Mathematics High School

Marisol is making a rectangular wooden frame. She wants the length of the frame to be no more than 12 inches. She has less than 30 inches of wood to use. Which system of inequalities represents the possible length, l, and the possible width, w, that her frame could have?

l ≤ 12
2l + 2w < 30
l > 12
2l + 2w < 30
l ≤ 12
l + w < 30
l > 12
l + w < 30

Answers

Answer 1
l ≤ 12
2l + 2w < 30 
the second and fourth option are saying she can make the length longer than twelve and the third option forgets to double the length and width so it is accurate. The first option is the right answer.
Answer 2

Answer: (A) The first option is the right answer.

Step-by-step explanation:

l ≤ 12

2l + 2w < 30

Related Questions

What's an equation for "Six more then twice a number is 72?"

Answers

the equation would be:

2x+6 = 72

2n + 6 = 72 <== ur equation

Find an equation for the nth term of the arithmetic sequence.

a15 = -53, a16 = -5

A) an = -725 - 48(n - 1)
B) an = -725 + 48(n + 1)
C) an = -725 + 48(n - 1)
D) an = -725 - 48(n + 1)

Answers

an=a1+d(n-1)

every term increases by d amount

so [tex]a_n+d=a_{n+1}[/tex]
therefor
[tex]a_{15}+d=a_{15+1}=a_{16}[/tex]

-53+d=-5
add 53 both sides
d=48

alright
an=a1+d(n-1)
an=a1+48(n-1)
use a15=-53
a15=-53=a1+48(15-1)
-53=a1+48(14)
-53=a1+672
minus 672 both sides
-725=a1

the equation is
an=-725+48(n-1)
answer is C

Solve the equation using square roots. x^2-15=34

Answers

Hello there!

First, let's take a look at our equation.
[tex] x^{2} [/tex] - 15 = 34
We need to isolate x^2 to completely square root both sides properly, so let's do so.
Add 15 to both sides to isolate [tex] x^{2} [/tex].

We are now left with:
[tex] x^{2} [/tex] = 49
Now, square root both sides.
[tex] \sqrt{x^2} [/tex] = x
[tex] \sqrt{49} [/tex] = 7

We are now left with the solution:
x = 7

I hope this helps!
X^2-15=34 add 15 to both sides
X^2=49 square both sides
X=7

"It was you who awoke me last summer out of a life-long stupid dream" write the conclusion for this quote

Answers

The person that "awoke [the author]" helped change the authors life around and helped him find the purpose for his life

hope this helps

Which of the following graphs best represents the solution to the pair of equations below? y = −x + 6 y = 2x − 3 A coordinate plane is shown with two lines graphed. One line passes through the y axis at 6 and through the x axis at 6. The other line passes through the y axis at negative 3 and the x axis at 1.5. The lines intersect at the point 3 comma 3. A coordinate plane is shown with two lines graphed. One line passes through the y axis at 6 and the x axis at 6. The other line passes through the y axis at 3 and the x axis at negative 1.5. The lines intersect at 1 comma 5. A coordinate plane is shown with two lines graphed. One line passes through the y axis at 6 and the x axis at negative 6. The other line passes through the y axis at negative 3 and the x axis at negative 1.5. The lines intersect at negative 3 and 3. A coordinate plane is shown with two lines graphed. One line passes through the y axis at 6 and the x axis at negative 6. The other line passes through the y axis at 3 and the x axis at 1.5. The lines intersect at negative 1 comma 5.

Answers

The lines are 

i)  y=-x+6
ii) y=2x-3

The solution of the system of equations is found by equalizing the 2 equations:

-x+6=2x-3

-2x-x=-6-3

-3x=-9

x=-9/(-3)=3

substitute x=3 in either i) or ii):

i)  y=-3+6=3
ii) y=2(3)-3=6-3=3

(the result is the same, so checking one is enough)

This means that the point (3, 3) is a point which is in both lines, so a solution to the system.

In graphs, this means that the lines intersect at (3, 3) ONLY


Answer: The graph where the lines intersect at (3, 3)

The point of intersection of the lines  y = −x + 6 and y = 2x − 3 is (3, 3)

Linear function

A linear function is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the y intercept.

Given the equations:

y = −x + 6    (1)

y = 2x − 3      (2)

Solving the equations 1 and 2 simultaneously gives:

x = 3, y = 3

The point of intersection of the lines  y = −x + 6 and y = 2x − 3 is (3, 3)

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Use the given graph to determine the limit, if it exists. A coordinate graph is shown with a downward sloped line crossing the y axis at two that ends at the open point 2, 1.3, a closed point at 2, -1, and an upward sloped line starting at the open point 2, 4. Find = limit as x approaches two from the right of f of x..

Answers

Answer: The right hand limit is 4

-------------------------------

Start on the right side of the value x = 2. In other words, start at some value larger than 2, say x = 4. Starting at x = 4, move closer to x = 2. Move as close as you can. The closer x gets to 2, the closer y gets to 4. You'll never actually get to x = 2 or y = 4 because of the hole. However, the right-hand limiting value is 4 assuming you can keep getting closer and closer. 

Note: if you approach x = 2 from the left side, you arrive at a different y value So this suggests that overall, the limit at x = 2 doesn't exist. But the right hand limit (RHL) does exist as described above.

what is the most efficient first step in the process to factor the trinomial 3x^3-24x^2+36x

Answers

the answer is factor out 3x on apex.

Answer:

Factor out 3x

Step-by-step explanation:

A P E X answer

Janet wins the lottery and receives $100 the first year. In the following years, she receives $50 more each year. (That is, Janet receives $150 the second year, $200 the third year, and so on.) How much will Janet receive, in total, after 10 years?

A) $2,500

B) $3,250

C) $1,450

D) $1,500

Answers

The correct answer is B) $3,250, because if you add up the numbers consecutively you get that.

What is the graph of x = -5?

Answers

hello: 
the graph is the line parralle of axis- y passing by the point : (-5 , 0 ) 

Which of the numbers listed below are solutions to the equation? Check all that apply. x2 = -36 A. 6 B. 1296 C. 18.0 D. 72 E. -6 F. None of these

Answers

When x^2 = -36, so -36 equals to x when squared.

So, to find the x square root both terms. But you can't. Why? Because we have a negative number, and you can't do the sqrt of a negative number. So, none of the above is the answer. Non-solvable

There are 325 students in ping pong club. There are 5 girls for every 7 boys in the club. Which is the correct proportion that can be used to determine the number of girls in the club?

Answers

It is 5 to 7 people eliminating A and C automatically. and because it is 5 to 7 and not 7 to 5 it eliminates B too.

Answer: D

Hope this helps :)
Please give brainliest
Final answer:

To find the number of girls in the club, you can set up a proportion using the given information. Cross-multiply the proportion and solve for the number of girls. The approximate number of girls in the club is 232.

Explanation:

To determine the number of girls in the club, we can set up a proportion using the given information. Since there are 5 girls for every 7 boys in the club, the proportion can be written as:

Girls/Boys = 5/7

To find the number of girls, we can solve the proportion by cross-multiplying:

Girls = (5/7) * Total Number of Students

Substituting the given total number of students as 325, we can calculate the number of girls in the club as:

Girls = (5/7) * 325

Girls = 232.14

Therefore, there are approximately 232 girls in the ping pong club.

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Find the area of a rectangular almond orchard that is 200 yards long and 100 yards wide.
300 square yards
2100 square yards
2000 square yards
20000 square yards

Answers

A = L * W
A = 200 * 100
A = 20,000 square yards

staircase of steps in a swimming pool has a vertical rise of 14 inches per step and a landing of 20 inches.

Answers

I think the question for this problem is to find the slope of the staircase. The slope is a ratio of change of the y-coordinates and x-coordinates of points. It is written as Δy/Δx especially in analytical geometry. It could also be simply the ratio of the rise or vertical height to the run or horizontal length.

Therefore, the slope of the stair case is

Slope = rise/run = 14/20 = 0.7

WILL MAKE BRAINLIEST!!! A triangular section of a lawn will be converted to river rock instead of grass. Maurice insists that the only way to find a missing side length is to use the Law of Cosines. Johanna exclaims, that only the Law of Sines will be useful. Describe a scenario where Maurice is correct, a scenario where Johanna is correct, and a scenario where both laws are able to be used. Use complete sentences and example measurements when necessary.

Answers

Let's consider the triangle ABC shown in the first diagram below. We name the sides with small letters: a, b, and c. We name the angles by the capital letters A, B, and C. Side a pairs with angle A° which are opposite each other. The same with side b and angle B° and side c and angle C°.

We can use the cosine rule when we know the length of two sides and the angle opposite the side that is unknown. For example, referring to the second diagram, we know the length of side a and side b and we are looking for the length of side c. We also know the angle that is located on the opposite of side c, then to solve this we can use the cosine rule

c² = a² + b² - 2ab(cos(C°))

The third diagram shows a scenario when sine rule can be used. Say we need the length of the side c. We know the length of side a, the size of angle A° and angle C° then we can use the sine rule

[tex] \frac{c}{sin(C)} = \frac{a}{sin(A)} [/tex]

We can also use sine rule if we know length of side b and the size of angle B° instead of side a and angle A°





What is the slope of this line y + 3 = -4(x - 5)?

Answers

y+3= -4x+20
y=-4x+17

Final answer: Slope=-4

Just a side note: This is written in point slope form or y-y1= m(x-x1). You could just look at the m value to find slope.

Angie baked 100 cookies and 20 brownies. She wants to  split them into equal groups  for the big sale. Each group must have the same number of cookies and brownies, with none left over. What is the greatest number of groups she can make? Angie baked 100 cookies and 20 brownies. She wants to  split them into equal groups  for the big sale. Each group must have the same number of cookies and brownies, with none left over. What is the greatest number of groups she can make? Angie baked 100 cookies and 20 brownies. She wants to  split them into equal groups  for the big sale. Each group must have the same number of cookies and brownies, with none left over. What is the greatest number of groups she can make? 

Answers

stop copying the question, it's confusing

so 100 cookies and 20 brownies
what is the greatest number you can divide them both by?

find the GCF
factor them
100=2*2*5*5
20=2*2*5
so the GCF is the common group to both or 2*2*5 or 20

100/20=5
20/20=1

there are 20 groups, each wit 5 cookies and 1 brownie


20 groups

Factor x2a2 + 3xa2 + 2a2

Answers

I'm going to assume the equation is x^2 a^2 + 3x a^2 + 2a^2

You factor out the common term, which is a^2.
You would then get a^2(x^2+3x+2) as the answer.
Factor out (x^2+3x+2)

a^2(x+1)(x+2)

Find the cost of twelve $1,000 bonds at a quotation of 84.50.

Answers

What we have so far:
*12 bonds
*1 bond = $1,000
*Quotation of 84.50% per bond ($845 each).

What to find:
*QT - Quotation Total. QT = (12 x $1,000) x Quotation
*TC - Total Cost. TC = (12 x $1,000) + QT

Solution:
Finding QT:
QT = (12 x $1,000) x Quotation
QT = (12 x $1,000) x 84.50%
QT = $12,000 x 84.50%
QT = $10,140

Finding TC:
TC = (12 x $1,000) + QT
TC = (12 x $1,000) + $10,140
TC = $12,000 + $10,140
TC = $22,140 <--- What we are looking for.

Therefore, the total cost of twelve $1,000 bonds at a quotation of 84.50% is: $22,140.

What is the simplified form of √ 2160x^8/60x^2

Answers

2160 x^8       36 x^6
------------ = 
60 x^2

The correct answer I found is 6x³

In a restaurant there are 3 choices for appetizers, 6 choices for entrees, and 4 choices for desserts. How many different meal choices are there if you were to have 1 appetizer, 1 entree, and 1 dessert?
24
72
13
18

Answers

The correct answer is B. 72 because you can multiply 3*6*4 to represent every combination possible.

In the figure, the horizontal lines are parallel and AB = BC = CD. If LM = 3 Find JM? A. 12 B. 6 C. 3 D. 9

Answers

 A.12 because i had same question
 

The value of JM is 9, the correct option is D.

What are Parallel Lines?

The lines that always have a constant distance between them and never intersect each other are called Parallel Lines.

The slope of parallel lines is equal to each other.

The parallel lines, AM, BL, CK, DJ can be seen in the figure.

As the distance between AB = BC = CD is equal,

The parallel line runs at same distance from each other and so, the distance between LM= LK = KJ,

The value of LM is 3.

Then the value of JM = LM + KL + KJ

JM = 3 + 3 + 3

JM = 9 units.

Your question seems incomplete, the complete question is attached as an image with the answer.

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posting a screenshot my loves

Answers

(x-blank)^2 because -14 is negative 

For (x-7)^2, we have -7 because it's -14/7. Next, 7^2=49, so we have to add 49 to the right, getting (x-7)^2+43=49. Subtract 43 from both sides to get
 (x-7)^2=6, and square root both sides to get x-7=sqrt(6) and add 7 to both sides to get x=sqrt(6)+7, which is approximately 9.45. I challenge you to do the next one on your own, using the techniques stated here :)

The length of a rectangle is twice its width. if the perimeter of the rectangle is 36 cm , find its area.

Answers

L = Length
W = Width

L x W = area
Length = 2w

Lets find the width by solving for w.
2w + w = 36 
3w = 36
3w/3 = 36 / 3 
w = 12

So
L = 2 x 12 = 24
W = 12
L X W = area
24 x 12 = 288 cm^2

An angle whose vertex is at the center of a circle is a middle angle of that circle.
A. True
B. False

Answers

B. False 

Because n angle whose vertex is at the center of a circle is a CENTRAL angle of that circle


An angle whose vertex is at the center of a circle is a middle angle of that circle.  

This is false because there can be numerous angles in the center of a circle. Moreover, the angle whose vertex is at the center is called a central angle. The two endpoints of this angle and located at the circumference or outline of the circle and the vertex is located at the center of that circle.

Malik solved this system of equations.

2x+4y=24
5x+y=15

As the first step, he decided to solve for x in the first equation because it has a small, even number for the coefficient. Jill told him there was a more efficient way. What reason can Jill give for her statement?

A.The variable y in the second equation has a coefficient of one so there will be fewer steps to the solution.
B. The variable x in the second equation has a coefficient of 5 so it will be easy to divide 15 by 5.
C. The variable y in the first equation is divisible by 2 so it will be the most efficient way to start.
D. The variable y in the first equation has a larger even number. When dividing by 4, the solution will be a smaller number.

Answers

The variable y in the 2nd equation has a coefficient of 1...so there will be fewer steps to the solution

The variable y in the second equation has a coefficient of one so there will be fewer steps to the solution.

System of equations

Given the simultaneous equation

2x+4y=245x+y=15

The best way to solve this kind of equation is by the substitution method. To do that in an easy way, you can locate which of the variables in the equations has a coefficient of 1.

From equation 2, we can see that the variable "y' has a coefficient of 1, hence the reason that Jill can give for her statement is that the variable y in the second equation has a coefficient of one so there will be fewer steps to the solution.

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What is the answer to

-18= 117/p-9

Answers

-18 = 117/(p-9)
(p-9)(-18) = 117
p-9 = 117/-18
p = (117/-18) +9
p = 2.5
Hey there!

So here are the steps you need to follow to get the answer!

-18 = 117/(p - 9)
-18(p - 9) = 117    ----->  multiply "(p - 9)" on both sides
-18p + 162 = 117   ------>  distribute the "-18"
-18p = -45  ------>  subtract "162" on both sides
p = 2.5   ------>  divide "-18" on both sides

I hope this helps! :D

Please vote me for Brainliest if there is a second answer!!!

David wants to buy a game system and his favorite game.The game costs $25 and is 1/5 of the price of the game system.How much does the game system cost?

Answers

multiply 25 by 5 = 125

 the game system cost 125

 

As per linear equation, the game system costs $125.

What is a linear equation?

"A linear equation is an equation in which the highest power of the variable is always 1."

Given, the cost of the game is $25.

The cost of of the game is [tex]\frac{1}{5}[/tex] of the price of the game system.

Therefore, the cost of the game system is

= 5 × cost of the game

= $(5 × 25)

= $125

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Helppppp! Which answer choice correctly describes the relationship between two of the lines in the figure?

Answers

I would have to say that it is the 3rd answer choice due to the right angle that is formed between line C and line A. 
The correct answer is:  [C]:   " а ⊥ с " .
_____________________________________________________________
Take note of the "right angle" — which indicates that "a" is perpendicular to "c" .
_____________________________________________________________

The graph represents the piecewise function

Answers

left equatoin seems to be x is less than or equal to -1
the slope seems to be 2 and y intercep tis -1 so 2x-1


right equation is x is greater than or equal to 1
slope is 1 and y intercept is 4 so x+4




top left blank is x+4, top right blank is x is greater than or equal to 1
bottom left blank is 2x-1, bottom right blank is x is less than or equal to -1
Answer:

Hence, we have:

        f(x)= 2x-1   when  x ≤ -1

                x+4    when  x ≥ 1

Step-by-step explanation:After looking at the graph we observe that in the region:  x ≤ -1

The graph is a straight line that passes through (-1,-3) and (-2,-5)

Hence, the equation of line is:

[tex]f(x)-(-3)=\dfrac{-5-(-3)}{-2-(-1)}\times (x-(-1))\\\\\\f(x)+3=\dfrac{-5+3}{-2+1}\times (x+1)\\\\\\f(x)+3=2(x+1)\\\\\\f(x)=2x+2-3\\\\\\f(x)=2x-1[/tex]

Also, in the interval  x ≥ 1

The graph is a straight line that passes through (1,5) and (2,6)

Hence, the equation of line is:

 [tex]f(x)-5=\dfrac{6-5}{2-1}\times (x-1)\\\\\\f(x)-5=x-1\\\\\\f(x)=x-1+5\\\\\\f(x)=x+4[/tex]

what is the smallest positive integer that is divisible by each of the integers from 3 to 7, inclusive

Answers

The integers from 3 to 7, inclusive are:

{3, 4, 5, 6, 7}

these numbers can be written as multiplication of prime factors as :

{3, 2*2, 5, 2*3, 7}

The smallest common multiple of these numbers must have factors which divide all the factors of these 5 numbers.

So the multiple must have these factors: 3, 2*2 (one two is not enough to divide 4), 5 and 7. We do not need to write 2 and three again, because we already have them.

so the smallest common multiple is 3*2*2*5*7=420


Answer: 420
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