Answer:
[tex]125m {}^{3}n {}^{6} [/tex]
Step-by-step explanation:
Since
[tex]a {}^{b} \times a {}^{c} = a {}^{b + c} [/tex]
[tex](5mn {}^{3} ) {}^{3} = (5) {}^{3}(m) {}^{3} (n {}^{3}) {}^{3} = 125m {}^{3}n {}^{3 + 3} = 125m {}^{3}n {}^{6} [/tex]
Hope this helps :) ❤❤❤
Answer:
[tex]125m^3n^9[/tex]
Step-by-step explanation:
[tex](a*b)^n=a^nb^n\\\\(5mn^3)^3=5^3m^3(n^3)^3\\\\125m^3(n^3)^3\\\\(a^b)^c=a^{bc}\\\\\rightarrow (n^3)^3=n^{3*3}=n^9\\\\\boxed{125m^3n^9}[/tex]
Brainilest Appreciated.
What is the domain of the function shown on the graph? A. -10
Answer:
Option (C)
Step-by-step explanation:
Domain of any graph is defined by the x-values or the input values of a function.
Similarly, y-values on the graph of a function define the Range.
In the graph attached, x-values varies from (-∞) to (+∞).
Therefore, Domain of the graphed function will be (-∞, ∞)
Or -∞ < x < ∞
Similarly, y-values of the graph varies from (-∞) to (1)
Therefore, range of the graphed function will be (-∞, 1).
Or -∞ < y < 1
Option (C) will be the answer.
Please answer it now in two minutes
Answer:
[tex] C = 28.9 [/tex]
Step-by-step explanation:
Given the right angled triangle, ∆BCD, you are required to find the measure of angle C.
Apply the trigonometric ratio formula to find m < C.
Adjacent side = 7
Hypotenuse = 8
Trigonometric ratio formula to apply would be:
[tex] cos(C) = \frac{7}{8} [/tex]
[tex] cos(C) = 0.875 [/tex]
[tex] C = cos^{-1}(0.875) [/tex]
[tex] C = 28.9 [/tex]
(To nearest tenth)
What is the slope of the line through the points (2,8) and (5,7)
Answer:
-1/3
Step-by-step explanation:
The slope of the line can be found by
m = (y2-y1)/(x2-x1)
= ( 7-8)/(5-2)
= -1/3
Answer:
-1/3.
Step-by-step explanation:
The slope can be found by doing the rise over the run.
In this case, the rise is 8 - 7 = 1.
The run is 2 - 5 = -3.
So, the slope is 1 / -3 = -1/3.
Hope this helps!
GEOMETRY
1.) find the value of z and show work
a) Explain the difference in how an inscribed angle and central angle are draw
b) Explain the difference in how their measures compare to the subtended arc.
Answer:
z = 8.5
Step-by-step explanation:
Let O be the center of the circle, and A, B, C are three points on the circle.
Draw OA and OC are shown in the figure. To make the central angle.
In the figure the measure of arc AC is 118 degrees. measure of central angle and subtrahend arc is same. So, central angle is
[tex]\angle AOC=118^{\circ}[/tex]
Subtended angle on arc AC is
[tex]\angle ABC=(6z+8)^{\circ}[/tex]
According to central angle theorem of circle, central angle is twice of angle subtended by the arc.
[tex]\angle AOC=2\times \angle ABC[/tex]
[tex]118^{\circ}=2\times (6z+8)^{\circ}[/tex]
[tex]118=12z+16[/tex]
[tex]118-16=12z[/tex]
[tex]102=12z[/tex]
[tex]\dfrac{102}{12}=z[/tex]
[tex]8.5=z[/tex]
Therefore, the value of z is 8.5.
Suppose 45% of the worlds population has type "O" blood type. A study was done to see if the percent differs for college students. 47% of the 1000 random selected college students have type O blood. conduct a hypothesis test to determine if the percent of college students with type o blood differs for college students?
Answer:
We accept H₀, with CI = 90 %, porcentage of O blood type in college students does not differ from the world population porcentage
Step-by-step explanation:
The test is a proportion two-tail test ( note: differs)
p₀ = 45 % or p₀ = 0,45
n = 1000
p = 47 % or p = 0,47
Test Hypothesis
Null hypothesis H₀ p = p₀
Alternative hypothesis Hₐ p ≠ p₀
CI we assume 90 % then α = 10 % α = 0,1 α/2 = 0,05
z score from z-table z(c) = 1,64
To calculate z(s) = ( p - p₀ ) / √ p₀q₀/ n
z(s) = ( 0,47 - 0,45 )/ √( 0,45)*(0,55)/1000
z(s) = 0,02/√( 0,2475)/1000
z(s) = 0,02/0,01573
z(s) = 1,2714
Now we compare z(s) and z(c)
z(s) < z(c) 1,2714 < 1,64
Then z(s) is in the acceptance region we accept H₀
A car can go from rest to 90 km⁄h in 10 s. What is its acceleration?
Answer:
2.5 m/s^2
Step-by-step explanation:
Answer:
2.5 m/s²
Step-by-step explanation:
First, convert to SI units.
90 km/h × (1000 m/km) × (1 h / 3600 s) = 25 m/s
a = Δv / Δt
a = (25 m/s − 0 m/s) / 10 s
a = 2.5 m/s²
Triangle RST was dilated with the origin as the center of dilation to create triangle R'S'T'. The triangle was dilated using a scale factor of 34. The coordinates of the vertices of triangle RST are given. You can use the scale factor to find the coordinates of the dilated image. Enter the coordinates of the vertices of triangle R'S'T' below. (Decimal values may be used.)
Answer:
Multiply every coordinate from the old one by 0.75
Step-by-step explanation:
I just did this question so I didn't need your photo. And I got it right. Hope this helps anyone else stuck on a similar question.
The rule is to multiply the old coordinates/sides by the scale factor, if its a fraction convert it to a decimal and then multiply like I did.
Answer:
x, y ----> 3/4x, 3/4y
Step-by-step explanation:
Please help I will give out brainliest
Answer:
All the points change, there are no invariant points
Step-by-step explanation:
The given parameters are
To translate the square OABC by the vector [tex]\dbinom{1}{3}[/tex], we have;
The coordinates of the point O is (0, 0)
The coordinates of the point A is (3, 0)
The coordinates of the point B is (3, 3)
The coordinates of the point C is (0. 3)
The translation is by moving 1 step right and three steps up to give;
O' is (0+1, 0+3) which is (1, 3)
A' is (3+1, 0+3) which is (4, 3)
B' is (3+1, 3+3) which gives (4, 6)
C' is (0+1, 3+3) which gives (1, 6)
As all the points change, there are no invariant points and the number of invariant points is zero.
Select the correct answer. Write (21 − 4i) − (16 + 7i) + 28i as a complex number in standard form. A. 5 + 39i B. 5 + 17i C. 5 − 39i D. 5 − 17i
Answer:
b. 5 + 17i
Step-by-step explanation:
Given f(x) = log x and g(x) = -x + 1,
which is the graph of
(fog)(x)?
Answer:
the third graph is correct
Step-by-step explanation:
edge
the second part is x<1
Answer:
the third graph and the send part it is x<1
Step-by-step explanation:
Help asap please and please explain so I could try the rest on my own
Answer:
7
Step-by-step explanation:
It has a 45 45 90 ratio, so if the hypotenuse is 7 root 2, then the two sides have to be 7.
can someone explain how to use sin cos and tan on right angled triangles
Round this however you need to
=================================================
Explanation:
The reference angle is 56 degrees. The side 26.5 is adjacent to this angle as it is the leg closest to the angle (in contrast to the opposite leg or opposite side that is furthest from the reference angle)
The hypotenuse is d. The hypotenuse is always the longest side. The longest side is always opposite the largest angle of a triangle.
We will use the cosine ratio as it is the ratio of adjacent over hypotenuse
cos(angle) = adjacent/hypotenuse
cos(56) = 26.5/d
d*cos(56) = 26.5
d = 26.5/cos(56)
d = 47.3897287242421
You use your calculator for the last step shown above. Make sure your calculator is in degree mode. Round that value however you need to.
Here is the formula of sin cos tan :
sin x = opposite/hypotenuse
cos x = adjacent / hypotenuse
tan x = opposite / adjacent
d = hypotenuse
x = the angle known in your pic
like example if in your picture:
adjacent = 26.5
if want to find the d
cos x = adjacent / hypotenuse
cos 56 = 26.5 / d
d = 26.5 : cos(56)
d = 47.390 (3 significant figures)
and if want to find the opposite
tan x = opposite/adjacent
tan 56 = opposite/ 26.5
opposite = 26.5 × tan(56)
opposite = 39.288
-> Sorry if im wrong
Angles α and β are angles in standard position such that: α terminates in Quadrant III and sinα = - 5/13 β terminates in Quadrant II and tanβ = - 8/15
Find cos(α - β)
-220/221
-140/221
140/221
220/221
Answer:
140/221.
Step-by-step explanation:
For the triangle containing angle α:
The adjacent side is -√(13^2-5^2) = -12.
For the triangle containing angle β:
Hypotenuse = √(-8)^2 + (15)^2) = 17.
cos(α - β) = cos α cos β + sin α sin β
= ((-12/13) * (-15/17) + (-5/13)* (8/17)
= 180/221 + - 40/221
= 140/221.
Mr rigo bought 49 bags
Answer:
77 bags
Step-by-step explanation:
if he brought 49 bags then he brought 28 more bags49+28=77
Using leaner combination method what is the solution to the system of linear equations 7x-2y=-20 and 9x+4y=-6
Answer:
x = -2 and y = 3
Step-by-step explanation:
In linear combination method we try one of the variables from bopth of equations by
first making the variable equal in vlaue
then either subtracting or adding the two equation as required to eliminate the variable.
_____________________________________________
7x-2y=-20 equation 1
and 9x+4y=-6 equation 2
we see that y has
has value -2 and +4
4 = 2*2
thus, if we multiply equation1 with 2 we will give value for variable y as 4y and hence y can be eliminated easily.
7x-2y=-20
multiplying the LHS and RHS with 2
2(7x-2y)=-20 *2
=> 14x - 4y = -40 eqaution 3
now that we have got 4y
lets add equation 2 and equation 3
9x +4y= -6
+14x - 4y = -40
________________________________
=> 23x + 0 = -46
x = -46/23 = -2
Thus, x = -2
substituitinng x = -2 in 7x-2y=-20
7*-2 -2y=-20
=> -14 -2y = -20
=> -2y = -20+14 = -6
=> y = -6/-2 = 3
Thus, y = 3
solution is x = -2 and y = 3
if p(x) = x+ 7/ x-1 and q (x) = x^2 + x - 2, what is the product of p(3) and q(2)? a. 50 b. 45 c. 40 d. 20 e. 6
Answer:
d. 20
Step-by-step explanation:
To answer the question given, we will follow the steps below:
we need to first find p(3)
p(x) = x+ 7/ x-1
we will replace all x by 3 in the equation above
p(3) = 3+7 / 3-1
p(3) = 10/2
p(3) = 5
Similarly to find q(2)
q (x) = x^2 + x - 2,
we will replace x by 2 in the equation above
q (2) = 2^2 + 2 - 2
q (2) = 4 + 0
q (2) = 4
The product of p(3) and q(2) = 5 × 4 = 20
Could someone help me understand this?
Answer: the correct answer is D.
Step-by-step explanation:
Since we are given the values of angle B and side(a) we can set up an equation cos43.2=3.2/x
we will get 4.4 so c=4.4
using the paythagorion theorm (4.4)^2=x^2+(3.2)^2
we will get an approximate value of 3 so b=3
and for the finding the third angle x+43.2+90=180
x=46.8 degrees
Answer D
What is the angle of rotation from figure A to figure A? Assume that the center of rotation is the origin.
A. 360° clockwise
B. 270° clockwise
C. 180° clockwise
D. 90° clockwise
Answer:
the answer is C. 180°clockwise
find the value of x in the triangle shown below
Answer:
x=70
Step-by-step explanation:
the angles opposite 3.5 equal 55 degrees
180-55-55=70
Answer:
70°
Step-by-step explanation:
since the both size are equal which is 3.5,it is equal length, so the other angle should be 55 also. Just use the triangle =180° ，180-55-55=70°
Which describes how square S could be transformed to square S prime in two steps? Assume that the center of dilation is the origin. A.) a dilation by a scale factor of Two-fifths and then a translation of 3 units up B.) a dilation by a scale factor of Two-fifths and then a reflection across the x-axis C.) a dilation by a scale factor of Five-halves and then a translation of 3 units up D.) a dilation by a scale factor of Five-halves and then a reflection across the x-axis
Answer:
The correct option is;
A.) A dilation by a scale factor of two-fifths and then a translation of 3 units up
Step-by-step explanation:
The given information are;
Square S undergoes transformation into square S'
From the figure, the dimension of S' = 2/5 dimension of S
Therefore, the scale factor of the dilation is two-fifths
The center of dilation = The origin
Therefore, given that the top right edge of S is at the center of dilation, the initial location of the dilated figure will be (0, 0), (2, 0), (2, -2), and (0, -2)
Given that the lowermost coordinates of S' are (0, 1) and (2, 1), and the lowermost coordinates of the initial dilation are (0, -2) and (2, -2), we have that the translation to S' from the initial dilation is T (0 - 0, 1 - (-2)) = T(0, 3) which is 3 units up.
Answer:
A
Step-by-step explanation:
Chris purchased a tablet for $650. The tablet depreciates at a rate of $25 per month.
Write and simplify an equation that models the value V(m) of the tablet after m months.
Let d equal the final amount it depreciates.
Let m equal the number of months.
Since d is the final amount, we put this at the very end of the equation.
Since it depreciates $25 every month, this number is going to be subtracted from the total price of the tablet ($650).
The final equation comes out too: d = 650 - 25m
Best of Luck!
I need the answers to the questions highlighted with the black rectangles.
Answer:
b) P(more than 10) = 2/9
c) P(less than 7) = 2/9
Step-by-step explanation:
a) Yaniq spins both spinners and then adds up the results together.
The results are as follow:
5
7
9
6
8
10
7
9
10
These are a total of 9 outcomes.
b) What is the probability that Yaniq gets a total of more than 9?
The probability is given by
P = Number of favorable outcomes/Total number of outcomes
For this case, the favorable outcomes are all those outcomes where the total score is more than 9.
Count the number of times Yaniq got a score of more than 9.
Yes right!
2 times (10 and 10)
P(more than 10) = 2/9
c) What is the probability that Yaniq gets a total of less than 7?
For this case, the favorable outcomes are all those outcomes where the total score is less than 7.
Count the number of times Yaniq got a score of less than 7.
Yes right!
2 times (5 and 6)
P(less than 7) = 2/9
please solve this using quadratic formula :")
Answer:
Step-by-step explanation:
The given equation is expressed as
(x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12
Simplifying the right hand side of the equation, it becomes
[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)
x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)
(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)
4x/(x - 1)(x + 1)
Therefore,
4x/(x - 1)(x + 1) = 7/12
Cross multiplying, it becomes
4x × 12 = 7(x - 1)(x + 1)
48x = 7(x² + x - x - 1)
48x = 7x² - 7
7x² - 48x - 7 = 0
Applying the quadratic formula,
x = - b ± √(b² - 4ac)]/2a
from our equation,
b = - 48
a = 7
c = - 7
Therefore
x = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)
x = [48 ± √(2304 + 196]/14
x = (48 ± √2500)/14
x = (48 ± 50)/14
x = (48 + 50)/14 or x = (48 - 50)/14
x = 98/14 or x = - 2/14
x = 7 or x = - 1/7
Answer: The given equation is expressed as (x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12Simplifying the right hand side of the equation, it becomes[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)4x/(x - 1)(x + 1)Therefore, 4x/(x - 1)(x + 1) = 7/12Cross multiplying, it becomes4x × 12 = 7(x - 1)(x + 1)48x = 7(x² + x - x - 1)48x = 7x² - 77x² - 48x - 7 = 0Applying the quadratic formula,x = - b ± √(b² - 4ac)]/2a from our equation, b = - 48a = 7c = - 7Thereforex = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)x = [48 ± √(2304 + 196]/14x = (48 ± √2500)/14x = (48 ± 50)/14x = (48 + 50)/14 or x = (48 - 50)/14x = 98/14 or x = - 2/14x = 7 or x = - 1/7
Step-by-step explanation:
what is 92.5% of 200
Answer:
185
Step-by-step explanation:
All you have to do is multiply 200 by 92.5/100 (because it is 92.5%). This gives you 185.
Hope this helps!
Answer:
185
We know 92.5% of 100 is 92.5%, so 92.5 of 200 is just 92.5×2.
Kelly needed to use 3 pounds 15 ounces of clay to make a bowl and twice as much to make a vase. If she had a 12-pound bag of clay available, did she have enough clay to make both items?
Answer:
yes
Step-by-step explanation:
so first you would convert pounds into ounces (It's easier for me)
and there are 16 ounces in one pound so for 3 pounds you would have 48 ounces then add the 15 ounces to get 63 ounces and if she needs twice as much to make a vase she would need 126 ounces for a vase then you would add the other 63 to that to get a total of 189 ounces of clay in order to create the bowl and vase, and in order to find out how many ounces are in a 12 pound bag you would just multiply 12 by 16 to get 192 ounces. So yes she does have enough clay to make a bowl and a vase.
The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains pure fruit juice. How many pints of each of the two existing types of drink must be used to make pints of a mixture that is pure fruit juice
Complete question:
The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 70% pure fruit juice?
Answer:
Juice A = 15
Juice B = 35
Step-by-step explanation:
Given the following:
Juice A:
Let juice A = a
35% pure fruit juice
Juice B:
Let juice B = b
85% pure fruit juice
We need to make 50 pints of juice from both: that is ;
a + b = 50 -------(1)
In terms of pure fruit:
a = 0.35 ; b = 0.85 ;
Our mixed fruit juice from a and b should be 70% pure fruit = 0.7
Mathematically,
0.35a + 0.85b = 50(0.7)
0.35a + 0.85b = 35 -------(2)
Multiply (2) by 100
35a + 85b = 3500 --------(3)
We can then solve the simultaneous equation:
a + b = 50 -------(1)
35a + 85b = 3500 --------(3)
Multiply (1) by 35
35a + 35b = 1750 -----(4)
35a + 85b = 3500 ---(5)
Subtract (5) from (4)
-50b = -1750
b = 35
Substitute b = 35 into (2)
0.35a + 0.85(35) = 35
0.35a + 29.75 = 35
0.35a = 35 -29.75
0.35a = 5.25
a = 5.25/0.35
a = 15
Juice A = 15
Juice B = 35
Mr. SMITH had 4 daughters, each daughter had a brother ... How many sons does Mr. Smith have?
He tells us that the 4 daughters have a brother, so, since they belong to the same family, the sisters are the same because they have only one brother.
Answering our question:
or Mr. Smith has 4 daughters and also 1 son.
Answer:
one son
Step-by-step explanation:
each daughter had a brother, means there is only one son
Mr. smith has 1 son
Andy spins the spinner and rolls a standard number cube. Find the probability that the spinner will stop on yellow and the cube will show a three or five. Write the probability as a fraction in simplest form.
Answer: 1/5 , 1/2, and 5/6
Step-by-step explanation:
given;
probability that the cube shows a three (3) or five (5).
probability that it stops on yellow.
1. the probability p of the spinner stopping on yello
= 1/5 times
a cube has 6 sides
2. probability that it shows a 3
this is going to be 3 divided by the total sides on the cube which is 6
P = ( 3 ) = 3/6
Divide both side by 3
= 1/2.
3. probability that it shows a 5,
this is going to be 5 divided by the total sides on the cube which is 6
P = ( 5 )
= 5/6.
Which is the best estimate of 90/7 divided by 1 3/4? 2 6 12 24
Answer:
6 is the best estimate.
Step-by-step explanation:
(90/7) / (1 & 3/4) == (90/7) / (7/4) == (90/7) * (4/7) == 360/49 > 7.
Choose 6 as your best approximation.
What is the least common denominator of the rational expressions below?
Answer:
x(x-3) ( x+4)
Step-by-step explanation:
2 5
---------- + ------------
x^2 -3x x^2 + x - 12
Factor the denominator
2 5
---------- + ------------
x(x -3) (x-3) (x+4)
The common denominator is
x(x-3) ( x+4)