Answer:
See below
Step-by-step explanation:
[tex]d ) (-3x^3) (4xy)(-2x^2y^2),\\3x^3\cdot \:4xy\cdot \:2x^2y^2,\\24x^3x^2xy^2y,\\24yx^6y^2,\\24x^6y^{1+2},\\\\Solution = 24x^6y^3[/tex]
First I removed the ( ) off the " main expression. " Afterwards I multiplied the terms, and through the exponential rule, I added exponents of like terms, simplifying the expression to the solution 24x^6y^3. The rest of these questions are performed in a like manner, so I don't think I need to explain them.
[tex]e ) (-28a^6 / -7a^5),\\\frac{28a^6}{7a^5},\\\frac{4a^6}{a^5},\\\\4a^{6-5},\\4a,\\\\Solution = 4a[/tex]
____________________________________________
For part f ) can you be a bit more clear on the exponent part. One could say that this expression is ( 8z^3 )( 7z^1 * 1 ) or ( 8z^3 )( 7z^11 ). You never know, an exponent and a multiplied number can be confused considering that a number next to another is taken to be multiplied. After you confirm the expression I will be happy to change my response!
What is the slope-intercept form of the equation of the line through the
point (-3, 3) with slope -1.
Answer: y=-1x+0
so, y=-1x
45/30 in its simplest form
Answer:
3/2
Step-by-step explanation:
45/30 can be simplified.
The highest common factor of 45 and 30 is 15.
45÷15/30÷15
Divide.
3/2
The height of a triangle is 3 feet greater than the base. The area of the triangle is 54 square feet. Find the length of the base and the height of the triangle
Answer:
Step-by-step explanation:
The length of the base is 3 feet and the height of the triangle is 6 feet.
What is the area of a triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees. The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.
Given that the height of a triangle is 3 feet greater than the base. The area of the triangle is 54 square feet.
The dimensions of the triangle will be calculated as,
A = (1/2) x b x h
A = (1/2) x b x ( b + 3 )
54 = ( 1 / 2 ) x ( b² + 3b )
108 = ( b² + 3b )
( b² + 3b - 108) = 0
( b² + 12b -3b -108 ) = 0
(b - 3 ) ( b+ 12 ) = 0
b = 3 and b = -12 ignore negative value.
The height will be calculated as,
h = b + 3
h = 3 + 3
h = 6 feet
Therefore, the length of the base is 3 feet and the height of the triangle is 6 feet.
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The distance between points (1, 2) and (x 1 ,y 1 ) is the square root of (x 1 -1)^ 2 +(y 1 -2)^ 2
Answer:
True
Step-by-step explanation:
The distance between the given points is [tex]\sqrt{(x_{1}-1 )^{2}-(y_{1}-2 )^{2} }[/tex].
The given points are (1, 2) and [tex](x_{1} , y_{1})[/tex] .
We to find the distance between the given points.
What is the formula to find the distance between points?The formula to find the distance between points is [tex]\sqrt{(x_{1}-x_{2} )^{2}-(y_{1}-y_{2} )^{2} }[/tex].
Now, [tex]\sqrt{(x_{1}-1 )^{2}-(y_{1}-2 )^{2} }[/tex]
Therefore, the distance between the given points is [tex]\sqrt{(x_{1}-1 )^{2}-(y_{1}-2 )^{2} }[/tex].
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2. The average age of 25 students is 10years
and the average age of another class
30 Students is 15 years. Find the average age
of students of the two classes
Answer:
12.7 years to the nearest tenth.
Step-by-step explanation:
The total of the ages for the 25 students = 10*25 = 250.
For the 30 students it is 15*30 = 450.
The average for the 2 classes = (250 + 450) / (25 + 30)
= 700 / 55
= 12.7 years to the nearest tenth.
I need help answering this question, Asap
Answer:
(-65)/17
Step-by-step explanation:
Evaluate 3/(x - 2) - sqrt(x - 3) where x = 19:
3/(x - 2) - sqrt(x - 3) = 3/(19 - 2) - sqrt(19 - 3)
19 - 3 = 16:
3/(19 - 2) - sqrt(16)
19 - 2 = 17:
3/17 - sqrt(16)
sqrt(16) = sqrt(2^4) = 2^2:
3/17 - 2^2
2^2 = 4:
3/17 - 4
Put 3/17 - 4 over the common denominator 17. 3/17 - 4 = 3/17 + (17 (-4))/17:
3/17 - (4×17)/17
17 (-4) = -68:
3/17 + (-68)/17
3/17 - 68/17 = (3 - 68)/17:
(3 - 68)/17
3 - 68 = -65:
Answer: (-65)/17
Answer:
-3.86
Step-by-step explanation:
Replace x with 19.
f(19) = 3/(19+2) - √19-3
f(19)= 1/7 - 4
f(19) = -3.86
please help me with this
Answer:
The answers are below
Step-by-step explanation:
a)67.592
b)21.748
c)241.402
The following scatter plot demonstrates the relationship between to two variables x and y. The scatter plot shows what. correlation between the variables
Answer:
Positive correlation
Step-by-step explanation:
From the scatter plot shown in the graph above, we can observe that the data points that are clustered in a band run upwards from left of the graph to the right.
In simple terms, both variables move along the same direction, which means, as variable on one axis increases, the variable on the other axis increases as well.
This shows that the variables depicted on the scatter plot are positively correlated. It shows a positive correlation between the variables.
The relationship between the variables on the scatter plot it a positive correlation
From the graph, we have the following highlights
As the x-values increase, the y-values also increase The points appear to be on a straight lineWhen the x and the y values increase or decrease in the same direction, then the correlation of the graph is positive.
Hence, the relationship between the variables on the scatter plot it a positive correlation
Read more about correlation at:
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On a coordinate plane, point A is 2 units to the left and 3 units up. Point B is 2 units to the right and 3 units up.
How many units away are each of the points from the y-axis?
2
3
4
5
Answer:
2 for both
Step-by-step explanation:
The distance between the points and the y-axis will be the value of the x coordinate, as x is the horizontal distance from 0 and the y-axis.
Answer:
Answer 4
Step-by-step explanation:
In the diagram, m = 128° and m = 76°. What is m∠ABC? A. 104° B. 116° C. 128° D. 102° E. 96°
Answer:
B. 116
Step-by-step explanation:
Answer:
D) 102
Step-by-step explanation:
Angle ABC is an inscribed angle.
Inscribed angle = 1/2 * Intercepted Arc
The intercepted arc is arc CD + arc DA, which would be 128 + 76 = 204
m<ABC = 1/2(204)
m<ABC = 102 degrees
You answer is D) 102
which words have vertical symmetry for all of the letters in the word?
Answer:
palindromes
Step-by-step explanation:
palindromes are spelled the same forward and backward, thus have vertical symmetry.
The polynomial 6x2 + x - 15 has a factor of 2x - 3. What is the other factor?
Answer:
I hope this is helpful (2x-3)(3x+5)
Step-by-step explanation:
(2x-3)(3x+5)
6x2-9x+10x-15
6x2+x-15
Answer:
your answer is 3x+5
Step-by-step explanation:
on edge 2021
find a quadratic polynomial whose sum and and product is -7 and -2
Answer:
x²+7x-2 = 0Step-by-step explanation:
The general form of a quadratic equation with roots a and b is expressed as shown;
x²-(sum of root) x + (product of roots) = 0
x² - (a+b)x + ab = 0 ... 1
Given the sum of roots a+b = -7
Product of roots ab = -2
Substituting this values in equation 1 above wil give;
x²-(-7)x+(-2) = 0
x²+7x-2 = 0
The resulting quadratic polynomial is x²+7x-2 = 0
Which is the area of the rectangle?
69
115
100
Answer:
A
Step-by-step explanation:
Translate into an algebraic expression: If I travel d miles in h hrs downstream on a river with a current of c mph, what would my speed in still water have been?
Answer:
The speed is still water is [tex]v = \frac{d}{h} - c[/tex].
Step-by-step explanation:
Dimentionally speaking, speed is distance divided by time. Since, the person is travelling downstream, absolute speed is equal to the sum of current speed and speed of the person regarding current. Both components are constant. That is:
[tex]c + v = \frac{d}{h}[/tex]
Where:
[tex]c[/tex] - Current speed, measured in miles per hour.
[tex]v[/tex] - Speed of the person regarding current, measured in miles per hour.
[tex]d[/tex] - Distance travelled downstream, measured in miles.
[tex]h[/tex] - Time spent on travelling, measured in hours.
Speed in still water occurs when current speed is zero. Then, such variable is obtained after subtracting current speed on both sides of the expression. Hence:
[tex]v = \frac{d}{h} - c[/tex]
The speed is still water is [tex]v = \frac{d}{h} - c[/tex].
Which is the correct formula to calculate the volume of a sphere?
a.
Four-thirds pi r squared
c.
One-third pi r cubed
b.
Four-thirds pi r cubed
d.
4 pi r cubed
Please select the best answer from the choices provided
A
B
C
D
Not a
Answer:
B
Step-by-step explanation:
Volume of Sphere = 4/3 x 3.14 (pi) x r^2
Starting from rest the motor boat travels around the circular path (radius of curvature= 40 m),at a speed (v= 0.8 t m/s),where (t) is in seconds. The magnitude of the boat's velocity when it has traveled 20 m is
Answer:
The magnitude of the boat's velocity is 5.66 m/s
Step-by-step explanation:
Given;
Radius of curvature of the circular path, r = 40 m
speed of the boat, v = 0.8 t m/s
The magnitude of the boat's velocity when it has traveled 20 m is ?
a = dv / dt,
v = 0.8 t (differentiate with respect to t)
dv / dt = 0.8 = a
thus, a = 0.8 m/s²
If the boat starts from rest, initial velocity, u = 0
Apply kinematic equation, to solve for the boat velocity at 20 m
v² = u² + 2as
v² = 0 + 2 x 0.8 x 20
v² = 0 + 32
v² = 32
v = √32
v = 5.66 m/s
Therefore, the magnitude of the boat's velocity when it has traveled 20 m is 5.66 m/s
Calculate the volume in litres of the cuboid shown above
Answer:
0.06 l
Step-by-step explanation:
Volume of cube = 3 x 4 x 5 = 60 cm cubed.
1 cm cubed = 0.001 liters
So 60 cm cubed = 0.06 liters.
Hope this helps
HELP I'M BEING TIMED A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? A) The test contains 4 three-point questions and 20 five-point questions. B) The test contains 10 three-point questions and 14 five-point questions. C) The test contains 14 three-point questions and 10 five-point questions. D) The test contains 20 three-point questions and 8 five-point questions.
Answer:
b)
Step-by-step explanation:
the easy way of doing this in my opinion is just to multiply the options by their corresponding values so in this case 3x10=30 and 5x14=70 then add those together and it equals 100 points with a total of 24 questions
!! 25 points !! Find x. Do not round your answer.
Answer:
12
Step-by-step explanation:
X=12
Because chords are the same size
Answer:16.6 is the correct answer.
Step-by-step explanation:
Hi, can I get some help with this question? DON'T WORRY ITS JUST A ASSIGNMENT. NOT A TEST. Thank you
Answer:
d.
Step-by-step explanation:
i looked at the graph!
A line contains the point (-4,6) and has a slope of -2/3 write the equation of the line using point-slope form
Answer:
(y-6)=-2/3(x+4)
Step-by-step explanation:
43046721 as a single power of 9
Answer:
[tex]9^8[/tex]
Step-by-step explanation:
[tex]9^8=43046721[/tex]
[tex]ln(9^x)=xln(9)[/tex]
so we search [tex]x=ln(43046721)/ln(9)[/tex]
hope this helps
Answer:
9^8=43046721
Step-by-step explanation:
The exponent 9 of a number is found by multiplying that number by itself 9 times.
IWhat is the slope of the line whose equation is y-4=5/2(x-2)?
Answer:
5/2
Step-by-step explanation:
You slope is always mx
In point-slope form, your mx is just in factored form. All you need to do is distribute to find m.
What is the vertex of the quadratic function?
f(x) = (x – 8)(x – 4)
A. (4,8)
B. (-6,4)
C. (6,-4)
D. (-4,8)
Answer:
C(6,-4)
Step-by-step explanation:
-8+-4=-12
-12÷2=-6
I hope this helps
Answer:
C
Step-by-step explanation:
(6,-4)
What is a reasonable estimate of the rate of change for the interval 300 <= x <= 400?
Answer:
The correct option is;
B. -2
Step-by-step explanation:
From the graph, we have;
At x₁ = 300, y₁ = 800
At x₂ = 400, y₂ = 600
The formula for the slope, m, of a graph is given as follows;
[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{600 - 800}{400 - 300}= \dfrac{-200}{100} = -2[/tex]
Therefore, a reasonable estimate of the rate of change for the interval 300 ≤ x ≤ 400 is -2 which is a negative slope as expected as the y-coordinate values, which is the value of the function, decreases while the x-coordinate values which is the independent variable increases as we go from 300 ≤ x ≤ 400.
Verify inverse functions
Answer:
Step-by-step explanation:
Hello
(fog)(x)=f(g(x))=10(x-6)/10+6=x-6+6=x
(gof)(x)=(10x-6+6)/10=10x/10=x
So YES the functions are inverse
hope this helps
Lim x-> n/2 (2e^x cos x)
Answer:
A
Step-by-Step Explanation:
We want to find the limit:
[tex]\displaystyle{\lim_{x\to\frac{\pi}{2}}(2e^x\cos(x))}[/tex]
Use direct substitution.
Hence:
[tex]\displaystyle{\Rightarrow 2e^\frac{\pi}{2}\cos(\frac{\pi}{2}})[/tex]
Recall the unit circle. cos(π/2) is simply 0. Hence:
[tex]\displaystyle{\Rightarrow 2e^\frac{\pi}{2}(0)=0[/tex]
Therefore:
[tex]\displaystyle{\lim_{x\to\frac{\pi}{2}}(2e^x\cos(x))}=0[/tex]
So, our answer is A.
Solve log x = 4. x = 4 x = 40 x = 1,000 x = 10,000
Answer:
x = 10000
Step-by-step explanation:
log x = 4
Raise each side to the base of 10
10^log x = 10 ^4
x = 10 ^4
x = 10000
Answer:
x = 10,000
Step-by-step explanation:
I got it right on the test.
need help asap!! please
Answer: 12.5
Step-by-step explanation:
25 / 2 = 12 1/2
12 1/2 in decimal form is 12.5
Answer:
12.5
Step-by-step explanation:
=> [tex]\frac{25}{2}[/tex]
In mixed form, it is
=> [tex]12\frac{1}{2}[/tex]
And in decimal form, it becomes
=> 12.5