Answers
[tex]\frac{x}{2}-2+2x^2+x-3=2x^2+\frac{2}{2}x+\frac{1}{2}x-2-3=[/tex]
[tex]2x^2+\frac{3}{2}x-5[/tex]
[tex](f+g)(x)=2x^2+\frac{3}{2}x-5[/tex]
Related Questions
Express each repeating decimal as a fraction.
1.
1.8[4]
2.
2.1[26]
Answers
1.8444444....=1.8+1/10*0.44444....
=1.8+1/10*4/9
=1.8+4/90
=162/90+4/90
=166/90
=83/45
2.126262626...=2.1+1/10*0.262626...
=2.1+1/10*26/99
=2.1+26/990
=2079/990+26/990
=2105/990
=421/198
Answer:
1.8444444....=1.8+1/10*0.44444....
=1.8+1/10*4/9
=1.8+4/90
=162/90+4/90
=166/90
=83/45
2.126262626...=2.1+1/10*0.262626...
=2.1+1/10*26/99
=2.1+26/990
=2079/990+26/990
=2105/990
=421/198
Distributive property of 68/4
Answers
The trick here is to rewrite 68 as 4(17).
Find the range of the graphed function?
Answers
B is true
B is the correct answer
Solve For L: A = L ⋅ W ⋅ H
L=aw/h
L=wh/a
L=a/wh
L=w/ha
Answers
A=L*WH
[tex] \frac{A}{WH} [/tex]=L
So you answer would be: C
Store A advertises a sale for 3 loaves of bread for $5.94. Explain how to use an equivalent rate to find the unit price of the bread at Store A.
Answers
Answer: I wrote the rate, with $5.95 in the numerator and 3 loaves in the denominator. I needed to find an equivalent rate expressed as a fraction with the denominator of 1. I noticed 3 loaves divided by 3 gave a denominator of 1, so I divided $5.94 by 3 to find that each loaf costs $1.98.
Just did it on Edge 2021
Btw Can you mark me brainlest pls
The equivalent rate of the bread is $1.98.
Since the store advertises a sale for 3 loaves of bread for $5.94, in order to find the equivalent rate, the person has to divide $5.94 by 3. This will be:
= $5.94/3
= $1.98
Therefore, the equivalent rate of the loaves of bread will be $1.98
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I have 5 digits. My 4s are worth 4 [10,000s] and 4 * 10. One of my 3s is worth 3,000. The other is worth 1/10 as much. My other digit is a 2. What number am I?
Answers
4(10,000) + 4(10) + 3,000 + 3,000(1/10) + 2 = 43,342
Thus, the 5-digit number is 43,342.
Tyquan uses the greatest common factor and the distributive property to rewrite this sum: 75 + 60 What expression does Tyquan write? 3(25 + 20) 5(15 + 12) 25(3 + 60) 15(5 + 4)
Answers
75/15 = 5
60/15 = 4
so ur expression is : 15(5 + 4) <==
There are six different sixth roots of 64. That is, there are six complex numbers that solve x^6=64
Please help
Answers
1)
When we know that:
[tex]\sqrt[n]{z}=\sqrt[n]{|z|}\Big(\cos\frac{\phi+2k\pi}{n}+i\sin\frac{\phi+2k\pi}{n}\Big)\qquad\text{for}\quad k=0,1,\ldots,n-1[/tex]
when [tex]z=|z|(\cos\phi+i\sin\phi)[/tex]
then:
[tex]x^6=64\quad|\sqrt[6]{(\ldots)}\\\\x=\sqrt[6]{64}[/tex]
For [tex]x=64[/tex] we have:
[tex]64=|64|(\cos0+i\sin0)\quad\Rightarrow\quad \phi=0[/tex]
and:
[tex]\sqrt[6]{64}=\sqrt[6]{64}\Big(\cos\frac{0+2k\pi}{6}+i\sin\frac{0+2k\pi}{6}\Big)\qquad\text{for}\quad k=0,1,\ldots,5\\\\\\ \sqrt[6]{64}=2\Big(\cos\frac{k\pi}{3}+i\sin\frac{k\pi}{3}\Big)\qquad\text{for}\quad k=0,1,\ldots,5 [/tex]
k = 0
[tex]2\Big(\cos\frac{0}{3}+i\sin\frac{0}{3}\Big)=2(1+0i)=2\cdot1=\boxed{2}[/tex]
k = 1
[tex]2\Big(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\Big)=2\Big(\frac{1}{2}+i\frac{\sqrt{3}}{2}\Big)=\boxed{1+i\sqrt{3}}[/tex]
k = 2
[tex]2\Big(\cos\frac{2\pi}{3}+i\sin\frac{2\pi}{3}\Big)=2\Big(-\frac{1}{2}+i\frac{\sqrt{3}}{2}\Big)=\boxed{-1+i\sqrt{3}}[/tex]
k = 3
[tex]2\Big(\cos\frac{3\pi}{3}+i\sin\frac{3\pi}{3}\Big)=2\Big(\cos\pi+i\sin\pi\Big)=2(-1+0i)=\boxed{-2}[/tex]
k = 4
[tex]2\Big(\cos\frac{4\pi}{3}+i\sin\frac{4\pi}{3}\Big)=2\Big(-\frac{1}{2}-i\frac{\sqrt{3}}{2}\Big)=\boxed{-1-i\sqrt{3}}[/tex]
k = 5
[tex]2\Big(\cos\frac{5\pi}{3}+i\sin\frac{5\pi}{3}\Big)=2\Big(\frac{1}{2}-i\frac{\sqrt{3}}{2}\Big)=\boxed{1-i\sqrt{3}}[/tex]
So the answer is:
[tex]x=\{2,\,1+i\sqrt{3},\,-1+i\sqrt{3},\,-2,\,-1-i\sqrt{3},\,1-i\sqrt{3}\}[/tex]
2)
We don't know method (1). If so, we could use following identities:
[tex](1)\quad a^2-b^2=(a+b)(a-b)\\\\(2)\quad a^3-b^3=(a-b)(a^2+ab+b^2)\\\\(3)\quad a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
There will be:
[tex]x^6=64\\\\x^6-64=0\\\\(x^3)^2-8^2=0 \qquad\text{from (1)}\\\\(x^3+8)(x^3-8)=0\\\\(x^3+2^3)(x^3-2^3)=0\qquad\text{from (2) and (3)}\\\\ (x+2)(x^2-2x+4)(x-2)(x^2+2x+4)=0\qquad(\star)[/tex]
Now, we complete the square for:
[tex]x^2-2x+4=x^2-2x+1+3=(x^2-2x+1)+3=(x-1)^2+3=\\\\=(x-1)^2+(\sqrt{3})^2=(x-1)^2-(-1)(\sqrt{3})^2=(x-1)^2-i^2(\sqrt{3})^2=\\\\=(x-1)^2-(i\sqrt{3})^2=\text{from (1)}=\boxed{(x-1-i\sqrt{3})(x-1+i\sqrt{3})}[/tex]
and for:
[tex]x^2+2x+4=x^2-2x+1+3=(x^2+2x+1)+3=(x+1)^2+3=\\\\=(x+1)^2+(\sqrt{3})^2=(x+1)^2-(-1)(\sqrt{3})^2=(x+1)^2-i^2(\sqrt{3})^2=\\\\=(x+1)^2-(i\sqrt{3})^2=\text{from (1)}=\boxed{(x+1-i\sqrt{3})(x+1+i\sqrt{3})}[/tex]
When we return to [tex](\star)[/tex]:
[tex](x+2)(x^2-2x+4)(x-2)(x^2+2x+4)=0\\\\(x+2)(x-1-i\sqrt{3})(x-1+i\sqrt{3})(x-2)(x+1-i\sqrt{3})(x+1+i\sqrt{3})=\\=0[/tex]
And we have answer:
[tex]x=\{-2,\,1+i\sqrt{3},\,1-i\sqrt{3},\,2,\,-1+i\sqrt{3},\,-1-i\sqrt{3}\} [/tex]
To find the six sixth roots of 64, you can use polar form and De Moivre's Theorem to calculate the complex numbers. The roots are 2, 1+i√3, -1+i√3, -2, -1-i√3, and 1-i√3.
[tex]X^6 = 64[/tex]
The sixth roots of 64 are complex numbers and can be found by writing 64 in polar form and applying De Moivre's Theorem. Let's find the six roots:
First root: 2(cos(0) + i sin(0)) = 2
Second root: 2(cos(π/3) + i sin(π/3)) = 2(1/2 + i√3/2) = 1 + i√3
Third root: 2(cos(2π/3) + i sin(2π/3)) = 2(-1/2 + i√3/2) = -1 + i√3
Fourth root: -2
Fifth root: -2(cos(-π/3) + i sin(-π/3)) = -2(1/2 - i√3/2) = -1 - i√3
Sixth root: -2(cos(-2π/3) + i sin(-2π/3)) = -2(-1/2 - i√3/2) = 1 - i√3
How many pairs of whole numbers have a sum of 99
Answers
Which of the following is a true equation?
1) 10 + 3 + 1 = 13 + 6
2) 4 - 3 = 7
3) 4 + 3 - 3 = 7 - 3
4) 4 + 3 = 7 + 3
Answers
4 = 4
answer
3) 4 + 3 - 3 = 7 - 3
domain of the function
Answers
y exist : x+6 ≥ 0
x ≥ -6
What is the value of x? 58 92 121 63
Answers
126/2 = x
63 = x
Answer:
Angle x = 63 °.
Step-by-step explanation:
Given : A circle larger arc angle 184° and smaller arc angle 58°.
To find: What is the value of x.
Solution : We have given that larger arc angle 184°
Smaller arc angle 58°.
Angle formed by tangent and chord = x
m∠x = [tex]\frac{1}{2}( 184 - 58 )[/tex].
m∠x = [tex]\frac{1}{2}( 126)[/tex].
m∠x = 63 °.
Therefore, Angle x = 63 °.
A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth. Area of a triangle = bh
Answers
Answer:
162.8 cm²
Step-by-step explanation:
The formula for the area of a triangle is
A = 1/2bh, where b is the base and h is the height.
The base can be represented as the given leg, 27.6 cm. We do not know the height. We must use the Pythagorean theorem to find this:
a²+b² = c²
27.6²+b² = 30²
761.76+b² = 900
Subtract 761.76 from each side:
761.76+b²-761.76 = 900-761.76
b² = 138.24
Take the square root of each side:
√(b²) = √(138.24)
b = 11.8
Now we use the area formula:
A = 1/2(11.8)(27.6) = 162.84 ≈ 162.8
The area of a given right triangle is 162.8 cm².
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
Given that, the base can be represented as the given leg, 27.6 cm. We do not know the height.
Using Pythagorean theorem,
a²+b² = c²
27.6²+b² = 30²
761.76+b² = 900
761.76+b²-761.76 = 900-761.76
b² = 138.24
b = √(138.24)
b = 11.8
The formula for the area of a triangle is
A = 1/2bh, where b is the base and h is the height
A = 1/2(11.8)(27.6) = 162.84 ≈ 162.8
Therefore, the area of a given right triangle is 162.8 cm².
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Use the function below to find f(4).
Answers
f(4) = 1/3 * 4^4
f(4) = 1/3 * 256
f(4) = 256/3 <===
Answer: The correct option is (C) [tex]\dfrac{256}{3}.[/tex]
Step-by-step explanation: The given function is
[tex]f(x)=\dfrac{1}{3}\times 4^x.[/tex]
We are to find the value of f(4).
To find the value of f(4), we need to substitute the value of x as 4 in the given definition of function f(x).
Substituting x = 4 in f(x), we have
[tex]f(4)=\dfrac{1}{3}\times 4^4=\dfrac{1}{3}\times 256=\dfrac{256}{3}.[/tex]
Therefore, the value of f(4) is [tex]\dfrac{256}{3}.[/tex]
Option (C) is correct.
what is (9x^4-x^2y^2-5y^4)-(3x^4+2x^2y^2-7y^4)
Answers
9x⁴ - x²y² - 5y⁴ - 3x⁴ - 2x²y² + 7y⁴
6x⁴ - 3x²y² + 2y⁴
There are 60 minutes in 1 hour. What fraction of an hour is 4 minutes? Write your answer in lowest terms.
Answers
Divide the numerator and denominator by 4
1/15
Final answer: 1/15
The fraction of an hour is 4 minutes in lowest terms is 1/15.
What fraction of an hour is 4 minutes in lowest terms?To find the fraction of an hour that 4 minutes represents, we need to compare the number of minutes to the total number of minutes in an hour, which is 60.
We can set up a fraction where the numerator represents the number of minutes we want to find the fraction for (4 minutes) and the denominator represents the total number of minutes in an hour (60 minutes).
So, the fraction can be written as 4/60.
To simplify the fraction to its lowest terms, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 60 is 4.
Dividing both the numerator and denominator by 4, we get:
4/60 = (4 ÷ 4) / (60 ÷ 4) = 1/15.
Therefore, 4 minutes in lowest terms is equal to 1/15th of an hour.
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How do write 21,070 in standard form
Answers
Final answer:
The number 21,070 is already in standard form. Standard form is a straightforward expression of a number as commonly written, without the need for scientific notation for simple numbers like this one.
Explanation:
The number 21,070 written in standard form is simply 21,070 itself. In mathematics, standard form refers to the way a number is commonly written. This number is already in standard form because it is expressed in a direct and straightforward manner. There is no need for further simplification or conversion. When numbers are very large or very small, they can be cumbersome to write out in full, which is why scientists and mathematicians may use scientific notation to express them.
For instance, if we had a larger number like 77,123,450, we could write it in scientific notation as 7.712345 × 10⁷, emphasizing that it is 7.712345 times ten to the seventh power.
For the provided number 21,070, no such conversion is necessary, and it remains 21,070 in standard notation.
The sample variance is 18.7. what is the sample standard deviation? answer to two decimal places.
Answers
What is 8.038×108 in standard form?
80,308,000
80,380,000
83,800,000
803,800,000
Answers
Answer:
803,800,000
Step-by-step explanation:
8.038×10^8 in standard form
To get standard form we multiply the decimal number by 10^8
10^8 is 100000000
Now we multiply
8.038×100000000
Move the decimal number 3 places to the right and add 5 more zeros
803800000
So the standard form of the given expression is
803,800,000
What is the value of x?
6 + 8x
-------------- = 5x
2
A) -2
B) -1
C) 1/3
D) 3
Answers
The tensile strength of paper is modeled by a normal distribution with a mean of 35 pounds per square inch and a standard deviation of 2 pounds per square inch. what is the probability that the strength of a sample is less than 38 lb/in2? round your answer to 4 decimal places.
Answers
mean=35 psi
std dev=2 psi
distribution normal
For probability that X<38,
calculate
Z score = (X-mean)/std dev
=(38-35)/2=1.5
P(X<38)
=P(Z<1.5)
=0.9331928 from tables.
So probability that the strength of a random sample <38 pis = 0.9332
Besides the 90° angle measure, what are the other two angle measures of a right triangle with side lengths 5, 12, and 13? Round to the nearest degree.
Answers
Let α be the angle opposite to the side with a length of 12 units, then according to the Law of sines:
[tex] \frac{13}{sin90^o}= \frac{12}{sin \alpha } \ \ \to \ \ sin \alpha = \frac{12 \cdot sin90^o}{13}= \frac{12*1}{13} \approx 0.923 \ \ \to \ m\angle \alpha \approx 67^o[/tex]
In a triangle, the three interior angles always add to 180° ⇒
third angle = 180 - 90 - 67 = 23°
Answer:
67° and 23° (to the nearest degree).
The other two angles are 23 degrees and 67 degrees.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given,
Given a right angled triangle with one angle 90 degrees.
We need to find the other two angle measures of a right triangle with side lengths 5, 12, and 13
The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.
The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.
The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.
In this problem, the hypotenuse is the largest size of 13.
The angle opposite to the side of length 5 is found as follows:
sinθ=5/13
θ=sin⁻¹5/13
θ=23
By angle sum of 3 angles is of 180º, the other angle is of 67º.
Hence, the other two angles are 23 degrees and 67 degrees.
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Simplify the expression 3 1/3/3 1/3. Explain how the expression and its simplified form show that the set of irrational numbers is not closed under division
Answers
From the context, I assume it to mean
(3^(1/3)) / (3^(1/3)) = 1
Since 3^(1/3) is the cube-root of 3, and is thus irrational.
However, the quotient is exactly 1, which is a rational number.
The example is therefore a counter-example for the statement that "set of irrational numbers is closed under division", or stated differently,
"the set of irrational numbers is not closed under division"
McDonald's is the king of the burger world, as it has more hamburger joints than any other restaurant chain. In 2013, McDonald's had 1427 locations in Canada. If the population of Canada was approximately 35.16 million citizens in 2013, what was the number of McDonald's restaurants per capita in Canada in 2013? Express your answer in scientific notation rounded correctly to three decimal places.
Answers
In 2013, there were approximately 4.509 McDonald's restaurants per 100,000 people in the US.
To calculate the number of McDonald's restaurants per capita in the US in 2013, we divide the total number of McDonald's locations (14267) by the population of the US (316,500,000).
[tex]\[ \text{McDonald's per capita} = \frac{14267}{316500000} \][/tex]
Performing the division, we get [tex]\( 4.509 \times 10^{-5} \)[/tex].
This means there were approximately 4.509 McDonald's restaurants per 100,000 people in the US in 2013.
So, the number of McDonald's restaurants per capita in the US in 2013 is [tex]\( 4.509 \times 10^{-5} \) or \( 4.509 \times 10^{-5} \)[/tex] McDonald's per person.
In the numer 6,666.666 how does the 6 in the hundredths place compare to 6 in the place to its left
Answers
the six to the left is worth more than the six in the hundredths
hope
i helped
the 6 in the hundreths place is 1/10 the value of the 6 in the place to the left
The following formula relates three quantities force mass and acccelerations
F=ma
Answers
Bess practices trumpet 1/2 hr on Monday and 1 3/5 hr on Wednesday.
How many hours does Bess practice trumpet?
Answers
You want to replace the countertops in a kitchen. One counter measures 24 inches by 6 feet. The other is 30 inches by 4 feet. If the new countertop costs $42.00 per square foot, what will be the cost of the new top?
Answers
2 ft x 6 ft=12 square feet
2.5 ft x 4 ft=10 square feet
Total square feet of the counter is 22 square feet.
To find the total cost, just multiply the area by the cost per square foot.
$42 x 22=$924
Answer:
The cost of the new top $924.
Step-by-step explanation:
You want to replace the counter-tops in a kitchen.
The dimensions of the first counter is 24 inches by 6 feet.
i.e [tex]24 \text{ inch} \times 6 \text{ feet}[/tex]
or [tex]2\text{ feet} \times 6 \text{ feet}[/tex]
As 1 feet =12 inches
Hence the area of the counter is [tex]2\times 6=12\text{ feet}^2[/tex]
The dimensions of the second counter is 30 inches by 4 feet.
i.e [tex]30 \text{ inch} \times 4 \text{ feet}[/tex]
or [tex]2.5\text{ feet} \times 4 \text{ feet}[/tex]
Hence the area of the counter is [tex]2.5\times 4=10\text{ feet}^2[/tex]
Hence, the total area will be [tex]12+10=22 \text{ feet}^2[/tex]
The unit cost of the counter-top is [tex]\$42.00\text{ feet}^2[/tex]
So the net cost will be,
[tex]=42\times 22=\$924[/tex]
Jacks has 18 marbles,he loses 6 of them.
What fraction of the marbles does he lose?
Answers
1/3
Hope this helps!
A coin is tossed 10 timesWhat is the probability of getting all heads?
Answers
there is two sides, one head an one tail, or 1/2 chance of getting heads
Tossed 10 times, it still has 1/2
hope this helps