Answer:
[tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = 9 ,\ x \neq 0[/tex]
General Formulas and Concepts:
Pre-Algebra
Evaluations
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Distributive Property
Terms/Coefficients
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle \frac{4(3x)^2}{(2x)^2}[/tex]
Step 2: Simplify:
Rewrite [Exponential Distributive Property]: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = \frac{4(3^2x^2)}{2^2x^2}[/tex][Order of Operations] Evaluate exponents: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = \frac{4(9x^2)}{4x^2}[/tex][Order of Operations] Multiply: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = \frac{36x^2}{4x^2}[/tex]Simplify: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = \frac{36}{4} ,\ x \neq 0[/tex][Order of Operations] Divide: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = 9 ,\ x \neq 0[/tex][tex]\\ \sf\longmapsto \dfrac{4(3x)^2}{(2x)^2}[/tex]
[tex]\\ \sf\longmapsto\dfrac{ 4(9x^2)}{4x^2}[/tex]
[tex]\\ \sf\longmapsto \dfrac{36x^2}{4x^2}[/tex]
Take x^2 common and cancel.[tex]\\ \sf\longmapsto \dfrac{x^2}{x^2}\left(\dfrac{36}{4}\right)[/tex]
[tex]\\ \sf\longmapsto \dfrac{36}{4}[/tex]
[tex]\\ \sf\longmapsto 9[/tex]
Chose the justification for each step in the solution to the given equation stop application subtraction property of equality multiplication property of equality division property of equality addition property of equality
Answer:
Step-by-step explanation:
Given the point and the slope, write the function in point-slope form:
(2,−5);m=23
Group of answer choices
y−5=23(x−2)
y+5=23(x−2)
y−5=23(x+2)
y+5=23(x+2)
Answer:
2nd answer choice
Step-by-step explanation:
point slope form: y-y1=m(x-x1)
y-(-5)=23(x-2)
y+5=23(x-2)
Answer:
(b) y+5=23(x−2)
Step-by-step explanation:
The point-slope form for the equation of a line is ...
y -k = m(x -h) . . . . . . point (h, k), slope m
You have point (2, -5) and m=23, so the equation becomes ...
y -(-5) = 23(x -2)
y +5 = 23(x -2) . . . . . . simplify a bit
please i need help with this
Given :-
Line p has an equation of y = 5/3x - 4 .Line q includes point (-10,-3) and is perpendicular to the line p .To Find :-
The equation of line q .Solution :-
The equation of the line p is ,
[tex]\sf\blue{\longrightarrow}[/tex] y = 5/3x - 4
On comparing to slope intercept form of the line which is y = mx + c , we have ,
[tex]\sf\blue{\longrightarrow}[/tex] m = 5/3
Now as we know that the product of slopes of two perpendicular lines is -1 . So the slope of the perpendicular line will be ,
[tex]\sf\blue{\longrightarrow} m_{\perp} = -3/5[/tex]
Now here the line q passes through the point (-10,-3) . So on using the point slope form of the line we get ,
[tex]\sf\blue{\longrightarrow} y - y_1 = m(x-x_1)[/tex]
[tex]\sf\blue{\longrightarrow}[/tex] y - (-3) = -3/5[ x-(-10)]
[tex]\sf\blue{\longrightarrow}[/tex] y +3 = -3/5(x+10)
[tex]\sf\blue{\longrightarrow}[/tex] y+3 = -3/5x - 6
[tex]\sf\blue{\longrightarrow}[/tex] y +9 = -3/5x
[tex]\sf\blue{\longrightarrow}[/tex] y = - 3/5x - 9
Hence the required answer is y = -3/5x - 9 .
Answer:
For Perpendicular lines you have to know
Step-by-step explanation:
Slope of P ×slope of q=-1 (always since they are perpned..)
so as P has the slope 5/3 in order to optain - 1 the slope of q should be negative of the inverse of p
so q solpe =-3/5 then lets try (5/3)×(-3/5)? =-1 yes
And be aware that you have to know the formula of straight line : y-ypoint=slope(x-xpoint) or y=ax+b
so y+3=-3/5(x+10) ===> y=-3/5x - 30/5 - 3
uniting the denominater ==>y=-3/5x - 45/5
so that q equation is :y=-3/5x - 9
A middle school principal is signing the diplomas of the school's graduating eighth graders.
She previously signed 37 diplomas. Now, she is signing more diplomas at a rate of 0.5 per
second. If the principal signs diplomas for 60 seconds, what will the total number of signed
diplomas be?
Answer: 67 diplomas
Step-by-step explanation:
0.5 diplomas per second = 1 diploma per 2 seconds
60/2 = 30
30+37 = 67
Correct me if I am incorrect
An equation that shows how the total number of diplomas signed depends on the number of seconds the principal spends signing them is y = 37 + 0.5x.
What is an equation?
An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
In this case, let x be number of seconds the principal spends signing them. The principal already signed 37 diplomas. Th equation to illustrate this is 37 + 0.5x.
Write a quadratic function whose zeros are 2 and -12. 60 Point question Answer ASAP for brainliest!
Answer:
x^2 + 10x - 24 = 0
Step-by-step explanation:
Two zeros are 2 and -12:
x - 2 = 0x + 12 = 0So the function is (x-2)(x+12) = 0
<=> x^2 + 12x - 2x - 24 = 0
<=> x^2 + 10x - 24 = 0
Karl’s rectangular vegetable garden is 20 feet by 45 feet, and Makenna’s is 25 feet by 40 feet. Whose garden is larger in area?
Answer:
Makennas
Step-by-step explanation:
Area of rectangle = length * width
Area of Karl's garden = 20 * 45 = 900ft²
Area of Makenna's garden = 25 * 40 = 1000ft²
1000 is greater than 900 therefore makennas garden has a greater area than Karls garden
Hence, Makenna's garden is larger in area than Karl's because 1000 > 900.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
What is the domain? (Type your answer with commas and no spaces)
Answer:
The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.
Step-by-step explanation:
Find the greatest common factor of the
following monomials:
18xy^ 30xy3
NO LINKS
Answer:
Step-by-step explanation:
6xy^3
can someone help me please?
Answer:
1) x = 3, y = 2 or (3, 2)
2) x = 0, y = 2 or (0, 2)
6) x = 3, y = – 4 or (3, – 4)
Step-by-step explanation:
I will only provide solutions for questions 1, 3, and 6 in accordance with Brainly's guidelines.
Question 1:[tex]\displaystyle\mathsf{\left \{ {{\:\:Equation\:1:\:y\:=\:-2x\:+\:5} \atop{Equation\:2:\:y\:=\:-x\:+\:2}} \right. }[/tex]
Substitute the value of y in equation 2 into the first equation:
y = -2x + 5
-x + 2 = -2x + 5
Add 2x on both sides:
-x + 2x + 2 = -2x + 2x + 5
x + 2 = 5
Subtract 2 from both sides to isolate x:
x + 2 - 2 = 5 - 2
x = 3
Substitute the value of x into Equation 2 to solve for the value of y:
y = -x + 5
y = -(3) + 5
y = 2
Solution of the given systems of linear equations:Therefore, the solution to the given systems of linear equations is: x = 3, y = 2 or (3, 2).
Question 3:
[tex]\displaystyle\mathsf{\left \{ {{Equation\:1:\:3x\:+\:5y=\:10} \atop{Equation\:2:\:y\:=\:-5x\:+\:2}} \right. }[/tex]
Substitute the value of y from Equation 2 into Equation 1:
3x + 5y = 10
3x + 5(-5x + 2) = 10
Distribute 5 into the parenthesis:
3x + -25x + 10 = 10
Combine like terms:
-22x + 10 = 10
Subtract 10 from both sides:
-22x + 10 - 10 = 10 - 10
-22x = 0
Divide both sides by -22 to solve for x:
[tex]\displaystyle\mathsf{\frac{-22x}{-22}\:=\:\frac{0}{-22}}[/tex]
x = 0
Substiute the value of x into Equation 2 to solve for y:
y = -5x + 2
y = -5(0) + 2
y = 2
Solution of the given systems of linear equations:Therefore, the solution to the given systems of linear equations is: x = 0, y = 2 or (0, 2).
Question 6:[tex]\displaystyle\mathsf{\left \{\quad\:Equation\:1:\:-2x+6y=\:-30} \atop{Equation\:2:\:y-2x=\:-10}} \right.}[/tex]
Add 2x to both sides of Equation 2 to isolate y:
y – 2x = –10
y – 2x + 2x = 2x – 10
y = 2x – 10
Substitute the value of y from the previous step into Equation 1:
– 2x + 6y = – 30
– 2x + 6(2x – 10) = – 30
Distribute 6 into the parenthesis:
– 2x + 12x – 60 = – 30
Combine like terms:
10x – 60 = – 30
Add 60 to both sides:
10x – 60 + 60 = – 30 + 60
10x = 30
[tex]\displaystyle\mathsf{\frac{10x}{10}\:=\:\frac{30}{10} }[/tex]
x = 3
Substitute the value of x into Equation 2 to solve for y:
y – 2x = –10
y – 2(3) = –10
y – 6 = –10
y – 6 + 6 = –10 + 6
y = – 4
Solution of the given systems of linear equations:Therefore, the solution to the given systems of linear equations is: x = 3, y = – 4 or (3, – 4).
REPOST BECAUSE OF LINKS ASAP WORTH 70 POINTS IF U ANSWER
It is recommended that you work this out on graph paper to help answer the questions. Maria plots the locations of 4 places on a coordinate grid as given below (It is recommended that you work this out on graph paper to help answer the questions.):
Her house is at (−4, 9).
Her school is at (−4, 3).
The community center is at (1, 3).
The grocery store is at (−4, −8).
Is the total distance from Maria's house to the school to the grocery store greater than the total distance from Maria's house to the school to the community center? Justify your answer.
Answer/Step-by-step explanation:
9-3= 6 units (since x coordinates are same). We can also show by manually counting the squares (1 square= 1 unit)
Yes, its greater. Distance from house to school is 6. Distance from school to grocery is 3-(-8)= 11. Thus, distance is 11+6= 17 units.
Distance from house to school is 6. Distance from school to community center is 1-(-4)=5. Thus, distance= 6+5=11 units.
Can someone plz help me?
Answer:
A. 5(y+3) = 5(3+y)
Step-by-step explanation:
my Christmas present to you
Answer:
yay thx
Step-by-step explanation:
merry xmas
10x1+2x60/10
Hi! Um I have only four questions on an assignment thats due Friday, this is one of them and I keep getting stuck, can someone please help me out?
Answer:
2
Step-by-step explanation:
HELP!!!! I WILL GIVE 100 POINTS!
Answer:
x = 17y = 18Step-by-step explanation:
8x - 17 + 3x + 10 = 180 => 11x - 7 = 180=> 11x = 187=> x = 187/11=> x = 17=> 8(17) - 17 = 6y + 11=> 136 - 17 - 11 = 6y=> 108 = 6y=> y = 18Conclusion:
Therefore:
x = 17y = 18Hoped this helped.
[tex]GeniusUser[/tex]
The arcs in the photo at the right appear to
be paths of stars rotating about the North Star, To produce this effect, the
photographer set a camera on a tripod and left the shutter open for an
extended time. If the photographer left the shutter open for a full 24 hours,
each are would be a complete circle. You can model a star's rotation" in the
coordinate plane. Place the North Star at the origin. Let P(1, 0) be the position
of the star at the moment the camera's shutter opens. Suppose the shutter is
left open for 2 h 40 min, with the arc ending at P. a. What angle of rotation
maps Ponto P? b. What are the x and y coordinates of P to the nearest
thousandth? c. What translation rule maps P onto P?
Answer:
a. What angle of rotation maps Ponto P?
30.25 degrees
b. What are the x and y coordinates of P to the nearest thousandth?
(83.3, 33.3)
c. What translation rule maps P onto P?
Rotation
write 1+√-32/4 as a complex number in the form a + bi, where a and b are real numbers.
a. 1/4+1/2√2i
b. 1/4+1/4√2i
c. 1/4+√2i
d. 1/4+4√2i
Work Shown:
[tex]\frac{1+\sqrt{-32}}{4}\\\\\frac{1+\sqrt{-1*16*2}}{4}\\\\\frac{1+\sqrt{-1}*\sqrt{16}*\sqrt{2}}{4}\\\\\frac{1+i*4*\sqrt{2}}{4}\\\\\frac{1+4i*\sqrt{2}}{4}\\\\\frac{1}{4}+\frac{4i*\sqrt{2}}{4}\\\\\boldsymbol{\frac{1}{4}+i\sqrt{2}}\\\\[/tex]
This matches with choice C. The imaginary 'i' term is not under the square root.
Write an equation in point-slope form of the line that passes through the point (-6,6) and has a slope of m=3/2
Answer:
y=3/2 x+15
Step-by-step explanation:
Calculate the measure of angle L
==================================================
Explanation:
Lines LM and LP are tangent to the circle at points M and P respectively. The dashed radius lines are perpendicular to those tangents, which means we have 90 degree angles at points M and P.
For any quadrilateral, the four angles always add to 360 degrees.
L+M+O+P = 360
L+90+165+90 = 360
L+345 = 360
L = 360-345
L = 15
Another route you can use is the fact that opposite angles L and O are supplementary
L+O = 180
L+165 = 180
L = 180-165
L = 15
What would the graph look like
Answer I cant read the thing sorry
Step-by-step explanation:
hoped that hepled:)
evaluate 5(ax4)+b,
when a=1/3 and b=12
you just need to put the values of a and b where they have to be
.
hope I helped!
Hey y’all please help me ASAP.
Answer:
the top right box
Step-by-step explanation:
Answer:
-g-8≥9
Step-by-step explanation:
Just ask.
Hope this helps. :)
Question 4 of 10
Which statement about setting is true as it relates to a story?
A. Setting helps to define a story's point of view.
B. Setting is another word for characterization.
Ο Ο Ο
C. Setting affects character behavior, which drives the plot.
D. Setting comes into play at the end of a story.
SUBMIT
Answer:
First of all not a math question but wtv
the answer is C since where the story takes place affects what the characters do
Hope This Helps!!!
In which of the following numbers does the digit 2 represent tens? *
2517
342
720
518.2
Answer:
720
Step-by-step explanation:
The digit 2 is the second digit left of the decimal point in the number ...
720
_____
2517 --- 2 is in the thousands place
342 --- 2 is in the ones place
720 --- 2 is in the tens place
518.2 --- 2 is in the tenths place
(8y²)(-3x²y²)(2/3xy⁴)
HELP PLEASEEEEEEEE
Step-by-step explanation:
1 Remove parentheses.
8{y}^{2}\times -3{x}^{2}{y}^{2}\times \frac{2}{3}x{y}^{4}
8y
2
×−3x
2
y
2
×
3
2
xy
4
2 Use this rule: \frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}
b
a
×
d
c
=
bd
ac
.
\frac{8{y}^{2}\times -3{x}^{2}{y}^{2}\times 2x{y}^{4}}{3}
3
8y
2
×−3x
2
y
2
×2xy
4
3 Take out the constants.
\frac{(8\times -3\times 2){y}^{2}{y}^{2}{y}^{4}{x}^{2}x}{3}
3
(8×−3×2)y
2
y
2
y
4
x
2
x
4 Simplify 8\times -38×−3 to -24−24.
\frac{(-24\times 2){y}^{2}{y}^{2}{y}^{4}{x}^{2}x}{3}
3
(−24×2)y
2
y
2
y
4
x
2
x
5 Simplify -24\times 2−24×2 to -48−48.
\frac{-48{y}^{2}{y}^{2}{y}^{4}{x}^{2}x}{3}
3
−48y
2
y
2
y
4
x
2
x
6 Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x
a
x
b
=x
a+b
.
\frac{-48{y}^{2+2+4}{x}^{2+1}}{3}
3
−48y
2+2+4
x
2+1
7 Simplify 2+22+2 to 44.
\frac{-48{y}^{4+4}{x}^{2+1}}{3}
3
−48y
4+4
x
2+1
8 Simplify 4+44+4 to 88.
\frac{-48{y}^{8}{x}^{2+1}}{3}
3
−48y
8
x
2+1
9 Simplify 2+12+1 to 33.
\frac{-48{y}^{8}{x}^{3}}{3}
3
−48y
8
x
3
10 Move the negative sign to the left.
-\frac{48{y}^{8}{x}^{3}}{3}
−
3
48y
8
x
3
11 Simplify \frac{48{y}^{8}{x}^{3}}{3}
3
48y
8
x
3
to 16{y}^{8}{x}^{3}16y
8
x
3
.
-16{y}^{8}{x}^{3}
−16y
8
x
3
Done
Convert 34/8 to a decimal using long division
Answer: Using a calculator, if you typed in 34 divided by 8, you'd get 4.25. You could also express 34/8 as a mixed fraction: 4 2/8.
Step-by-step explanation:
Answer:
answer
Step-by-step explanation:
is using a cancalator duh
Tien works in a music store and earns 10.4% commission on each sale. If Tien sells a guitar and earns $142.25, what is the price of the guitar? Round your answer to the nearest cent.
$1,367.79
$14.79
$13.68
$1,492.79
Harry and Matthew, have 56 toys to build. harry builds three fourths of the toys, while matthew builds one seventh of the toys. How many toys are there left to build?
Answer:
i don't know
Step-by-step explanation:
how can you identify symmetry in a figure?
Answer:
You can identify symmetry by if on both sides it looks the same.
1) Derrick is sharing pizza with his 3 friends. They have 6/8 of a pizza. If they split the pizza evenly, how much pizza does each person get? Show your work with both a model and an equation.
Answer:
3/16
Step-by-step explanation:
So Derrick is sharing pizza with 3 friend, so in total, there are 4 people.
There is 6/8 pizza in current total pizza.
[tex]\frac{\frac{6}{8}}{4} =6/32=3/16[/tex]
Answer:
2/8
Step-by-step explanation:
each person would get 2/8
James is from Rochester. Today, he has to travel to Cannon Falls for a morning meeting and then to Austin for an afternoon meeting and then home again. Cannon Falls is 45 miles directly north of Rochester. Austin is 42 miles directly west of Rochester. There is a nice straight road from Cannon Falls to Austin. Calculate the total distance he will be driving. Round your answer to the nearest mile.
(Drawing a map may be helpful.)
Answer:
His total distance is 149 miles.
Step-by-step explanation:
Use the Pythagorean theorem to find the value of the straight road from cannon falls to austin. Then add that value with 42 and 45.