Part a)
Given the expression
[tex]54m^3n\:+\:81m^4n^2[/tex]
Apply exponent rule: [tex]a^{b+c}=a^ba^c[/tex]
[tex]54m^3n\:+\:81m^4n^2=54m^3n+81m^3mnn[/tex] ∵ [tex]m^4n^2=m^3mnn[/tex]
Rewrite 81 as 3 · 27
Rewrite 54 as 2 · 27
[tex]=2\cdot \:27m^3n+3\cdot \:27m^3mnn[/tex]
Factor out the common term: 27m³n
[tex]=27m^3n\left(2+3mn\right)[/tex]
Therefore,
[tex]54m^3n\:+\:81m^4n^2=54m^3n+81m^3mnn=27m^3n\left(2+3mn\right)[/tex]
Part B)
Given the expression
[tex]15x^2y^3z+25x^3y^2z+35x^2y^2z[/tex]
Apply exponent rule: [tex]a^{b+c}=a^ba^c[/tex]
[tex]15x^2y^3z+25x^3y^2z+35x^2y^2z=15x^2y^2yz+25x^2xy^2z+35x^2y^2z[/tex]
Rewrite as
[tex]=3\cdot \:5y^2x^2zy+5\cdot \:5y^2x^2zx+7\cdot \:5y^2x^2z[/tex]
Factor out common term 5y²x²z
[tex]=5y^2x^2z\left(3y+5x+7\right)[/tex]
Therefore,
[tex]15x^2y^3z+25x^3y^2z+35x^2y^2z=5y^2x^2z\left(3y+5x+7\right)[/tex]
can someone explain what im supposed to do here
1) equation: f(x) = 6e^(ln(⅓) • x) or 6(10)^(log(1/3) • x)
table:
x | y
-1 20
0 6
1 2
2) is cut off, I can't see the rest of the graph.
A football team gained 7 yards in one play. What integer represents the amount of yards the football team gained?
Answer:
y + 7 = x
Step-by-step explanation:
0.5÷7/10
please help me with this my teacher is driving me crazy
Answer: 0.714286
turn 7/10 into .7 and divide normally
HELP ME QUICKLY DUE TODAY
For the expression below, combine like terms to simplify the expression. -4x + 3y - 6 -15x + 23y - 10
Answer: -19x + 26y - 16
Step-by-step explanation:
Combine like terms:
= -4x + 3y - 6 -15x + 23y - 10
= -4x - 15x + 3y + 23y - 6 - 10
Simplifying the expression:
= -4x - 15x + 3y + 23y - 6 - 10
= -19x + 26y - 16
Find the equation of the line passing through point (4,2) and perpendicular to AB
Answer:
a. -⅓
b. 3
c. y = 3x - 10
Step-by-step explanation:
a. Gradient of line AB:
A(1, 3), B(7, 1)
[tex] Gradient = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 3}{7 - 1} = \frac{-2}{6} = -\frac{1}{3} [/tex]
Gradient (m) = -⅓
b. The of the line that is perpendicular to line AB would be the negative reciprocal of the gradient of line AB.
Thus, the negative reciprocal of -⅓ = 3
Gradient of the line perpendicular to line AB = 3
c. Equation of the line that passes through (4, 2) and is perpendicular to line AB:
We can write the equation using the point-slope form equation, y - b = m(x - a), where,
(a, b) represents a point on the line, and,
m = gradient/slope
We know that the gradient/slope (m) = 3
Also, a point, (a, b) = (4, 2).
Therefore, substitute a = 4, b = 2, and m = 3 into y - b = m(x - a)
Thus:
y - 2 = 3(x - 4)
y - 2 = 3x - 12
Add 2 to both sides
y = 3x - 12 + 2
y = 3x - 10
helpppp !
preston can paint 375 square feet in 3 hours . at the same rate how long would it take him to paint 812.5 square feet ?
a ; 0.15 hours
b ; 1.4 hours
c ; 7.5 hours
d ; 6.5 hours
Answer:
It would take D.)6.5 hours to paint 812.5 square
Step-by-step explanation:
Answer:
It would take D.)6.5 hours to paint 812.5 square
Step-by-step explanation:
3 Dave can drive from Abdet to Bentall by two routes. The old route goes in roughly a straight line while the new faster route is 26% longer. Dave's average speed on the new faster route is 40% higher than his average speed on the old route. (a) By what percentage is Dave's journey time reduced by taking the new route compared to the old? [2]
Answer:
10 % of the total time will be saved on the new route with the new speed.
Step-by-step explanation:
Let x miles be the old route. Then the new route would be 1.26 x miles
Let y be the speed on the old route . Then the speed on the new route would be 1.4 y .
And let t be the time on the old route
Speed = Distance / Time
or
Time = Distance / Speed
t= x/y
Time for the new route = 1.26x/ 1.4y= 0.9 t
0.9 t means 90% of the old time will be required to cover 1.26x miles with 1.4 y speed.
And 10 % of the total time will be saved on the new route with the new speed.
alr, this is the last question im asking for today. pls help
you already know i gotchu :)
Answer: u = 5
Step-by-step explanation:
first, i moved the terms.
-4u + 10u = 37 - 7
then, i collected the like terms and calculated them.
6u = 30
finally, i divided both sides.
u = 5
PLEASE HELP
GIVE BRAINLIEST
Answer:
(f ￮ g)(- 64) = - 8
Step-by-step explanation:
Evaluate g(- 64) by substituting x = - 64 into g(x), then substitute the value obtained into f(x) , that is
g(- 64) = [tex]\sqrt[3]{-64}[/tex] + 1 = - 4 + 1 = - 3 , then
f(- 3) = (- 3 + 1)³ = (- 2)³ = - 8
Equilateral triangle has a side of 8 inches long find the area
Answer:
36 inches²
Step-by-step explanation:
area of a triangle = length x base x ½
= 8 × 8 × ½
= 36in²
1.3.PS-44 Question Help A housekeeper had 2 3 of a spray bottle of a cleaning solution. She used 1 4 of the solution in a day. How much of the bottle did she use?
Answer:
[tex]\bold{\frac{1}{6}}[/tex] of the bottle was used
Step-by-step explanation:
Amount of cleaning solution present in spray bottle = [tex]\frac{2}3[/tex] of the bottle
Amount of cleaning solution present in the spray bottle used = [tex]\frac{1}4[/tex] of the cleaning solution present initially
To find:
How much of the bottle was used?
Solution:
Here, we need to find how much amount of the cleaning solution spray was used from the complete bottle.
Amount of spray used = [tex]\frac{1}{4}\times \frac{2}{3}[/tex] of the cleaning solution = [tex]\bold{\frac{1}{6}}[/tex] of the cleaning solution.
Therefore, the answer is:
[tex]\bold{\frac{1}{6}}[/tex] of the bottle was used
Factor completely. 3x2 + 8x + 5
Answer:
(x + 1)(3x + 5)
Step-by-step explanation:
[tex]3 {x}^{2} + 8x + 5 \\ \\ = 3 {x}^{2} + 3x + 5x + 5 \\ \\ = 3x(x + 1) + 5(x + 1) \\ \\ = (x + 1)(3x + 5)[/tex]
Answer:
The answer is (x+1)(3x+5)
let me know if this helps:)
can someone please tell me what the range is?
Answer: y > -1.5 which is the same as y > -3/2
==========================================================
Explanation:
As x goes off to negative infinity, the term 3^x gets closer to 0.
So the expression 0.5*(3^x - 3) approaches 0.5*(0-3) = 0.5*(-3) = -1.5 = -3/2
The y value will never actually get to -1.5 because 3^x never actually reaches 0. It only gets closer and closer.
So the range is the set of possible y outputs such that y > -1.5 or y > -3/2
This means the horizontal asymptote is y = -3/2 or y = -1.5 which is the horizontal "electric fence" of sorts that the function curve gets closer to, but never touches.
Question 7 Mai wants to construct a regular hexagon inscribed in the
circle centered at C. Will these instructions work to finish the hexagon
from the construction given? Why? Step 1 Draw the circle centered at D
with radius CD. Step 2 Mark the intersection of the circle with the circle
centered at C, and label that point E. Step 3 Draw the circle centered at E
with radius DE. Step 4 Mark the intersection of the circle with the circle
centered at D, and label that point F. Step 5 Connect ABCDEF to make a
regular hexagon.
Answer:
Yes
Step-by-step explanation:
Help me please there’s a time limit on this
Answer:
B
Step-by-step explanation:
12x = 72
x = 6
12 x 6 = 72
Answer:
it would be b.
Step-by-step explanation:
if u plug a number into the x spot it would be 12 x 6 = 72
What is 12ab+6ab
Please
Can u help me pls
This homework was due last week
I really need help
thx xxx
What is the slope of y=-x+7
Answer:
-1
Step-by-step explanation:
This is the slope because x is the slope, and if there is no number in front of x then x is 1. There is also a negative in front of x which means the answer is -1.
The slope of the equation y = -x + 7 equals -1.
I NEED HELP ASAP PLEASE DONT JUST TYPE FOR POINTS ACTUALLY HELP MEE
Answer:
i think it's A but don't quote me on it
Step-by-step explanation:
Answer:
D.
Step-by-step explanation:
Plz help it due in a hour
And show workings
Mia, Thomas, and Jasmine are competing in a barrel race. Thomas's time is 8 seconds more than Mia's time. Jasmine's time is į times the quantity of 21 seconds more than Mia's time. The sum of all three times is 71 seconds. what represents this situation and what is the value of m
Given that,
Thomas's time is 8 seconds more than Mia's time.
Jasmine's time is į times the quantity of 21 seconds more than Mia's time
The sum of all three times is 71 seconds.
To find,
The value of m.
Solution,
Let Mia's time is m.
Thomas's time = 8+m
Jasmine's time = 21 + 8+ m
ATQ,
m + 8 + m + 21 + 8 + m = 71
3m + 37 = 71
3 m = 71 - 37
m = 34/3
m = 11.34
So, the value of m or Mia's time is 11.34 seconds.
Answer:
m+1/3(m+21)+m+8=71, m=24
Step-by-step explanation:
Helen drives 195 miles in 3 hours
A) what is her average speed in mph
Answer:
First 195 dived by 3, then the answer is 65.
Which choice is equivalent to the expression below?
2^7.19
Answer:
B
Step-by-step explanation:
Exponents Law:
[tex]a^{m}*a^{n} = a^{m+n}[/tex]
In exponent multiplication, if bases are same, add the powers(exponents).
Write 7.19 in expanded form: 7.19 = 7 + 0.1 + 0.09. Now apply the exponent rule.
[tex]2^{7.19}=2^{7+0.1+0.09}\\\\=2^{7}*2^{0.1}*2^{0.09}\\\\= 2^{7}*2^{\frac{1}{10}}*2^{\frac{9}{100}}[/tex]
* Select all the expressions whose value is larger than 100.
A 120% of 100
50% of 150
C250% of 50
20% of 800
E 200% of 30
G 19 of 1,000
Answer please
I am in dire need of an answer
Please please
7 kg of apples cost $14. How much would 41 kg cost?
pls help me
Answer:
41 kg of apples would cost $82.
Step-by-step explanation:
41 kg divided by 7 kg is 5.85714285714. 5.85714285714 multiplied by $14 is $82.
What is the slope-intercept form of the function described by this table? x 1 2 3 4 y 8 13 18 23 Enter your answer by filling in the boxes. y = x +
Answer:
y = 5 x + 3
Step-by-step explanation:
I took the quiz
Which relationship is an example of a proportional relationship?
helppp?
Answer: “samuel earns $20 for each lawn he mows”
Step-by-step explanation:
The statements that represent proportional relationship are statement [1], [2] and [4].
What is proportional relationship? What is equation modelling? What is a mathematical equation and expression?The proportional relationship between [y] and [x] is given by -y = mx + c
for [c] = 0
m = y/x
where [m] is the constant of proportionality.
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given are some statements depicting proportional relationship.
For the statement [1], we can write the equation as -
y = 0.08x + 59
For the statement [2], we can write the equation as -
y = 25x + 45
For the statement [1], we can write the equation as -
y = 20x
Therefore, the statements that represent proportional relationship are statement [1], [2] and [4].
To solve more questions on functions, expressions and equation modelling, visit the link below -
brainly.com/question/17421223
#SPJ2
Simplify Combine like terms
4a-5a+2a+6a
Answer: 7a
Step-by-step explanation: Since they are like terms, you can just add or subtract them.
4a - 5a = -1a
2a + 6a = 8a
-1a + 8a = 7a