My answers are in the picture above.
A line segment has endpoints at 3,2 and 2,-3 which reflection will produce an image with endpoints at 3,-2 and 2,3
Answer:
The reflection is across the x-axis
Step-by-step explanation:
* Lets revise the reflection
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
- If point (x , y) reflected across the line y = x
∴ Its image is (y , x)
- If point (x , y) reflected across the line y = -x
∴ Its image is (-y , -x)
* Now lets solve the problem
∵ The endpoints of a line segment are (3 , 2) and (2 , -3)
∵ The image of the endpoints after the reflection are (3 , -2) and (2 , 3)
* Lets study the change
# The x-coordinates of the points are 3 and 2
# The x-coordinates of the images are 3 and 2
# The y-coordinates of the points are 2 and -3
# The y-coordinates of the images are -2 and 3
- The change is in the signs of the y-coordinates
∴ The reflection is across the x-axis
7 and 1/2 divided by 1
If you divide any number by 1, the answer is itself. The answer is 7 and 1/2.
Hope this helps!
Answer:
7 1/2
Step-by-step explanation:
Take it like the following scenario.
There are 7 1/2 M&M's left in a bag.
Neither of your friends want any so you get to have all of them.
So, the 7 1/2 M&M's divided by one person is 7 12 since all of the M&M's go to you.
[Rememember that any number you divide by 1, the answer is itself
Ex: 4 divided by 1 = 4]
I hope this helps!
Please help! :)
Solve for x to the nearest tenth.
X^2+x-5=0
Answer:
1.8, -2.8
Step-by-step explanation:
1.8, -2.8 in decimal form rounded to the nearest tenth.
In quadratic form its originally [tex]x=\frac{-1+\sqrt{21} }{2} ,\frac{-1-\sqrt{21} }{2}[/tex]
Hope this helps
1) What is the slope of the trend line ?
2) what is the y-intercept for the trend line ? What is the real world meaning of this point?
Answer:
slope m=0.5, y-intercept b=5, the price of a 0 page book starts off at 5 and increases 0.5 every 50 pages
Step-by-step explanation:
point slope formula
[tex]y = mx + b[/tex]
choose a point on the line, I chose (2.00,6.00)
and b is the y-intercept at (0,5)
then plug those numbers in
[tex]6.00 = m2.00 + 5.00[/tex]
simplify & isolate the variable
[tex]6.00 - 5.00 = m2.00 + 5.00 - 5.00 [/tex]
[tex]1 = m2[/tex]
[tex]1 \div 2 = m2 \div 2[/tex]
solve for m
[tex]0.1 = m[/tex]
the y intercept is were the line crosses the y axis.
the y axis represents cost in dollars, the x axis represents number of pages
PLEASE ANSWER RIGHT AWAY
ANSWER
The explicit formula is :
[tex]a_n = 8+ 3(n - 1)[/tex]
EXPLANATION
The given sequence is
8,11,14,17,20,23,26,...
The first term is
[tex]a_1=8[/tex]
The common difference is
d=11-8
d=3
The explicit formula is given by:
[tex]a_n = a_1 + d(n - 1)[/tex]
We substitute the values to get,
[tex]a_n = 8+ 3(n - 1)[/tex]
Which of the following are the factors of m2 – 14m + 48? A. (m + 6)(m + 8) B. (m – 12)(m + 4) C. (m – 12)(m – 4) D. (m – 6)(m – 8)
For this case we must factor the following expression:
[tex]m ^ 2-14m + 48[/tex]
We must look for two numbers that when multiplied give as a result "48", and when summed, give as a result "-12". These numbers are:
-6 and -8
[tex]-6 * -8 = 48\\-6-8 = -14[/tex]
So, we have:
[tex](m-6) (m-8)[/tex]
ANswer:
Option D
Answer:
Step-by-step explanation:
DDDDDDDDDDDDDDDDDD
The area of a rectangle, A = 1 x w is represented by the expression 24x^6y^15 Which could be the dimensions of the
rectangle?
Answer:
A. 2x^5y^8 and 12xy^7
Step-by-step explanation:
The question is on laws of indices
when we have x^a × x^b = x^(a+b)
Given in the question 24x^6y^15
24 could be 2×12............for the length and width
Then x^6 = x^1 × x^5 = x^(1+5) = x^6
And y^15 = y^8 ×y^7 = y^(8+7) = y^(15)
Answer:
The correct answer is :[tex]l=2x^5y^8,w = 12xy^7[/tex]
Step-by-step explanation:
Let the dimension of the rectangle be l and w.
A = [tex]24x^6y^{15}[/tex]
[tex]24x^6y^{15}=l\times w[/tex]
A) If the dimension are :
[tex]l=2x^5y^8,w = 12xy^7[/tex]
Area of the rectangle
[tex]= 2x^5y^8\times 12xy^7=24x^6y^{15}=A[/tex]
B) If the dimension are :
[tex]l=6x^2y^3,w = 4x^3y^5[/tex]
Area of the rectangle
[tex]= 6x^2y^3\times 4x^3y^5=24x^5y^{8}\neq A[/tex]
C) If the dimension are :
[tex]l=10x^6y^{15},w = 14x^6y^{15}[/tex]
Area of the rectangle
[tex]= 10x^6y^{15}\times 14x^6y^{15}=140x^{12}y^{30}\neq A[/tex]
D) If the dimension are :
[tex]l=9x^4y^{11},w = 12x^2y^4[/tex]
Area of the rectangle
[tex]= 9x^4y^{11}\times 12x^2y^4=108x^6y^{15}\neq A[/tex]
Harold took a total 8 quizzes over the course of 2 weeks. How many weeks of school will Harold have to attend this quarter before he will have taken a total of 20 quizzes?
Answer:
5
Step-by-step explanation:
8 quizzes / 2 weeks = 20 quizzes / x weeks
Cross multiply:
8x = 40
Divide:
x = 5
Harold will have to attend 5 weeks.
How many points does the graph of the function below intersect the x-axis? y=9x^2 -12x+4
Answer:
One point: (2/3, 0)
Step-by-step explanation:
The fastest way to determine this is to find the discriminant, b^2-4ac:
discriminant = (-12)^2 - 4(9)(4) = 144 - 144 = 0
The rule here states that if the discriminant is 0, the function has two real, equal roots. Those roots are
-(-12) ± √0
x = ---------------- = 12/18, or 2/3.
2(9)
The graph touches the x-axis at x = 2/3, but does not cross it. In other words, the graph intersects the x-axis at only one x value: 2/3.
x = ------------------
The graph of the function y = 9x² - 12x + 4 intersect the x-axis at [tex]x = \frac{2}{3}[/tex] only.
What is x-intercepts ?The x-intercepts are the points where the graph intersects the x-axis. The vertex is the point that defines the minimum or maximum of a parabola.
We have,
y = 9x² - 12x + 4
Now,
So, to get the x-intercept,
Put y = 0,
i.e.
0 = 9x² - 12x + 4
Now,
Using the mid term splitting method,
0 = 9x² - 12x + 4
0 = 9x² - 6x - 6x + 4
0 = 3x(3x - 2) -23(x - 2)
i.e.
0 = (3x - 2) (3x - 2)
Now,
3x - 2 = 0
⇒ [tex]x = \frac{2}{3}[/tex]
And,
Now,
3x - 2 = 0
⇒ [tex]x = \frac{2}{3}[/tex] ,
So,
The x -intercept is only at one point, i.e. [tex]x = \frac{2}{3}[/tex].
Hence, we can say that the graph of the function y = 9x² - 12x + 4 intersect the x-axis at [tex]x = \frac{2}{3}[/tex] only.
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Find the solutions to the equation below. Check all that apply. 30x^2-26x+4=0
A.x=1/2
B.x=1/5
C.x=4/5
D.x=1/3
E.x=3/5
F.x=2/3
Answer:
B. x = 1/5F. x = 2/3Step-by-step explanation:
[tex]30x^2-26x+4=0\\\\30x^2-20x-6x+4=0\\\\10x(3x-2)-2(3x-2)=0\\\\(3x-2)(10x-2)=0\iff3x-2=0\ \vee\ 10x-2=0\\\\3x-2=0\qquad\text{add 2 to both sides}\\\\3x=2\qquad\text{divide both sides by 3}\\\\x=\dfrac{2}{3}\\\\10x-2=0\qquad\text{add 2 to both sides}\\\\10x=2\qquad\text{divide both sides by 10}\\\\x=\dfrac{2:2}{10:2}\\\\x=\dfrac{1}{5}[/tex]
Find the surface area of the cylinder to the nearest whole number. The figure is not drawn to scale
Answer:
The best possible answer is A
Step-by-step explanation:
Answer:
Option A is correct that is Surface Area of the Cylinder is 1659 in.²
Step-by-step explanation:
Given:
Radius of the Cylinder , r = 11 in.
Height of the Cylinder , h = 13 in.
We have to find the Surface Area of Cylinder to the nearest Whole number.
We know that,
Surface Area of the Cylinder = 2πr(r+h)
= 2 × 22/7 × 11 ( 11 + 13 )
= 2 × 22/7 × 11 × 24
= 1659.42 in.²
= 1659 in.² (nearest whole number)
Therefore, Option A is correct that is Surface Area of the Cylinder is 1659 in.²
How do I ace my algebra eoc?
Answer:
The EOC is an exam that is more logical, what I can recommend is to study the packages the teacher gave you and also study at USATESTPREP that can help you a lot
What is the range of the function f(x)=(x-1)^2 when the domain is {-5,0,5}?
The range of the function f (x) = (x - 1)² when the domain is {-5,0,5} is,
⇒ {36, 1, 16}
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable
Given that;
The function is,
⇒ f (x) = (x - 1)²
And, domain is {-5,0,5}.
Now, We can find the value of range as;
Put x = - 5 in above function,
⇒ f (x) = (x - 1)²
⇒ f (x) = (- 5 - 1)²
⇒ f (x) = (- 6)²
⇒ f (x) = 36
Put x = 0 in above function,
⇒ f (x) = (x - 1)²
⇒ f (x) = (0 - 1)²
⇒ f (x) = (- 1)²
⇒ f (x) = 1
Put x = 5 in above function,
⇒ f (x) = (x - 1)²
⇒ f (x) = ( 5 - 1)²
⇒ f (x) = ( 4)²
⇒ f (x) = 16
Thus, The range of the function f (x) = (x - 1)² when the domain is {-5,0,5} is,
⇒ {36, 1, 16}
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Jason and Henry go to the movie theater and purchase refreshments for their friends.
Jason spends a total of $66.75 on 12 drinks and 1 bag of popcorn.
Henry spends a total of $82.50 on 3 drinks and 10 bags of popcorn.
Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn.
Using these equations, determine and state the price of a drink, to the nearest cent.
Answer:
Part 1) The system of equations is equal to
12x+y=66.75
3x+10y=82.50
Part 2) The cost of one drink is $5
Step-by-step explanation:
Part 1) Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn
Let
x----> the price of one drink
y ----> the price of one bag of popcorn
we know that
Jason
12x+y=66.75 -----> equation A
Henry
3x+10y=82.50 -----> equation B
Part 2) Using these equations, determine and state the price of a drink, to the nearest cent
12x+y=66.75 -----> equation A
3x+10y=82.50 -----> equation B
Solve the system of equations by elimination
Multiply the equation A by -10 both sides
-10*(12x+y)=66.75*(-10)
-120x-10y=-667.5 -----> equation C
Adds equation B and C and solve for x
3x+10y=82.50
-120x-10y=-667.5
-----------------------------
3x-120x=82.50-667.5
120x-3x=667.50-82.50
117x=585
x=5
therefore
The cost of one drink is $5
A hyperbolic mirror can be used to take panoramic photos, if the camera is pointed toward the mirror
with the lens at one focus of the hyperbola. Write the equation of the hyperbola that can be used to
model a mirror that has a vertex 4 inches from the center of the hyperbola and a focus 1 inch in front of
the surface of the mirror. Assume the mirror has a horizontal transverse axis and the hyperbola is
centered at (0, 0).
Answer:
The equation of the hyperbola is x²/16 - y²/9 = 1
Step-by-step explanation:
* Lets study the equation of the hyperbola
- The standard form of the equation of a hyperbola with
center (0 , 0) and transverse axis parallel to the x-axis is
x²/a² - y²/b² = 1
- The length of the transverse axis is 2a
- The coordinates of the vertices are (±a , 0)
- The length of the conjugate axis is 2b
- The coordinates of the co-vertices are (0 , ±b)
- The coordinates of the foci are (± c , 0),
- The distance between the foci is 2c where c² = a² + b²
- The distance between the vertex and the focus in-front of it is c - a
* Now lets solve the problem
- The distance from a vertex to the center of the mirror
∵ The vertex of the mirror is (a , 0)
∵ The distance between a vertex and the center of the mirror
is 4 inches
∴ a = 4
∵ The distance between the vertex and a focus in front of the surface
of the mirror is 1
∵ The distance between the vertex and the focus in-front of it is c - a
∴ c - a = 1
∴ c - 4 = 1 ⇒ add 4 to the both sides
∴ c = 5
- The mirror has a horizontal transverse axis and the hyperbola is
centered at (0, 0)
∴ The equation of the hyperbola is x²/a² - y²/b² = 1
- Lets find b from a and c
∵ c² = a² + b²
∵ c = 5 and a = 4
∴ (5)² = (4)² + b²
∴ 25 = 16 + b² ⇒ subtract 16 from both sides
∴ 9 = b² ⇒ take √ for both sides
∴ b = ±3
- Lets write the equation
∴ x²/(4)² - y²/(3)² = 1
∴ x²/16 - y²/9 = 1
* The equation of the hyperbola is x²/16 - y²/9 = 1
The distance of the focus from the center is the sum of the distance from
the focus to the surface and the vertex distance.
Correct response:
[tex]The \ equation \ of \ the \ hyperbola \ that \ models \ the \ mirror \ is \ \underline{\dfrac{x^2}{16} - \dfrac{y^2}{9} = 1}[/tex]Details of the method used to find the equationGiven:
Distance of the vertex from the center = 4 inches
Distance of the focus from the mirror surface = 1 inches
Coordinates of the center of the mirror = (0, 0)
Required:
To write the equation of the hyperbola that can be used to model the mirror
Solution:
The equation of an hyperbola having an horizontal transverse axis is presented as follows;
[tex]\mathbf{\dfrac{(x-h)^2}{a^2} - \dfrac{(y-k)^2}{b^2}} = 1[/tex]Where;
(h, k) = The coordinate of the center
a = Center to vertex distance
b² = c² - a²
Where;
c = The from the center to the vertex
Therefore;
a = 4
(h, k) = (0. 0)
c = 4 + 1 = 5
b² = 5² - 4² = 9
b = √9 = 3
The equation of the hyperbola is therefore;
[tex]\dfrac{(x - 0)^2}{4^2} - \dfrac{(y - 0)^2}{3^2} = \underline{ \dfrac{x^2}{16} - \dfrac{y^2}{9} = 1}[/tex]Learn more about the equation of a hyperbola here:
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Help, please!! 88points
Answer:
7.5 ab and cd
4 bd and ac
Step-by-step explanation:
Answer:
i believe the answer is 7.5 ab and cd, 4 bd and ac
A conical container can hold 120π cubic centimeters of water. The diameter of the base of the container is 12 centimeters.
The height of the container is ___ centimeters. If its diameter and height were both doubled, the container's capacity would be _____times its original capacity.
Answer: The height of the container is 10 centimeters. If its diameter and height were both doubled, the container's capacity would be 8 times its original capacity.
Step-by-step explanation:
The volume of a cone can be calculated with this formula:
[tex]V=\frac{\pi r^2h}{3}[/tex]
Where "r" is the radius and "h" is the height.
We know that the radius is half the diameter. Then:
[tex]r=\frac{12cm}{2}=6cm[/tex]
We know the volume and the radius of the conical container, then we can find "h":
[tex]120\pi cm^3=\frac{\pi (6cm)^2h}{3}\\\\(3)(120\pi cm^3)=\pi (6cm)^2h\\\\h=\frac{3(120\pi cm^3)}{\pi (6cm)^2}\\\\h=10cm[/tex]
The diameter and height doubled are:
[tex]d=12cm*2=24cm\\h=10cm*2=20cm[/tex]
Now the radius is:
[tex]r=\frac{24cm}{2}=12cm[/tex]
And the container capacity is
[tex]V=\frac{\pi (12cm)^2(20cm)}{3}=960\pi cm^3[/tex]
Then, to compare the capacities, we can divide this new capacity by the original:
[tex]\frac{960\pi cm^3}{120\pi cm^3}=8[/tex]
Therefore, the container's capacity would be 8 times its original capacity.
Answer:
i can’t see others answers
Avery weighs x pounds. Jada weighs 18 pounds more than Avery. Which expression tells how much the two of them weigh together? x + 18 x + x + 18 x + 18 + x + 18 x + x - 18
Answer:
Second option: [tex]x + x + 18[/tex]
Step-by-step explanation:
You know that "x" represents the Avery's weigth (in pounds).
Let be "y" the weight of Jada in pounds.
Since Jada weighs 18 pounds more than Avery, you can write this expression:
[tex]y=x+18[/tex]
The weight of them together is:
[tex]weight\ together=x+y[/tex]
Substituting, you get:
[tex]weight\ together=x+x+18[/tex]
Therefore, the expression that tells how much the two of them weigh together is the one provided in the second option:
[tex]x + x + 18[/tex]
Hello any help on this question would help. Can answer be in points(x,y)
Answer: The line that passes through the points (0,1) and (-7,0). Observe the graph attached.
Step-by-step explanation:
By definition, a line intersects the y-axis when the value of "x" is zero ([tex]x=0[/tex]), then if the y-intercept is 1, then the point where the line intersects the y-axis is:
(0,1)
By definition, a line intersects the x-axis when the value of "y" is zero ([tex]y=0[/tex]), then if the x-intercept is -7, then the point where the line intersects the x-axis is:
(-7,0)
Therefore, now you know this, you can graph a line that passes through the points (0,1) and (-7,0). Observe the graph attached.
Answer:
Check the attached graph
Step-by-step explanation:
Given that y-intercept is 1.
That means graph passes through the point (0,1).
Given that x-intercept is -7.
That means graph passes through the point (-7,0).
Now we need to graph the line using above information. So begin by graphing both points .
Now draw a line joining both points to get the final graph.
Simplify the expression 5xy^2(3+ 2x) - 6xy(4xy + 3y)
Factor completely 3x^4 - 3x ^3 - 18x ^2. Which of the following is one of the factors?
To factor the expression 3x^4 - 3x^3 - 18x^2 completely, factor out the GCF 3x^2, then factor the quadratic expression inside the parentheses (x^2 - x - 6) into (x - 3)(x + 2).
Explanation:To factor the expression 3x^4 - 3x^3 - 18x^2 completely, we can first factor out the greatest common factor (GCF), which in this case is 3x^2. This gives us 3x^2(x^2 - x - 6). To factor the quadratic expression inside the parentheses, we can use the quadratic formula or factor by grouping. The quadratic expression x^2 - x - 6 can be factored as (x - 3)(x + 2).
Therefore, the completely factored expression is 3x^2(x - 3)(x + 2).
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when the center line is one solid yellow line and one broken yellow line,who may cross the line to pass
A. Traffic on the side with the broken yellow line. The dashes signify the “openness” of the ability that the drivers on that side have to pass.
Answer:
A). Traffic on the side with broken yellow line
Step-by-step explanation:
A solid yellow line used in two lane roadways where passing or crossing is strictly prohibited. It is dangerous and may lead to serious accidents while violating this.
On the other hand, broken yellow line on the roadways indicates that vehicles moving can pass or cross the road when only it is safe to cross the lane.
Therefore, when the center line is one solid yellow line and one broken yellow line, then the vehicles on the side of the broken lines may cross the line to pass only when it is safe to cross.
Leah has 28 more marbles than Dan. 1/3 of Leah’s marbles is equal to 4/5 of Dan’s marbles. Find the number of marbles Leah has.
Answer:
Leah has 48 marbles.
Step-by-step explanation:
Represent the number of marbles that each person has by L and D.
Leah has 28 more marbles than Dan: L = D + 28.
Then (1/3)L = (4/5)D. Here the LCD is 15, and so multiplying this equation by 15 will remove the fractions: 15(1/3)L = 15(4/5)D.
Therefore, 5L = 12D, and D = 5L/12.
Then, since L = D + 28, L = (5/12)L + 28, or
12L = 5L + 336, or
7L = 336, or
L = 336/7 = 48.
Leah has 48 marbles. That means that Dan has 20 marbles.
The number of marbles Leah has is 48 and Dan is 20 if Leah has 28 more marbles than Dan. 1/3 of Leah’s marbles is equal to 4/5 of Dan’s marbles.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Leah has 28 more marbles than Dan. 1/3 of Leah’s marbles is equal to 4/5 of Dan’s marbles.
Let x be the number of marbles Leah has.
Let y be the number of marbles Dan has.
Leah has 28 more marbles than Dan:
x = y + 28
(1/3)x = (4/5)y
Solving above two linear equation, we get:
5x = 12y
5(y + 28) = 12y
5y + 140 = 12y
12y - 5y = 140
7y = 140
y = 140/7 = 20
x = 20 + 28 = 48
Thus, the number of marbles Leah has is 48 and Dan is 20 if Leah has 28 more marbles than Dan. 1/3 of Leah’s marbles is equal to 4/5 of Dan’s marbles.
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A five pound bag of apples costs $3.45. What is the unit cost of apples
Answer: Assuming a unit of apples is one pound, the answer is .69 cents
Step-by-step explanation:
3.45 / 5 = .69
distance between -3 1/4 and -6 1/2
ANSWER
[tex]3 \frac{1}{4} [/tex]
EXPLANATION
We want to find the distance between
[tex] - 3 \frac{1}{4} [/tex]
and
[tex] - 6 \frac{1}{2} [/tex]
This numbers can be located on the number line.
The distance between them is the absolute value of the difference between the two numbers.
[tex] | - 6 \frac{1}{2} - - 3 \frac{1}{4} | [/tex]
[tex] | - \frac{13}{4} | [/tex]
[tex] = \frac{13}{4} [/tex]
[tex] = 3 \frac{1}{4} [/tex]
Which of the following is the conjugate of 8 + 3r
Answer:
8-3r
Step-by-step explanation:
we know that
The conjugate is where we change the sign in the middle of two terms
In this problem
we have
8+3r
so
The conjugate is
8-3r
Answer:
8-3sqrt
Step-by-step explanation:
A gas can holds 10 liters of gas. How many cans could we fill with 35 liters of gas?
Answer:
3 and 1/2
Step-by-step explanation:
because if one can holds 10 liters of gas, three cans would hold 30 because 10 times 3 is 30 plus the extra 5 liters in the remaining can
Answer:
7/10
Step-by-step explanation:
We have liters of gas, and we need to figure out how many cans we can fill.
Hint #22 / 4
We need to divide the 7 liters by the 10 liters that each can holds.
Find the average rate of change between f(-7) and f(-1) in the function f(x)=x^2+2x -8
Solve the equation by replacing x with -7 and then -1.
Then subtract the two to find the difference and divide that by the difference between -7 and -1.
f(-7) = -7^2 + 2(-7) -8 = 49 -14 -8 = 27
f(-1) = -1^2 + 2(-1) -8 = 1 -2 - 8 = -9
Difference between 27 and -9 = -36
Difference between -1 and -7 = -6
Rate of change = -36 /-6 = 6
Paul is 2 meters tall. raymond is 6 feet tall who is taller?
Answer:
Paul is taller
2 meters is 6.5 feet.
Answer:Paul is taller the answer will be 6.5.
Step-by-step explanation:You had to convert the meters into feet to see which one will be taller.
PLSS HELP asap thank you
Answer:
68 - C = m
If he completes 33 it means :
c = 33
Substituting this in the equation we have :
m > 68 - 33
m > 35
Answer:
I think the first one is 68-c=m and the 2nd one is 35
Step-by-step explanation:
Jeez i hope im right i had to think really hard for some reason. I havent done this is a while >.<