Step-by-step explanation:
so you have the equation: [tex]\sqrt{32x^3y^2z^7}[/tex] which I'm assuming is what you meant to input. and the next step I'm assuming you wrote: [tex]\sqrt{8} * \sqrt{4} * \sqrt{x^2} * \sqrt{y^2} * \sqrt{x} * \sqrt{z^6} * \sqrt{z}[/tex], although I'm not 100% sure, I'm basing this assumption off of step 3. Anyways this will simplify to [tex]2xyz^3\sqrt{8xz}[/tex] which is correct kind of, but since they were asked to FULLY SIMPLIFY, then it's not completely done. This is because 8 has a factor of 4 which is a perfect square. This is because in step 1, the student rewrote 32 as sqrt(8) * sqrt(4) instead of writing it as sqrt(2) * sqrt(16) which is the greatest factor of 32 that is a perfect square. So they could've either done that in step 1, or they could've realized in step 2, that they can further simplify sqrt(8) and then have a step 3 showing that.
(-6) x 8
What is this ?????
Answer:
-(6) x 8
ans: - 48
I believe that is the ans:
Answer:
-48
Step-by-step explanation:
Integer multiplication:When we multiply a negative integer by a positive integer , we will get a negative integer.
(-6) * 8 = (-48)
negative integer * negative integer = positive integer
(-2) * (-3) = 6
negative integer * positive integer = negative integer
(-2) * 3 = (-6)
Positive integer *negative integer = negative integer
2 * (-3) = (-6)
Find the measure of angle 4.
O 130
O 75
O 4
O 69
Step-by-step explanation:
the sum of all angles in a triangle is always 180°.
so,
180 = 60 + 45 + angle4 = 105 + angle4
75° = angle4
Identify a horizontal or vertical stretch or compression of the function f(x)=\sqrt(x) by observing the equation of the function g(x)=\sqrt((3)/(2)x)
kind of urgent lol
By applying the concept of transformation, the transformed function g(x) = √[(3/2) · x] is the consequence of applying a stretch factor of 3/2 on the parent function f(x) = √x.
How to compare two functions by concepts of transformationIn this question we have a parent function g(x) = √[(3/2) · x] and a transformed function f(x) = √x. Transformations are operations in which parent functions are modified in their relationships between inputs and outputs.
In this case, the difference between f(x) and g(x) occurred because of the application of a operation known as vertical stretch, defined below:
f(x) = g(k · x), k > 0 (1)
Where k is the stretch factor. There is a compression for 0 ≤ k < 1.
By applying the concept of transformation, the transformed function g(x) = √[(3/2) · x] is the consequence of applying a stretch factor of 2/3 on the parent function f(x) = √x. (Right choice: C)
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In the following exercises, multiply the binomials. Use any method.
255. (a + b)(2a + 3b)
Answer:
Hence the expression [tex]$$(a+b)(2a+3b)=2a^2+5ab+3b^2$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (a + b)(2a+3 b).We have to multiply the given expression.Multiply the (a + b) by 3b, multiply the (a + b) by 2a then add like terms.[tex]$$\begin{matrix}{} & {} & {} & {} & a & + & b \\ \times & {} & {} & {} & 2a & + & 3b \\ \end{matrix}$$[/tex]
___________________
[tex]$$\begin{matrix}{} & {} & {} & {} & 3ab & + & 3{{b}^2} \\ {} & {} & 2{{a}^2} & + & 2ab & {} & {} \\ \end{matrix}$$[/tex]
___________________
[tex]$$\begin{matrix}{} & {} & 2{{a}^2} & + & 5ab & + & 3{{b}^2} \\ \end{matrix}$$[/tex]
Find the value of a.
The value of a is (c) 86
How to solve for a?The given parameter is:
Angle C = 86
By vertical angle theorem, we have:
Angle A = Angle C = 86
This implies that:
Angle A = 86
The arc A subtends angle A
This means that:
Arc A = 86
Hence, the value of a is (c) 86
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I need help ?
A model car is to be an exact replica of the original, but at the size. If
the actual car is 240 cm long, how many centimeters long should the
12
model be?
Answer:
20cm
Step-by-step explanation:
You divide by 12
Two hikers are wandering through heavy woods with walkie talkies. The walkie talkies have a range of 100 yards. From their starting point, they head off at an angle of 109°10' of each other. Hiker 1 walks 0.24 miles per hour, hiker 2 walks 0.17 miles per hour. If each continues to go straight, how long will it be before they can no longer communicate?
Answer: after t hours, the distance d between the hikers is
d^2 = (.24t)^2 + (.17t)^2 - 2(.24t)(.17t)cos109.167°
so, find t when d = 0.0568182
10 minutesStep-by-step explanation:
First person to solve this question with STEP BY STEP explanation will be marked as brainliest
Answer:
C. 2y²
Step-by-step explanation:
[tex] \sf{( {3}^{0}y) {}^{2} \times 2(xy {)}^{0} = }[/tex]
[tex] \boxed{\sf{X^{0} = 1}} [/tex][tex]\sf{ = (\red{1} \times y)^{2} \times (2 \times \red{1}) }[/tex]
[tex]\sf{ = (y)^{2} \times 2 }[/tex]
[tex]\sf{ =2 {y}^{2} }[/tex]
Answer:
[tex]\textsf{C.} \quad 2y^2[/tex]
Step-by-step explanation:
Given:
[tex](3^0y)^2 \times 2(xy)^0[/tex]
[tex]\textsf{Apply exponent rule} \quad a=a^1:[/tex]
[tex](3^0y^1)^2 \times 2(x^1y^1)^0[/tex]
[tex]\textsf{Apply exponent rule} \quad(a^n)^c=a^{nc} \implies (a^nb^n)^c=a^{nc}b^{nc}:[/tex]
[tex]\implies 3^{(0 \times 2)}y^{(1 \times 2)} \times 2 \left(x^{(1 \times 0)}y^{(1 \times 0)} \right)[/tex]
[tex]\implies 3^0y^2 \times 2\left(x^0y^0\right)[/tex]
[tex]\textsf{Apply exponent rule} \quad a^0=1:[/tex]
[tex]\implies (1)y^2 \times 2\left(1 \times 1 \right)[/tex]
Simplify:
[tex]\implies (1)y^2 \times 2(1)[/tex]
[tex]\implies y^2 \times 2[/tex]
[tex]\implies 2y^2[/tex]
Name the variable in each algebraic expression
4y+12
Answer:
y is the variable in that expression.
PLEASE HELP I HAVE 45 min to SUBMIT WILL GIVE BRAINLY
Answer:
Step-by-step explanation:
Jon teaches a fourth grade class at an elementary school where class sizes are always at least 20 students and at most 28. One day Jon decides that he wants to arrange the students in their desks in a rectangular grid with no gaps. Unfortunately for Jon he discovers that doing so could only result in one straight line of desks. How many students does Jon have in his class
Based on the information provided and the requirements to organize the students, Jon most likely has 23 students.
How many students are needed to organize them in a rectangular grid?In general, Jon will need a number that is not prime as this type of number will not allow him to complete all the grid.
Which are possible numbers?20 = A rectangular grid of 5 x 4 seats can be arranged
21= A rectangular grid of 7 x 3 can be arranged
22 = A rectangular grid of 2 x 11 can be arranged
23 = It is impossible to organize 23 seats in a rectangular grid without gaps
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Jon has 23 students in his class.
How to determine the number of studentsNumber of students = Least 20 and most 28
In this case, we are getting a 1 * x rectangle of desks, which is the only possible arrangement.
'x' is a prime number.
Since his classes can't have less than 20 and more than 28, it means we are looking out for a prime number between 20 and 28.
Let's sort out a prime number between the numbers, 20 and 28
20: 1,2,4,5,10,20
21: 1,3,7,21
22: 1,2,11,22
23: 1,23
24: 1,2,3,4,6,8,12,24
25: 1,5,25
26: 1,2,13,26
27: 1,3,9,27
28: 1,2,4,7,14,28
From what we have, 23 is a prime number because it is only divisible by one and itself.
Therefore, Jon has 23 students in his class.
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A medical researcher has two petri dishes containing viruses. Dish B has a population density of 1.2 viruses per square millimeter. Dish A has an area of about 2,826 square millimeters.
If both petri dishes have the same population density, approximately how many viruses are in Dish A?
2,355 viruses
3,391 viruses
23,550 viruses
33,912 viruses
The population of viruses in the dish A is 3,391 viruses.
What is the population?Population density measures the amount of organisms in 1 square millimeters of a place (in this case the dish)
Population density = population / area
Population = population density x area
1.2 x 2826 = 3,391 viruses
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M angle DPR=
Help me please thank u:)
Formula:
[tex]\frac{1}{2}(Big Arc- Small Arc)[/tex]
[tex]\frac{1}{2} (118-26)[/tex]
[tex]\frac{1}{2}(92)\\[/tex]
=46
m∠DPR = 46°
I hope it helps! :)
cho Q(x)=x^2+mx-12.Biết Q(-3)=0.tìm nghiệm còn lại
Answer: m=-1.
Step-by-step explanation:
[tex]Q(x)=x^2+mx-12\ \ \ \ Q(-3)=0\ \ \ \ \ m=?\\Q(-3)=(-3)^2+m*(-3)-12=0\\9-3m-12=0\\-3m-3=0\\3m=-3\ |:3\\m=-1.[/tex]
For which value of b can the expression x2 + bx + 18 be factored?
Answers:
b = -19b = -11b = -9b = 19b = 11b = 9====================================================
Explanation:
Here are all the ways to multiply to 18 when using integers only:
-1*(-18) = 18-2*(-9) = 18-3*(-6) = 181*18 = 182*9 = 183*6 = 18Sum each pair of factors to find out a possible value of b.
-1 + (-18) = -19-2 + (-9) = -11-3 + (-6) = -91 + 18 = 192 + 9 = 113 + 6 = 9Therefore, the possible values of b are
b = -19b = -11b = -9b = 19b = 11b = 9which are the final answers.
----------------------
An example:
Let's say b = 11. This would mean [tex]x^2+bx+18[/tex] becomes [tex]x^2+11x+18[/tex]
It would factor to [tex](x+2)(x+9)[/tex] since it was stated earlier that:
2+9 = 11
2 * 9 = 18
You can use the FOIL rule, distributive property, or the box method to confirm that [tex]x^2+11x+18 = (x+2)(x+9)[/tex] is a true equation for all real numbers x.
This same idea applies for the other values of b.
----------------------
If you're curious why this works, consider multiplying the two factors (x+p) and (x+q)
Use the FOIL rule to get [tex](x+p)(x+q) = x^2+qx+px+pq = x^2+(p+q)x + pq[/tex]
The middle term [tex](p+q)x[/tex] has the components add to the coefficient, while those same two components multiply to get the last term. This is why when factoring we're looking for two numbers that multiply to 18, and also add to the value of b (which in the case of the last example was 11).
To estimate the percentage of a state's voters who support the current
governor for reelection, three newspapers each survey a simple random
sample of voters. Each paper calculates the percentage of voters in its
sample who support the governor and uses that as an estimate for the
population parameter. Here are the results:
• The Tribune.n=700 voters sampled; sample estimate = 68%
• The Herald. n = 500 voters sampled; sample estimate = 64%
• The Times. n = 300 voters sampled; sample estimate = 78%
All else being equal, which newspaper's estimate is likely to be closest to the
actual percentage of voters who support the governor for reelection?
OA. The Tribune, at 68%
B. The Herald, at 64%
C. The Times, at 78%
Using the Central Limit Theorem, the percentage that is expected to be the closest to the actual percentage is:
A. The Tribune, at 68%.
What does the Central Limit Theorem state?It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard error [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].
From this, a larger sample size leads to a smaller error estimate. Since the Tribune had the largest sample size, option A is correct.
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Find a39 of the arithmetic sequence given a1 = -28 and d = -4.
-
A. -104
B. -106
C. 8
D. -180
Reset Selection
Hello !
[tex]a_{n} = a_{1} + (n - 1) \times d[/tex]
[tex]a_{39} = - 28 + (39 - 1) \times ( - 4) = - 28 + 38 \times ( - 4) = - 180[/tex]
The required a39 of the arithmetic sequence is -180.
Given that,
To find a39 of the arithmetic sequence given a1 = -28 and d = - 4.
Arithmetic progression is the series of numbers that have common differences between adjacent values.
What is geometric progression?Geometric progression is a sequence of series whose ratio with adjacent values remains the same.
The nth term of an arithmetic sequence is given as
an = a1 + (n - 1) * d
for term n = 39
a39 = -28 + (39 - 1) * -8
a39 = -28 - 152
a39 = - 180
Thus, the required a39 of the arithmetic sequence is -180.
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factor this polynomial expression. x2 – 16
Answer:
(×-4) (x + 4)
Step-by-step explanation:
first of all, recognize that the polynomial expression is a difference of two squares.
thus
X^2-16
(x -4)(x+4)
⊱________________________________________________________⊰
[tex]\\[/tex][tex]\\[/tex]
Answer:
(x+4)(x-4), by using the difference of squares ruleStep-by-step explanation:
[tex]\large\begin{gathered} \sf{To \ factor \ this \ polynomial, \ we \ must \ first \ recognise \ it. \ Isn't \ it \ the \ difference} \\ \sf{of \ two \ squares?} \\ \rm{It \ is! } \\ \sf{Polynomials \ like \ (a^2-b^2) are \ factored \ like \ this\!\!:} \\ \sf{(a+b)(a-b).} \\ \sf{Similarly, \ (x^2-16) \ is \ factored \ as \ (x+4)(x-4). \end{gathered}[/tex]
Done!!
⊰_____________________________________________________⊱
[tex]\\[/tex][tex]\\[/tex]
[tex]\boldsymbol{\rm{\triangleright\overbrace{C}\triangleleft\underbrace{A}\triangleright\overbrace{L}\triangleleft\underbrace{L}}\triangleright\overbrace{\stackrel\bigstar{I}}\triangleleft\underbrace{G}\triangleright\overbrace{R}\triangleleft\underbrace{A}\triangleright\overbrace{P}\triangleleft\underbrace{H}\triangleright{Y}}}[/tex]
what is the definition of prime and composite numbers??please answer fast
Answer:
'A prime number is a number which has exactly two factors i.e. '1' and the number itself. A composite number has more than two factors, which means apart from getting divided by 1 and the number itself, it can also be divided by at least one positive integer.'
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
What is the definition of prime & composite numbers?
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
A prime number can be evenly divided by 1 and itself. These are its only two factors.
A composite number can be evenly divided by 1, itself, and something else. In other words, composite numbers have more than 2 factors.
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{\begin{cases}\bf{Primes\;have\;only\;2\;factors} \\ \bf{Composites\;have\;3\;or\;more\;factors} \end{cases}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic\not1\theta l}}[/tex]
Volume=
Please help thankss
Answer:
Volume = 64
Step-by-step explanation:
To find the volume of the cube use the formula.
Formula: l×b×h
l=length
b=base
h=height
Use the information given to solve using the formula.
4×4×4=64
The volume of this cube is 64.
Hope this helps!
If not, I am sorry.
please help me find the solution
Step-by-step explanation:
ATTACHED IS THE SOLUTION!!
A board game allows players to trade game pieces of equal value. The diagram shows two fair trades. The hotel is worth $2400. How much is a car worth?
Answer:
Step-by-step explanation:
I’m so confused on how to do this one pls help me out I would appreciate it
First of all, a pair of angles that are complementary means that they add up to 90 degrees. In this case, angle b + 63 degree = 90 degree (because they are complementary), which mean angle b = 90 - 63 = 27 degree.
Answer: 27°
Step-by-step explanation:
Hello.
Complementary angles add up to 90°
Therefore,
63° + ? = 90°
Now we can subtract!
90° - 63° = 27°
Hope this helps and have a nice day :)
Help me please find the value of x then find the measure of each unknown angle
The value of x is 103.
The value of x is 59.
The value of x is 134.
The value of x is 12
The value of x is 50
The value of x is 135
What is the value of x?
The sum of angles on a straight line add up to 180 degrees.
180 - 77 = 103
180 - 121 = 59
180 - 46 = 134
12 x + 36 = 180
12x = 180 - 36
12x = 144
x = 12
24 + 3x + 6 = 180
3x = 180 - 24 - 6
3x = 150
x - 50
[tex]\frac{x}{3}[/tex] + 99 + 36 = 180
[tex]\frac{x}{3}[/tex] = 180 - 36 - 99
[tex]\frac{x}{3}[/tex] = 45
x = 45 x 3
x = 135
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Coordinate Geometry Use the graph. Write each
ratio in simplest form.
33. BD
AC
AE
EC
34. A
35. slope of EB
36. slope of ED
8
6
D
O
y
E
6
LO
33) [tex]AC=6[/tex] and [tex]BD=6[/tex], so [tex]AC/BD=1[/tex]
34) By the distance formula,
[tex]AE=\sqrt{(-2-4)^2 + (8-0)^2 }=10\\[/tex]
Also, EC = 8. So, [tex]AE/EC = 5/4[/tex].
35) [tex]\frac{8-0}{4-2}=4[/tex]
36) [tex]\frac{8-0}{4-8}=-2[/tex]
sin 3x + 2cos^2 (3x) = 1
Recall the Pythagorean identity,
[tex]\sin^2(x) + \cos^2(x) = 1[/tex]
Then we can rewrite the equation as
[tex]\sin(3x) + 2 \cos^2(3x) = 1[/tex]
[tex]\sin(3x) + 2 (1 - \sin^2(3x)) = 1[/tex]
[tex]1 + \sin(3x) - 2 \sin^2(3x) = 0[/tex]
Factorize the left side.
[tex](1 + 2 \sin(3x)) (1 - \sin(3x)) = 0[/tex]
Then we have
[tex]1 + 2\sin(3x) = 0 \text{ or } 1 - \sin(3x) = 0[/tex]
[tex]\sin(3x) = -\dfrac12 \text{ or } \sin(3x) = 1[/tex]
Solve for [tex]x[/tex]. We get two families of solutions:
[tex]3x = \sin^{-1}\left(-\dfrac12\right) + 2n\pi \text{ or } 3x = \pi - \sin^{-1}\left(-\dfrac12\right) + 2n\pi[/tex]
[tex]\implies 3x = -\dfrac\pi6 + 2n\pi \text{ or } 3x = \dfrac{7\pi}6 + 2n\pi[/tex]
[tex]\implies \boxed{x = -\dfrac\pi{18} + \dfrac{2n\pi}3} \text{ or } \boxed{x = \dfrac{7\pi}{18} + \dfrac{2n\pi}3}[/tex]
and
[tex]3x = \sin^{-1}(1) + 2n\pi[/tex]
[tex]\implies 3x = \dfrac\pi2 + 2n\pi[/tex]
[tex]\implies \boxed{x = \dfrac\pi6 + \dfrac{2n\pi}3}[/tex]
(where [tex]n[/tex] is any integer)
Write the equation of the line that passes through the point (-8,-3) with : slope of -1/4
Answer:
In slope-intercept form:
[tex]y = - \frac{1}{4} x - 5[/tex]
In standard form:
[tex]x + 4y = - 20[/tex]
Step-by-step explanation:
[tex] - 3 = - \frac{1}{4} ( - 8) + b[/tex]
[tex] - 3 = 2 + b[/tex]
[tex]b = - 5[/tex]
[tex]y = - \frac{1}{4} x - 5[/tex]
[tex] - 4y = x + 20[/tex]
[tex] - x - 4y = 20[/tex]
[tex]x + 4y = - 20[/tex]
alyssa has 144 coins. of the coins 3/12 are nickels, 8/12 are dimes, and the rest are quarters what is the ratio of Alyssa’s nickels to dimes to quarters?
3:8:1
step-by-step explanation:3/12 x 144= 36
8/12 x 144= 96
96+36= 132
144-132= 12
12/12=1
Therefore, the ratio of Alyssa's nickels to dimes to quarters is 3:8:1
1. Are you given enough information to prove that these two triangles are congruent? If so,
what reason would you give?
Answer:
Yes, because they are congruent by AAS (angle angle side)
Step-by-step explanation:
One of the congruence theorem is AAS. If you follow the sides of the triangle, you will see that they are marked with an angle, another angle, and a side being congruent. I hope this helps!
f (1/2)pi = cos(1/2) pi
the answer to this equation should be 0 but i’m not sure how to do the work could someone help/ explain
Answer:
Step-by-step explanation:
1/2 pi is an angle ( in radians)
in degrees its 90 degrees.
cos 90 = 0.