) be (-2), find k
Answer:
k=4/5
Step-by-step explanation:
(-k+2)/(1-2k) = -2 ( using the slope formula (y2-y1)/(x2-x1) )
-k+2 = -2 (1-2k)
-k+2 = -2 + 4k
2= -2 +5k
4 = 5k
k=4/5
Answer:
k = 4/5Step-by-step explanation:
To find k use the formula for finding the slope of a line and equate it to the slope which is - 2
So we have
(2k, -2) and (1, - k)
[tex] - 2 = \frac{ - k + 2}{1 - 2k} [/tex]
Cross multiply
That's
- 2( 1 - 2k ) = - k + 2
Expand and simplify
- 2 + 4k = - k + 2
Group like terms
4k + k = 2 + 2
5k = 4
Divide both sides by 5
k = 4/5
Hope this helps you
find 1st, 2nd, 3rd, 4th and 10th nTh term. rule is 3n+4
Answer:
When n is 1
3n+4
=3*1+4
=3+4
=7
When n is 2
3n+4
=3*2+4
=6+4
=10
When n is 3
3n+4
=3*3+4
=9+4
=13
When n is 4
3n +4
=3*4+4
=12+4
=16
When n is 10
3n+4
=3*10+4
=30+4
34
There are eight marbles in a bag. Four marbles are blue (B), two marbles are red (R) and two marbles are green (G) Steve takes a marble at random from the bag. What is the probability that Steve will take a blue marble.
Answer:
1/2
Step-by-step explanation:
There are 8 marbles in total and 4 are blue, so 4/8 are blue. Then simplify 4/8 and you will get 1/2.
Answer:
1/2 or 50%
Step-by-step explanation:
Blue= 4, Red= 2, Green= 2
Total marbles= 8
P(B)= 4/8= 1/2 or 50%
pleaseee help me w dis asap!!
Answer:
x=2 f(x)=5-x
o≤x≤3 f(x)=x
2＜x＜3 f(x)=1
3＜x≤5 f(x)=5-x
Step-by-step explanation:
Zaheer, a boy of height 1.5m was watching the entire programme. Initially he observed the top of theflagpoleat an angle of elevation 300 . When he moved 10 m towards the flag post the angle of elevation of the top of the flagpole increased to 450. What is the height of the flag pole?
Answer:
[tex]h = 15.163\ meters[/tex]
Step-by-step explanation:
(Assuming the correct angles are 30° and 45°)
We can use the tangent relation of the angle of elevation to find two equations, then we can use these equations to find the height of the pole.
Let's call the initial distance of the boy to the pole 'x'.
Then, with an angle of elevation of 30°, the opposite side to this angle is the height of the pole (let's call this 'h') minus the height of the boy, and the adjacent side to the angle is the distance x:
[tex]tan(30) = (h - 1.5) / x[/tex]
Then, with an angle of elevation of 45°, the opposite side to this angle is still the height of the pole minus the height of the boy, and the adjacent side to the angle is the distance x minus 10:
[tex]tan(45) = (h - 1.5) / (x - 10)[/tex]
So rewriting both equations using the tangents values, we have that:
[tex]0.5774 = (h - 1.5) / x[/tex]
[tex]1 = (h - 1.5) / (x - 10) \rightarrow (h - 1.5) = (x - 10)[/tex]
From the first equation, we have that:
[tex]x = (h - 1.5) / 0.5774[/tex]
Using this value of x in the second equation, we have that:
[tex]h - 1.5 = \frac{ (h - 1.5) }{0.5774} - 10[/tex]
[tex]h + 8.5 = \frac{ (h - 1.5) }{0.5774}[/tex]
[tex]0.5774h + 4.9079 = h - 1.5[/tex]
[tex]0.4226h = 6.4079[/tex]
[tex]h = 15.163\ meters[/tex]
In a right-angled triangle, the hypotenuse is h cmlong aand the other two sides are f cm and g cm in height. Write down a formula which connects f g and h
Answer: f²+g²=h²
Step-by-step explanation:
In a right triangle, you use the Pythagorean Theorem: a²+b²=c² to find the hypotenuse of the triangle. I would believe that you could just substitute the variables in this equation with the ones that you have. This should show the relationship between the 3 unknown lengths of the sides.
When a certain number is subtracted from 10 and the result is multiplied by 2, the final result is 4. Find the number.
Answer:
8
Step-by-step explanation:
10-8 x 2 = 4
2 x 2 = 4
4 = 4
The number is 8, which is when subtracted from 10 and the result is multiplied by 2, then the result is 4.
What is Simplification?Simplification in mathematical terms is a process to convert a long mathematical expression in simple and easy form.
Let the required number is x.
According to given condition,
When x is subtracted from 10 and the result is multiplied by 2, final result comes as 4.
Implies that,
2 (10 - x) = 4
10 - x = 2
x = 10 - 2
x = 8
The required number is 8.
To know more about Simplification on :
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A machine lifts up containers of coal from the mine and lowers empty containers down. The machine uses an electric motor connected to a 600 V d.c. supply.The maximum current in the motor is 4000 A. *Calculate the maximum power available from the motor. Give your answer in MW* power = voltage x current i believe
Answer:
The maximum power available to the motor is 2.4 MW
Step-by-step explanation:
The power of a circuit that has a current, I, and a voltage, V, is given by the relation
Electrical power, P = I²R = I× I×R = I × V
Therefore given that the parameters are;
Voltage in the d.c. power supply = 600 V d.c.
Maximum current in the motor = 4000 A
Therefore, we can find the power as follows;
Maximum motor power = Voltage × Current
The maximum motor power, P available = 600 V × 4000 A = 2400000 W which on converting to MW becomes;
The maximum power available to the motor , P = 2.4 MW.
The length of the base of a right-angled triangle ABC is 6 centimeters and the length of the hypotenuse is 10 centimeters. Find the area of the triangle.
Answer:
24
Step-by-step explanation:
Ok, so we see that we have 6 as a leg of the right triangle and 10 as the hypotenuse. As we look closer, we can tell that this makes the Pythagorean triple 6, 8, 10. 6, 8, 10 is just the Pythagorean triple 3, 4, 5 but it is multiplied by 2. So now that we know both the legs of this right triangle, we can use the area of a triangle formula (bh)/2. 6*8=48 and 48/2 = 24 which gives us our answer.
Two cards are drawn in succession and without replacement from a standard deck of 52 cards. Find the probability that the second card is a face card if it’s known that the first card was a face card.
Answer:
The probability that the second card is a face card if it’s known that the first card was a face card is 0.0497
Step-by-step explanation:
Total number of face cards = 12
Total cards = 52
Probability of getting face card on first draw=[tex]\frac{12}{52}[/tex]
Remaining no. of face cards = 11
Remaining number of total cards = 51
Probability of getting face card on second draw=[tex]\frac{11}{51}[/tex]
The probability that the second card is a face card if it’s known that the first card was a face card =[tex]\frac{12}{52} \times \frac{11}{51}= \frac{12}{52} \times \frac{11}{51}=0.0497[/tex]
Hence The probability that the second card is a face card if it’s known that the first card was a face card is 0.0497
what is productivity?
a. quantity of input per unit of output
b. quantity of output per unit of input
c. quality of output per unit of input
d. quality of input per unit of output
Answer:
This is the quantity of output per unit of input.
Step-by-step explanation:
I'm very sure.
You have a wire that is 50 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum
Answer:
88.6647727273 cm²
Step-by-step explanation :
The perimeter of the square =(50/2)
= 25 cm
∴ Side of the square = (25/4)
= 6.25 cm
∴ Area of of the square = (6.25)²
= 39.0625 cm²
The circumference of the circle =(50/2)
= 25 cm
∴ 2πr = 25
⇒ r = 25/(22/7)(2)
Area of the circle = (22/7) { 25/(22/7)2} {25/(22/7)2}
= (25×25×7) / (2×2×22)
= 4365/88
= 49.6022727273 cm²
∴ Total area of the circle and the square =(49.6022727273+39.0625000000)
= 88.6647727273 cm²
Hope it helped
If yes mark BRAINLIEST!
A tree casts a 25 m shadow when the angle of elevation to the sun is
40°. Approximately how tall is the tree?
25 m
A 25 m
B 19 m
C 21 m
D 16 m
Answer:
C. 21 m
Step-by-step explanation:
As shown in the picture, we need to use tan∅ (opposite over adjacent) to solve for the height of the tree:
tan40° = h/25
25tan40° = h
h = 20.9775
h ≈ 21 m
What are the values of the variables in the triangle below? If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.
Answer:
x = 12y = 4√3Step-by-step explanation:
To find x we use cosine
cos∅ = adjacent / hypotenuse
x is the adjacent
8√3 is the hypotenuse
cos 30 = x / 8√3
x = 8√3 cos 30
x = 12To find y we use sine
sin∅ = opposite / hypotenuse
y is the opposite
8√3 is the hypotenuse
sin 30 = y / 8√3
y = 8√3 sin 30
y = 4√3Hope this helps you
Identify the level of measurement of the data, and explain what is wrong with the given calculation. In a survey, favorite sports of respondents are identified as 100 for basketball, 200 for baseball, 300 for football and 400 for anything else. The average (mean) is calculated for 740 respondents and the result is 256.1. The data are at the______level of measurement.
Answer:
The data are at the nominal level of measurement
Step-by-step explanation:
Nominal Level of measurement is irrespective of orders or classes. In this survey we do not find out which game is ranked the most favorite.
Nominal; level is used just for counting. Its cannot be used as a measure or for quantitative analysis.
Such data cannot give the mean of the sample. And the two means cannot be compared.
In the given question it only gives the number of likes nothing more. The average cannot be calculated for such data.
48/60 in its simplelest form
Answer:
[tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Given
[tex]\frac{48}{60}[/tex]
To simplify find the highest common factor of 48 and 60, that is 12
Divide both values by 12
[tex]\frac{48}{60}[/tex] = [tex]\frac{4}{5}[/tex] ← in simplest form
The fraction is in simplest form when no other factor but 1 divides into the numerator and denominator
Help im stuck on this question
Work out the area of the rectangle using a calculator and
giving your answer as a mixed number.
22 cm
5 cm
1
Note: To enter a mixed number in the answer boxes, please use the following method:
Type the fractional part of the mixed number first (e.g. for 6 first enter 5)
Then use the keyboard arrows to return to the front of the box and type the whole number (e.g. for 6
5 enter 6).
Answer:
11 17/21 cm²
Step-by-step explanation:
5 1/6 = (5*6 + 1)/6 = 31/6
2 2/7 = (2*7 + 2)/7 = 16/7
A = 31/6*16/7 = 496⁽²/42 = 248/21 = 11 17/21 cm²
HELP PLZZZZZZZZZZZ!!!!!!!
Answer:
A) 21/20
Step-by-step explanation:
Tangent = Opposite/Adjacent
pls help me!!! I WILL GIVE BRAINLIEST!!!!!! probability question
Answer:
B
Step-by-step explanation:
0 to 9 has 10 numbers, and 7 numbers are 0, 1, 2, 3, 4, 5, 6, so the ans is B.
---------------------------------------------------------------------------------------
Hope this helps you...
Write 3x 1/2 in radical form
Answer:
3x^1/2 in radical form is
[tex] \sqrt{3x} [/tex]
Hope this helps you
A True/False quiz has three questions. When guessing, the probability of getting a question correct is the same as the probability of getting a question wrong. What is the probability that a student that guesses gets at least 2 questions correct
Answer:
1/4 or 25% chance
Step-by-step explanation:
the probability of getting each question right is 1/2, so for getting 2 questions right its 1/2 × 1/2, which is 1/4
The probability that a student that guesses gets at least 2 questions correct is 1/4.
GivenThe probability of getting a question correct is the same as the probability of getting a question wrong.
The probability of getting the question is correct is;
[tex]= \dfrac{1}{2}[/tex]
The probability of getting the question is wrong is;
[tex]= \dfrac{1}{2}[/tex]
Therefore,
The probability that a student that guesses gets at least 2 questions correct is;
[tex]= \dfrac{1}{2} \times \dfrac{1}{2}\\\\= \dfrac{1}{4}[/tex]
Hence, the probability that a student that guesses gets at least 2 questions correct is 1/4.
To know more about Probability click the link given below.
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pleaseee help! i need the answer for x (look at picture)
Answer:
180 - 133
Step-by-step explanation:
Answer:
x = 47 degrees
Step-by-step explanation:
Solve for X:
x + 133 = 180
180 - 133 = 47
x = 47
Two lines AB and CD intersect at O. If ∠AOC + ∠COB + ∠BOD = 270°Find the measures of ∠AOC, ∠COB, ∠BOD, ∠DOA.
Answer:
all are 90°
Step-by-step explanation:
Vertical angles are congruent, and linear angles are supplementary, so we have ...
∠AOC + ∠COB + ∠BOD = 270°
180° + ∠BOD = 270°
∠BOD = 90°
Since the lines cross at right angles, all of the angles are 90°.
factor: (a+3)^2-a(a+3)
Answer:
Factor (a+3)2−a(a+3)
3a+9
=3(a+3)
Answer:
3(a+3)
I hope this help :)
Answer:
(a+3)(3)
Step-by-step explanation:
(a+3)^2-a(a+3)
(a+3)(a+3)-a(a+3)
Factor (a+3)
(a+3)(a+3-a)
(a+3)(3)
What the answer question
Answer:
Step-by-step explanation:
UV & UT are the sides
What is the slope of a line that is perpendicular to the line whose equation is y=45x−3 A. −45 B. −54 C. 54 D. 45
Answer:
B. -5/4
Step-by-step explanation:
We're going to assume that you don't mean
y = 45x -3
which has a perpendicular line with a slope of -1/45.
Rather, we're going to assume that you mean
y = 4/5x -3
so that the slope of the perpendicular line is -5/4.
__
Similarly, we're going to assume that the answer choices are supposed to represent fractions, so that the above slope matches choice B.
_____
If the slope of a line is m, the slope of the perpendicular line is -1/m. The reciprocal of a fraction is the fraction that has numerator and denominator swapped. -1/(4/5) = -5/4.
PLVHGCHVBJGUYFTDCGVHJGYUJH
Answer:
The correct option is (B).
Step-by-step explanation:
The conditional probability of an event, say A is the probability of that events (A) when it is known that another event, say X has already occurred.
For example, consider the experiment of drawing two marbles from jar consisting of 8 white and 2 red, without replacement. The probability of selecting a red marble after a white marble is known as conditional probability.
In this case it is provided that:
40% of the students are licensed drivers55% students are female.The statement:
"the probability that a student who is a licensed driver is a male"
Is a statement of conditional probability.
This is because it is known from previous information that the student is a licensed driver and we need to determine the probability of this student being a male.
Thus, the correct option is (B).
Tanya wants to order 50 pizzas for a party. However, the pizza supplier can deliver only 45 pizzas on the given date. How will you describe the relationship between demand and supply of pizzas? A. Demand is equal to supply. B. Demand is greater than supply. C. Demand is less than supply.
Answer:
B
Step-by-step explanation:
The demand is 50 and the supply is 45. Since 50 > 45 the answer is that the demand is greater than the supply.
Answer:
b
Step-by-step explanation: