The solution of the given radical expression√20 using factorization is [tex]2 \sqrt{5}[/tex]. Therefore, the correct option for the radical expression√20 is option A, i.e [tex]2 \sqrt{5}[/tex].
A collection of constants, variables or numbers connected using one or more arithmetic operator is called an expression.
Example = 4y, 3x+4.
An expression containing the values in the form of square root, cube root is called a radical expression.
The breaking of a number into its own factors, so that they multiply to give the same number again, is called factorization.
Given expression, √20
The solution of the expression can be obtained by the factors of 20.
[tex]\sqrt{20} = \sqrt{2\times2\times5}[/tex]
[tex]\sqrt{20}[/tex] = [tex]2 \sqrt{5}[/tex]
Here, 2 and 5 are factors of 20.
Thus, the value of the radical expression [tex]\sqrt{20}[/tex] is [tex]2 \sqrt{5}[/tex].
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Write down the first three and last two terms of the binomial expansion of:
a) (3x+(2/x))^15
b) (2x-(3/x))^20
Answer:
a) [tex](3x)^{15} + 15(3x)^{14}(\frac{2}{x}) + 105(3x)^{13}(\frac{2}{x})^2 + ... + 15(3x)(\frac{2}{x})^{14} + (\frac{2}{x})^{15}[/tex]
b) [tex](2x)^{20} + 20(2x)^{19}(-\frac{3}{x}) + 190(2x)^{18}(-\frac{3}{x})^2 + ... + 20(2x)(-\frac{3}{x})^{19} + (-\frac{3}{x})^{20}[/tex]
Step-by-step explanation:
The binomial expansion formula is:
[tex](a + b)^n = a^n + \binom{n}{1}a^{n-1} b + \binom{n}{2}a^{n-2}b^2 + ... + \binom{n}{r}a^{n-r}b^{r} + ... + b^n[/tex]
The (n r) in front of each term is the binomial coefficient. This can be calculated on a calculator using the nCr button (in this case, you'd put 15C1 for (n 1), 15C2 for (n 2), etc). This can be calculated without a calculator using this formula:
[tex]\binom{n}{r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}[/tex]
In a), a = 3x, b = 2/x and n = 15.
You can plug these into the formula above to get:
[tex](3x)^{15} + 15(3x)^{14}(\frac{2}{x}) + 105(3x)^{13}(\frac{2}{x})^2 + ... + 15(3x)(\frac{2}{x})^{14} + (\frac{2}{x})^{15}[/tex]
Here's how to do this without the formula:
Start with the a^nIn the second term, you subtract 1 from a's power (in this case, 15 to 14) and add 1 to b's power (0 to 1). Then you multiply it by nCr.This keeps going until you get to b^n. To check you've done it correctly, the powers of a and b in each term should add up to n. For example, in term 3 above, a's power is 13 and b's power is 2. These add to make 15.Remember, a's power goes down by 1 each time, and b's power goes up by 1 each time. There is no b in the first term because b^0 = 1.You could 'simplify' this by expanding the brackets, but this gives you massive numbers so it's probably best to leave it like this.
Applying this to b):
a = 2x, b = -3/x, n = 20
[tex](2x)^{20} + 20(2x)^{19}(-\frac{3}{x}) + 190(2x)^{18}(-\frac{3}{x})^2 + ... + 20(2x)(-\frac{3}{x})^{19} + (-\frac{3}{x})^{20}[/tex]
fractions and decimals
T_T
1. 0.0563
2. 0.05
3. 0.008
4. 0.6
5. eight tenths
6. six tenths three hundredths
7. eight five thousandth
8. six hundredths
Which statements are true about the solution 2< x -7
Here the options
First one to reply within 5 minutes gets 100 points and brainlist
B. x > 9
D. The graph has open circle.
F. The arrow to the right.
Solving Steps:⇒ 2 < x - 7
⇒ 2 + 7 < x
⇒ 9 < x
⇒ x > 9
Explanation:Here as the inequality sign is ">" it will be a open circle.
Note: "≤" and "≥" inequality signs have closed circle.
As x > 9, the arrow points will be towards right.
A soccer player stands at a point that is modeled by (0, 0) on the coordinate plane.
he then kicks a soccer ball that is modeled by a quadratic equation.
select all key features that help determine the vertical height that the soccer ball
traveled from when it left the ground to when it reached its maximum height.
- y-intercept
- zeros
- vertex
- end behavior
Answer:
the answer to the question above would be the option 3 (vertex)
please help me
i need this for my homework
Answer:
As ΔABC is an isosceles triangle:
⇒ BA = BC
(the dashes on the line segments indicate they are of equal measure)
⇒ ∠BAC = ∠BCA = 55°
⇒ ∠BCA = ∠BAD = 55°
Angles on a straight line sum to 180°
⇒ ∠ADE + ∠EDC = 180°
⇒ 98° + ∠EDC = 180°
⇒ ∠EDC = 82°
As BE intersects AC, the vertically opposite angles are equal:
⇒ ∠BDC = ∠ADE = 98°
⇒ ∠ADB = ∠EDC = 82°
Interior angles in a triangle sum to 180°
⇒ ∠BAD + ∠ADB + ∠ABD = 180°
⇒ 55° + 82° + ∠ABD= 180°
⇒ ∠ABD = 180° - 55° - 82°
⇒ ∠ABD = 43°
Answer:
∠ABD = 43°
Step-by-step explanation:
Let's solve !
⇒ ∠BAC = ∠BCA = 55° (Angles opposing equal sides)
⇒ ∠BDA = 180° - 98° (Linear pair)
⇒ ∠BDA = 82°
⇒ ∠BAC + ∠BDA + ∠ABD = 180° (Angle Sum Property)
⇒ ∠ABD + 82° + 55° = 180°
⇒ ∠ABD + 137° = 180°
⇒ ∠ABD = 43°
The quadrilaterals JKLM and PQRS are similar.
Find the length x of QR.
K
Q
7
M
2
Z
3.6
S
1.8
A
X
3.6
R
Answer:
x = 6.3
Step-by-step explanation:
since the quadrilaterals are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{QR}{KL}[/tex] = [tex]\frac{RS}{LM}[/tex] ( substitute values )
[tex]\frac{x}{7}[/tex] = [tex]\frac{3.6}{4}[/tex] ( cross- multiply )
4x = 7 × 3.6 = 35.2 ( divide both sides by 4 )
x = 6.3
Can someone help pls
Answer:
B.) No, because it fails the vertical line test.
Step-by-step explanation:
You can determine whether or not graphs represent functions by performing the vertical line test. This test states that to be a function, there must only be one output for every input. In other words, there must be only one "y" value per "x" value. As you can see, for some "x" values there is more than one "y" value.
The easiest way to perform this test is by placing your finger at the top of the graph and moving it downwards. If you cross the line twice, then it must not be a function.
What is the measure of USQ⌢
- 34+(- 23) please fast
Answer:
The answer to this question is -11
did I solve this problem right?
Step-by-step explanation:
¿qué es eso?¿es esto importante? :)
What is the area of a circle with a radius of 21?
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
[tex]\textsc{heya!}[/tex]
we need to find the area of a circle with a radius of 21.
we also need a formula for this, which is
⇒ [tex]\bold{A=\pi r^2}[/tex]
the known value is r, radius, 21.
after substituting the value into the formula, we obtain:
⇒ [tex]\bold{A=\pi (21)^2}[/tex]
now we multiply the radius times itself:
⇒[tex]\bold{A=\pi *441}[/tex]
which can be written as
⇒[tex]\bold{A=441\pi}[/tex]
and finally, multiply the values
⇒ [tex]\bold{A=1385.4\;units\;^2}[/tex]
[tex]\textsc{hopefully\:helpful}[/tex]
by: [tex]\textsc{$^da_nc^in_g$}[/tex]
have a great rest of your day ahead ~ = )
Mark is a professional race car driver. He has competed in 15 races and won 40% of them. How many races has Mark won?
3 races
6 races
9 races
37 races
Answer:
6 races
Step-by-step explanation:
If he won 40% of the races he competed in, and he raced 15 times, this means that he won roughly 4/10 races.
4/10= ?/15
cross multiply 4 and 15 = 60
60/10 = 6
He won 6 races
Give brainliest please!
hope this helps :)
sectors of circle. east points, this is due tomorrow help is appreciated
The big arc is 2.09 centimeters longer than the small arc.
How much longer is the big arc than the small arc?For a circle of radius R, if we define an arc with an angle θ, the length of that arc will be:
L = (θ/360°)*2πR
Where π = 3.14
in this case, for both arcs, we have θ = 120°.
For the smaller arc, the radius is R = 5cm, so we get:
L = (120°/360°)*2*3.14*5cm = 10.47 cm
For the larger arc, the radius is R = 5cm, so we get:
L' = (120°/360°)*2*3.14*6cm = 12.56 cm
Then we can see that:
L' - L = 12.56 cm - 10.47 cm = 2.09 cm
So the largest arc is 2.09 centimeters longer than the smaller arc.
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The diameter of a circle is 12 miles. What is the circle's area use 3.14
Step-by-step explanation:
Are of a circle is πr^2
to find the radius r=d/2
=12/2=6r
3.14x6x6
=169.56 cm^2
please mark as brainliest
A triangle has a base length of 2ac2 and a height 6 centimeters more than the base length. Find the area of the triangle if a = 4 and c = 2.
The area of the triangle is 608 cm².
What is area?Area is the region bounded by a plane shape.
To calculate the area of the triangle, we use the formula below.
Formula:
A = bh/2............................ Equation 1Where:
A = Area of the triangleb = Base of the triangleh = Height of the triangleFrom the question,
Given:
b = 2ac²If
a = 4, c = 2b = (2×4×2²) = 32 cmh = (32+6) = 38 cmSubstitute these values into equation 1
A = (32×38)/2A = 608 cm²Hence, the area is 608 cm².
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10 A group of young men decided to raise sh 480 000 to start a business.. Before the actual payment was made, four of the members pulled out and each of those remaining had to pay an additional sh 20 000. Determine the original number of members.
A group of young men decided to raise Ksh.480000 to start a business. Before actual payment was made four members pulled out and each of the remaining had to pay an additional Ksh.20000. Write an expression in terms of P for.
(a) (i) Original contribution of each member.
(ii) Contribution after withdrawal of four members.
(b) Form an equation in P and hence determine the number of initial members.
(c) Three men Kamau, James and Hassan shared Shs.480000 such that Kamau: James is 3: 2 and James: Hassan is 4: 2. Find how much each got.
An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 31 feet up. The ladder makes an angle of 78
with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.
Answer:
30.7 ft ladder length
Step-by-step explanation:
The ladder makes the hypotenuse of a right triangle
31 feet is the opposite leg of 78 degree angle
sin 78 = opposite / hypotenuse
sin 78 = 30/ hypot
30 / (sin 78 ) = hypotenuse = 30.7 ft
Answer:31.7
Step-by-step explanation:
Given various values of the linear functions f(x) and g(x) in the table, determine the y-intercept of (f- g)(x).
X -6 -4 -1 3 4
f(x) 15 11
5 -3 -5
g(x) -36 -26 -11 9 14
O (0,9)
O (0, 3)
O (0, -3)
O (0, -9)
The y-intercept of linear function (f- g)(x) is (0,9)
How to determine the y-intercept?The table of values is given as:
x -6 -4 -1 3 4
f(x) 15 11 5 -3 -5
g(x) -36 -26 -11 9 14
The equations of the functions is calculated using:
[tex]y = \frac{y_2 -y_1}{x_2-x_1} * (x -x_1) + y_1[/tex]
So, we have:
[tex]f(x) = \frac{11 -15}{-4 + 6} * (x + 6) + 15[/tex]
Evaluate
f(x) = -2x + 3
Also, we have:
[tex]g(x) = \frac{-26 + 36}{-4 + 6} * (x + 6) - 36[/tex]
Evaluate
g(x) = 5x - 6
Next, we calculate (f - g)(x) using:
(f - g)(x) = f(x) - g(x)
This gives
(f - g)(x) = -2x + 3 - 5x + 6
Substitute 0 for x
(f - g)(0) = -2(0) + 3 - 5(0) + 6
Evaluate
(f - g)(0) = 9
Hence, the y-intercept of (f- g)(x) is (0,9)
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An angle of measure to the angle opposite it is a right angle. True or false
Answer:
True
Step-by-step explanation:
Rewrite as a simplified fraction. 3.16 (6 is repeating)
0.16 (with 6 repeating) = 1/6
3.16 = 3 1/6
Mixed Number = 3 1/6
Improper Fraction = 19/6
Hope this helps!
Answer:
3 4/25
Step-by-step explanation:
[tex]\frac{3.16}{1} \cdot \frac{100}{100} = \frac{316}{100}[/tex]
[tex]\frac{316 \div 4}{100 \div 4} = \frac{79}{25}[/tex]
[tex]= 3\frac{4}{25}[/tex]
what is a good approximating for 4pi^3
Answer: 123.84
Step-by-step explanation: You can set pi as 3.14. Then, you get 123.836576. Round to the nearest hundredth to get 123.84.
could someone please help will give brainliest
Answer:
A - x = 4
Step-by-step explanation:
According to The Midsegment Trapezoid Theorem the length of the midsegment is the sum of both bases divided by 2.
So to find the value of x:
x + 3 + 4x 7 = 15*2 add like terms
5x + 10 = 30 subtract 10 from both sides
5x = 20 divide both sides by 5
x = 4
if abcd is a parallelogram with AB=3x-4 , BC= 2x+7 and CD = x+18 what type of paralleogram is ABCD
Answer:
rhombus
Step-by-step explanation:
If ABCD is a parallelogram, then AB and CD are opposite sides and should be equal
3x - 4 = x + 18
subtract x.
2x - 4 = 18
add 4.
2x = 22
divide by 2.
x = 11
Find the lengths of the sides.
AB= 3(11)-4 = 29
BC= 2(11)+7 = 29
CD = 11+18 = 29
If BC is 29, then DA must also be 29. So all four sides are the same, it is a rhombus.
Is believed that 80% of adults are honest an honesty experiment was conducted on a random sample of 50 adultsit was discovered that 42 of the adults were honestthe researcher would like to know if the data provide convincing evidence that more than 80% of adults are honest are the conditions for inference met? yesthe conditions for inference are met no, the 10% condition is not met no, the large counts condition is not met no, the randomness condition is not met
The first option, “yes, the conditions for inference are met” is correct.
What are population and sample?It is described as a collection of data with the same entity that is linked to a problem. The sample is a subset of the population, yet it is still a part of it.
Lets you're conducting an experiment on the honesty of a random sample of 50 persons. A total of 42 adults were assessed to be trustworthy.
It has to be determined whether the conditions of inference are satisfied.
A) The randomness of the sample.
The sample is given to be randomly selected. So, this condition is satisfied.
B) The number of success and failures must be at least 10.
The success rate is 0.80, and the sample size is 50. As a result, the following conditions must be met:
[tex]\rm n_p\geq 10 \ and \ n\left ( 1-p \right )\geq 10[/tex]
[tex]\rm 50\left ( 0.80 \right )=40 > 10[/tex]
[tex]\rm 50\left ( 1-0.80 \right )=10=10[/tex]
As a result, the sample size is sufficient, and the big numbers requirement is met.
C) 10% condition:
The sample size is modest, at 50 people, and hence represents less than 10% of the population.
As a result, the inference requirements are met.
Thus, the first option “yes, the conditions for inference are met” is correct.
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WILL GIVE BRAINLIEST Help me please! The questions are in the photos below.
Triangle PQR is given to be a right triangle, so the Pythagorean theorem can be used to determine that RQ² + PR² = PQ².
What is Pythagorean theorem?Pythagorean theorem is a mathematical expression in Euclidean geometry that can be used to solve for any of the three (3) side lengths of a right triangle.
Mathematically, Pythagorean's theorem is given by this formula:
x² + y² = z²
Triangle PQR is given to be a right triangle, so the Pythagorean theorem can be used to determine that RQ² + PR² = PQ². It is given that x² + y² = z² in triangle ABC, so z² = PQ² or AB = PQ.
The above information shows that the triangles are congruent because their three (3) sides are congruent. Therefore, to show that triangle PQR is a right triangle, we can use corresponding parts of the congruent triangles to show that PQ = AB, PR = AC and QR = BC.
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Question 2 of 10
If
f(x) = 4x-3, which of the following is the inverse of f(x)?
O A. f¹(x) = 4x+3
7
○ B. /-¹(x) = 7x-3
4
O c. f¯¹(x) = 4x-3
7
178x991x001 =? solve for brainiest
Answer:
176398Step-by-step explanation:
That comes out, hopefully it's not failing
Answer:
176,398
It wont always be easy, but always try to do what ' s right!
In a world of worriers, be the warrior!
When nothing goes right, go left.
1. There are 10 cards. 4 of them are of green color and another 6 are of
orange color. Steve picks a card at random. What is the
probability of green?
PLEASE HELPPP ITS WORTH 20 points!!!
Answer:
tanD =4/7
Step-by-step explanation:
tanD = P/B
Where P=4 and B=7
So;
tanD=4/7
Complete the function table.
Input (n) Output (n − 3)
0
2
8
A function assigns the value of each element of one set to the other specific element of another set. The output for the given inputs 0, 2, and 8 in the table is -3, -1, and 5, respectively.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
For the given function table, the function table can be filled as,
Input (n) Output (n − 3)
0 (0 - 3) = -3
2 (2 - 3) = -1
8 (8 - 3) = 5
Hence, the output for the given inputs 0, 2, and 8 in the table is -3, -1, and 5, respectively.
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