What metamorphic rock has nonfoliated texture?
Answer:
Marble, quartzite, and soapstone.Step-by-step explanation:
Non-foliated metamorphic rocks are those which don't have a rough texture, like foliated ones, their composition gives them this characteristics: not having layers or banded appearance.
Evan’s family drove to a theme park for vacation. Assume they drove the same speed throughout the trip. The first day, they drove 300 miles in 6 hours. The second day, they drove 250 miles in 5 hours. The third day, they arrived at the park by driving ________ miles in 3 hours. Which number correctly fills in the blank?
300/6 = 50 mph
250/5 =50mph
so they drove 50 miles per hour
so 50 *3 = 150 miles in 3 hours
A teacher has 100 pencils in a cup. 16 are more sharp than dull. How many are dull and how many are sharp?
A tortoise is walking in the desert. It walks for 3 minutes at a speed of 7.5 meters per minute. For how many meters does it walk?
Find the indefinite integral of [tex] \int\limits {\frac{5}{x^\frac{1}{2}+x^\frac{3}{2}} \, dx [/tex]
I have been able to simplify it to [tex] \int\limits {\frac{5\sqrt{x}}{x^3+x}} \, dx [/tex] but that is confusing,
I then did u-subsitution where [tex]u=\sqrt{x}[/tex] to obtain [tex] \int\limits {\frac{5u}{u^6+u^2}} \, dx [/tex] which simplified to [tex] \int\limits {\frac{5}{u^5+u}} \, dx [/tex], a much nicer looking integrand
however, I am still stuck
ples help
show all work or be reported
Answer:
[tex] \displaystyle10 \tan^{-1}( \sqrt {x}^{ } ) + \rm C[/tex]
Step-by-step explanation:
we would like to integrate the following integration:
[tex] \displaystyle \int \frac{5}{ {x}^{ \frac{1}{2} } + {x}^{ \frac{3}{2} } } dx[/tex]
in order to do so we can consider using u-substitution
let our
[tex] \displaystyle u = {x}^{ \frac{1}{2} } \quad \text{and} \quad du = \frac{ {x}^{ - \frac{1}{2} } }{2} [/tex]
to apply substitution we need a little bit arrangement
multiply both Integral and integrand by 2 and ½
[tex]\displaystyle 2\int \frac{1}{2} \cdot\frac{5}{ {x}^{ \frac{1}{2} } + {x}^{ \frac{3}{2} } } dx[/tex]
factor out [tex]x^{\frac{1}{2}}[/tex]:
[tex]\displaystyle 2\int \frac{1}{2 {x}^{ \frac{1}{2} } } \cdot\frac{5}{ (1+ {x}^{ } )} dx[/tex]
recall law of exponent:
[tex]\displaystyle 2\int \frac{ {x}^{ - \frac{1}{2} } }{2 } \cdot\frac{5}{ (1+ {x}^{ } )} dx[/tex]
apply substitution:
[tex]\displaystyle 2\int \frac{5}{ 1+ {x}^{ } } du[/tex]
rewrite x as [tex]\big(x^{\frac{1}{2}}\big)^{2}[/tex]:
[tex]\displaystyle 2\int \frac{5}{ 1+ ( {x ^{ \frac{1}{2} } })^{ 2 } } du[/tex]
substitute:
[tex]\displaystyle 2\int \frac{5}{ 1+ ( u)^{ 2 } } du[/tex]
recall integration rule of inverse trig:
[tex] \displaystyle 2 \times 5 \tan^{-1}(u)[/tex]
simplify multiplication:
[tex] \displaystyle10 \tan^{-1}(u)[/tex]
substitute back:
[tex] \displaystyle10 \tan^{-1}( {x}^{ \frac{1}{2} } )[/tex]
simplify if needed:
[tex] \displaystyle10 \tan^{-1}( \sqrt{x} )[/tex]
finally we of course have to add constant of integration:
[tex] \displaystyle10 \tan^{-1}( \sqrt {x}^{ } ) + \rm C[/tex]
and we are done!
Pablo's gas tank is 3/10 full. after he buys 10 gallons of gas, it is 4/5 full. how many gallons can pablo's tank hold?
I need help in math will give Brainliest
Sarah competes in a long jump competition Her first jump is 4.25m Her best jump is 12% more than this However, her best jump is 15% lower than the winning jump Work out the length Of The winning jump
>First jump = 4.25 m
>Best jump = 1.12 * First jump
Best jump = 1.12 * (4.25 m)
Best jump = 4.76 m
>Best jump = 0.85 * Winning jump
Hence,
Winning jump = Best jump / 0.85
Winning jump = 4.76 m / 0.85
Winning jump = 5.6 m
What is the measurements of ENV
I got it wrong !!! Please help and explain
25 * 2.5 = 62.5 *2 = 125
8x5 = 40
125 +40 = 165 square feet
what is the value of x in the equation 6= x/4 - 4
Answer:
c
Step-by-step explanation:
What number is 8.2% of 50?
8.2% = 0.082
50 * 0.082 = 4.1
the answer is 4.1
Find the unit rate with the second given unit in the denominator.
72 football cards on 12 pages
A.
B.
C.
D.
Solve -3x^2-4x-4=0. Use the quadratic formula.
Answer:
[tex]x1=\frac{-2(+)2i\sqrt{2}} {3}[/tex]
[tex]x2=\frac{-2(-)2i\sqrt{2}} {3}[/tex]
Step-by-step explanation:
we have
[tex]-3x^{2} -4x-4=0[/tex]
Rewrite (Multiply by [tex]-1[/tex] both sides)
[tex]3x^{2}+4x+4=0[/tex]
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]3x^{2}+4x+4=0[/tex]
so
[tex]a=3\\b=4\\c=4[/tex]
substitute
[tex]x=\frac{-4(+/-)\sqrt{4^{2}-4(3)(4)}} {2(3)}[/tex]
[tex]x=\frac{-4(+/-)\sqrt{-32}} {6}[/tex]
remember that
[tex]i=\sqrt{-1}[/tex]
[tex]x=\frac{-4(+/-)4i\sqrt{2}} {6}[/tex]
Simplify
[tex]x=\frac{-2(+/-)2i\sqrt{2}} {3}[/tex]
[tex]x1=\frac{-2(+)2i\sqrt{2}} {3}[/tex]
[tex]x2=\frac{-2(-)2i\sqrt{2}} {3}[/tex]
Prove that there exists a unique real number solution to the equation x3 + x2 − 1 = 0 between x = 2/3 and x=1
To prove that there exists a unique real number solution to the equation x³ + x² - 1 = 0 between x = 2/3 and x = 1, we can use the Intermediate Value Theorem and the property of the derivative.
Explanation:To prove that there exists a unique real number solution to the equation x³ + x² - 1 = 0 between x = 2/3 and x = 1, we can use the Intermediate Value Theorem.
First, we substitute x = 2/3 into the equation and get a negative value (-1/27). Then, we substitute x = 1 into the equation and get a positive value (1).
Since the function is continuous between x = 2/3 and x = 1, and it changes sign, there must exist a solution somewhere between them.
To show that the solution is unique, we can use the fact that the derivative of the function, 3x² + 2x, is always positive for all real numbers.
This implies that the function is strictly increasing, so it can only intersect the x-axis at one point.
Last weekend Jane studied 4 2 3 hours for her history final and 4 1 4 hours for her math exam. How many hours in all did Jane study for the two tests?
Jane studied a total of 5 11/12 hours for her history final and math exam.
Explanation:To find the total number of hours Jane studied for the two tests, we add together the number of hours she studied for each test. Jane studied 4 2/3 hours for her history final and 4 1/4 hours for her math exam.
To add these fractions, we need to have a common denominator. The least common multiple of 3 and 4 is 12. We can convert 2/3 to 8/12 and 1/4 to 3/12.
Now we can add the fractions: 4 8/12 + 4 3/12 = 5 11/12.
Therefore, Jane studied a total of 5 11/12 hours for the two tests.
Final answer:
Jane studied a total of 7 3/4 hours for her history and math exams.
Explanation:
To find out how many hours Jane studied for the two tests, we simply need to add the hours she studied for each test together.
Jane studied 4 2/3 hours for her history final and 4 1/4 hours for her math exam.
We can add these two fractions by finding a common denominator and then adding the numerators.
In this case, the common denominator is 12. So, we have (4 * 4 + 2) / 3 = 18/3 and (4 * 3 + 1) / 4 = 13/4.
Adding these fractions together, we get (18/3) + (13/4) = 54/12 + 39/12 = 93/12. Simplifying this fraction, we get 7 3/4 hours.
Therefore, Jane studied a total of 7 3/4 hours for the two tests.
The length of a rectangle is twice its width. if the area of the rectangle is 200 yd2 , find its perimeter.
The perimeter of the rectangle is 60 yards
What is the Perimeter of a Rectangle?
The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P = 2 ( Length + Width )
Given data ,
Let the length of the rectangle be = a
Let the width of the rectangle be = b
The length of the rectangle is twice the width
So ,
a = 2b
The area of the rectangle is A = 200 yards²
The area of the rectangle is given by
Area of Rectangle = Length x Width
And , substituting the values for length and width , we get
Area of Rectangle = 2b x b
2b² = 200
Divide by 2 on both sides , we get
b² = 100
Taking square root on both sides , we get
b = 10
a = 2b
a = 20
Therefore , the length of the rectangle is 20 yards and width of the rectangle is 10 yards
Now , the perimeter of the rectangle is P = 2 ( length + width )
Perimeter of the rectangle P = 2 ( 10 + 20 )
= 2 x 30
= 60 yards
Hence , the perimeter of the rectangle is 60 yards
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Triangle abc has been translated to create triangle a'b'c'. angles c and c' are both 32 degrees, angles b and b' are both 72 degrees, and sides bc and b'c' are both 5 units long. which postulate below would prove the two triangles are congruent? sss sas asa hl
ASA
Is the answer i got on my work
Ice-Cream Palace has received an order for 3 1⁄2 gallons of ice-cream. The shop packages its ice-cream in 1-quart containers. How many containers will the shop need for this order?
Kate has 21 coins (nickels and dimes) in her purse. How many nickels and dimes does she have if she has $1.50? 3 nickels and 18 dimes 5 nickels and 16 dimes 12 nickels and 9 dimes 15 nickels and 6 dimes
Carlos's gas tank is 19 full. after he buys 6 gallons of gas, it is 13 full. how many gallons can carlos's tank hold
Answer:
25
Step-by-step explanation:
You are on the way to the ski slopes to spend the week. the mountains are 678 miles from your home. if you drive 75 miles an hour and take six 15-minute rest breaks, how much time will you need to make the trip? round your answer to the nearest tenth.
MATH HELP!!!!!!!!!!!!!
Compare rational numbers what is bigger 4.9 vs 4.6
The equations of two lines are x - 3y = 6 and y = 3x + 2. determine if the lines are parallel, perpendicular or neither.parallelperpendicularneither
When two angles are complementary what is the sum of their measures is 90 degrees. two complementary angles have the measure of 2x-10 degrees and 3x-10 degrees?
how to solve a complex number
Complex numbers are "binomials" of a sort, and are added, subtracted, and multiplied in a similar way. (Division, which is further down the page, is a bit different.) First, though, you'll probably be asked to demonstrate that you understand the definition of complex numbers.
Solve 3 – 4i = x + yiFinding the answer to this involves nothing more than knowing that two complex numbers can be equal only if their real and imaginary parts are equal. In other words, 3 = x and –4 = y.To simplify complex-valued expressions, you combine "like" terms and apply the various other methods you learned for working with polynomials.
Simplify (2 + 3i) + (1 – 6i).(2 + 3i) + (1 – 6i) = (2 + 1) + (3i – 6i) = 3 + (–3i) = 3 – 3i
Simplify (5 – 2i) – (–4 – i).(5 – 2i) – (–4 – i)= (5 – 2i) – 1(–4 – i) = 5 – 2i – 1(–4) – 1(–i)= 5 – 2i + 4 + i= (5 + 4) + (–2i + i)= (9) + (–1i) = 9 – iYou may find it helpful to insert the "1" in front of the second set of parentheses (highlighted in red above) so you can better keep track of the "minus" being multiplied through the parentheses.
Simplify (2 – i)(3 + 4i).(2 – i)(3 + 4i) = (2)(3) + (2)(4i) + (–i)(3) + (–i)(4i)= 6 + 8i – 3i – 4i2 = 6 + 5i – 4(–1)= 6 + 5i + 4 = 10 + 5iFinal answer:
To solve a complex number, understand it as a sum of a real number and an imaginary number and use operations like conjugation. For division, multiply by the conjugate to simplify. Complex numbers ensure all polynomial equations have solutions.
Explanation:
To solve a complex number, one must understand that a complex number z is the sum of a real number and an imaginary number, which is written as z = a + ib. The terms a and b represent the real and imaginary parts respectively, often notated as Re(z) and Im(z).
To divide by a complex number, you multiply the numerator and the denominator by the conjugate of the denominator, simplifying to a form without imaginary numbers in the denominator. This can be expressed as z/z' = (aa' + bb')/(a'² +b'²) + i(ba' - ab')/(a'² + b'²). The conjugate of a complex number z is written as z* or z*.
Complex numbers are crucial in solving polynomial equations as they ensure that every polynomial equation has a solution. This is shown by the Fundamental Theorem of Algebra, which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. For instance, the equation x² - 2x + 5 = 0 has no real solutions but two complex solutions, x = 1±2i.
Use synthetic division and the Remainder Theorem to find P(a).
P(x) = x3 + 4x2 − 8x − 6; a = −2
−2
0
18
20
Answer:
c: 18
Step-by-step explanation:
Which expression is equivalent to sin^2 x-sin x - 2/sin x -2
A. sin x + 1
B. sin x − 1
C. sin2x
D. -sin2x
Which statement is true?