Karen's situation can be modeled by the following system of inequalities:
Total number of utensils: p + n ≤ 25 (p = number of pens, n = number of pencils)
Pencils vs. pens: n ≥ (3 - p)^2 (pencils must be at least the square of 3 less than the number of pens)
Viable solutions: All solutions within this system are viable.
Explanation:First inequality: This ensures that the total number of writing utensils (pens + pencils) doesn't exceed 25, Karen's desired maximum.
Second inequality: This accounts for Karen's preference for having at least as many pencils as the square of 3 less than the number of pens. It avoids solutions with fewer pencils than the squared difference.
Viable solutions: Since both inequalities are valid and independent, any solution that satisfies both is acceptable. This leaves a broad range of viable combinations of pens and pencils, allowing Karen flexibility within her limits.
Therefore, all solutions within the system of inequalities are valid possibilities for Karen's purchase. She can choose any combination of pens and pencils as long as their total is 25 or less and the number of pencils is greater than or equal to the square of 3 less than the number of pens.
Convert the rectangular coordinates (4, –4) into polar coordinates.
Solve the equation for y. Then graph the equation.
5x – 4y = 12
A.
B.
C.
D.
Describe the graph y=4[x+2] on [0, 3). Be specific in your description.
Answer: The description is mentioned in the below explanation.
Step-by-step explanation:
Since greatest integer function rounds down a real number to the nearest integer. for example, if f(x)=[x] and for x =1.3 f(x)= [1.3]= 1
or x= 0.9 f(0.9)= [0.9]= 0
Here, The given function, y=4[x+2]
Which is a greatest integer function and it is described on [0,3)
So, For the values of [tex]1 >x\geq 0[/tex],we take x=0 ⇒ y= 4(0+2)= 8
For, [tex]2>x\geq 1[/tex] , we take x=1, ⇒ y = 4(1+2)= 12
For, [tex]3>x\geq 2[/tex] we take x=2, ⇒ y = 4(2+2)=16
The graph description for the open or close interval, is mean describe values of variable for the interval. The graph [tex]y=4[x+2][/tex] is described and the values of y we get are 8,12, and 16 for the values of x as 0,1 and 2.
How to graph integer on a number line?Integer keeps the values as positive or the negative and graphed at the number line.
Given information-
The function of the graph given in the problem is,
[tex]y=4[x+2][/tex]
This function need to be describe on the points [0,3).
The close bracket is used in left side means the value 0 is included and the open bracket is used in right side means the value 3 is excluded.
Thus find the value of variable y for the different intervals o x,
The interval is,
[tex]0\leq x<3[/tex]
When the value of x is 0 at interval [tex]0\leq x<1[/tex],
[tex]y=4(0+2)\\y=4\times2\\y=8[/tex]
When the value of x is 1 at interval [tex]1\leq x<2[/tex],[tex]y=4(1+2)\\y=4\times3\\y=12[/tex]
When the value of x is 2 at interval [tex]2\leq x<3[/tex],[tex]y=4(2+2)\\y=4\times4\\y=16[/tex]
The graph of the given point is attached below.
Thus the graph [tex]y=4[x+2][/tex] is described and the values of y we get are 8,12, and 16 for the values of x as 0,1 and 2.
Learn more about the graph integer on a number line here;
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Bill and Greg are walking in opposite directions with speeds of 45 and 75 feet per minute. When they started, the distance between them was 20 feet. What will be the distance between them in 2.5 min?
Answer:
The distance between them in 2.5 min will be 320 ft
Step-by-step explanation:
Let
x--------------> Bill distance after 2.5 min------- > speed 45 ft/min
y--------------> Greg distance after 2.5 min------> speed 75 ft/min
z-------------> distance between them in 2.5 min
we Know that
z=x+y+20
Remember that
To find the distance multiply the speed by the time
so
x=45*2.5=112.5 ft
y=75*2.5=187.5 ft
therefore
z=x+y+20-----------> 112.5+187.5+20=320 ft
Final answer:
Bill and Greg's total distance apart after 2.5 minutes is 320 feet, calculated by adding their initial distance of 20 feet to the distance they covered in 2.5 minutes at their combined speed of 120 feet per minute.
Explanation:
Bill and Greg are walking away from each other with speeds of 45 and 75 feet per minute, respectively.
Since they are moving in opposite directions, their relative speed is the sum of their individual speeds, which is 45 + 75 feet per minute, or 120 feet per minute.
To find the distance between them after 2.5 minutes, we multiply their relative speed by the time elapsed. Therefore, the distance is:
Distance = Speed × Time = 120 feet/minute × 2.5 minutes = 300 feet.
We must also include the initial distance between them, which was 20 feet, so the total distance after 2.5 minutes is:
Total distance = Initial distance + Distance covered in 2.5 minutes = 20 feet + 300 feet = 320 feet.
What is 1 17/24 simplified
1(17/24) simplified is 41/24.
We have,
To simplify the mixed number 1 17/24, we need to convert it to an improper fraction.
To do that, we multiply the whole number (1) by the denominator of the fraction (24), and then add the numerator (17):
1 x 24 + 17 = 24 + 17 = 41
So, the mixed number 1 17/24 is equivalent to the improper fraction 41/24.
Therefore,
1(17/24) simplified is 41/24.
Learn more about expressions here:
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***Need answered ASAP***... PLEASE
What happens to the temperature of the remaining liquid when some if the liquid evaporates?
A. Increases
B. decreases
C. Does not change
D. The change cannot be determine
A is directly proportional to B.
If A is 9, when B is 3, then A is _____, when B is 6.
Factor 1-3
1. X to the second power -14x+45
2.X to the second power -15x+36
3.X to the second power -7x-44
Perform the indicated operation 7 1/8 times 5 2/3
Answer: The required result is [tex]40\dfrac{3}{8}.[/tex]
Step-by-step explanation: We are given to perform the following indicated operation :
[tex]E=7\dfrac{1}{8}\times5\dfrac{2}{3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To perform the given multiplication, first we need to convert the mixed fraction to improper fraction.
The simplification of the given operation is as follows :
[tex]E\\\\\\=7\dfrac{1}{8}\times5\dfrac{2}{3}\\\\\\=\dfrac{57}{8}\times\dfrac{17}{3}\\\\\\=\dfrac{19\times17}{8}\\\\\\=\dfrac{323}{8}\\\\\\=40\dfrac{3}{8}[/tex]
Thus, the required result is [tex]40\dfrac{3}{8}.[/tex]
Dave swam 6 laps and did 9 dives at the swimming pool. Crystal did 4 dives and swam 8 laps. How many more laps than dives did crystal and Dave do
The solution for the following system of equations is shown on the graph. What is the solution? y = 3x - 5 y = 1 3 x + 3 A) (3, 3) B) (3, 4) C) (4, 3) D) (4, 6)
Answer:3,4.b
Step-by-step explanation: Took the test.
Find two numbers if their sum is 3 and their difference is 21
PLZ HELP!!!!
22 gallons of gas cost $65.56 what is the unit rate for one gallon of gas
Which figure is the image of figure P after a rotation of 270° clockwise? Assume that the center of rotation is the origin.
A.
figure A
B.
figure B
C.
figure C
D.
figure P
In the figure, p || q.
Identify each pair of equal angles as vertical angles, corresponding angles, alternate interior angles, or alternate exterior angles.
m<3 = m<7:
m<1 = m<4:
m<5 = m<8:
m<1 = m<5:
m<1 = m<8:
m<2 = m<6:
m<2 = m<3:
m<4 = m<8:
m<6 = m<7:
m<3 = m<6:
m<2 = m<7:
m<4 = m<5:
Answer:
Vertical angles : Opposite angles made by two intersecting lines.
Corresponding angles : which occupy the same relative position at each intersection where a straight line crosses two others.
Alternate interior angles : when a transversal passes through two line then the angles that are formed on opposite sides of the transversal and inside the two lines.
Alternate exterior angles : angles on the outer side of each of those two lines but on opposite sides of the transversal.
Here, line k passes through the lines p and q,
Thus, by the above explanation,
Vertical pairs are, angle 1 and angle 4, angle 2 and 3, angle 5 and angle 8, angle 6 and 7,
Corresponding pairs,
angle 2 and angle 6, angle 1 and angle 5, angle 4 and angle 8, angle 3 and angle 7,
Alternate interior angles pair,
angle 4 and angle 5, angle 6 and angle 3,
Alternate exterior angles pair,
angle 2 and angle 8, angle 1 and angle 7,
Vertical angles are always equal in measure,
Now, the p and q are parallel lines,
So, the corresponding angles will be congruent as well as alternative interior or exterior will be congruent.
Therefore, the required pair,
Corresponding pairs :
m∠1=m∠5
m∠2=m∠6
Alternative interior pairs :
m∠3=m∠6
m∠4=m∠5,
Alternate exterior pairs :
m∠1=m∠8
m∠2=m∠7
Vertical pairs :
m∠1=m∠4
m∠5=m∠8
m∠2=m∠3
m∠6=m∠7
On which triangle can the law of cosines be applied once to find an unknown angle measure? Law of cosines: a2 = b2 + c2 – 2bccos(A)
options are in the pics
Answer: The correct option is 4.
Explanation:
The formula of law of cosine is,
[tex]a^2=b^2+c^2-2bc\cos(A)[/tex]
Where a,b,c are sides of the triangle and A is the interior angle of vertex A.
Reason for correct option:
From the above formula we can easily conclude that to find an unknown angle measure we need the length of all sides of the triangle.
In figure 4 all sides are given, so the correct option is 4.
Reason for incorrect option:
In figure 1,2 and three all sides are not known, so we can apply the cosine rule to mind the unknown angle measure.
Therefore option 1,2 and 3 are incorrect.
Jackson's kitten weighted 2 pounds and 3 ounces. A month later the kitten weighted 56 ounces. How much weight did the kitten gain in that month?
1 pound= 16 ounces
help me please !!! Surface area
a sperm whale can stay underwater 7 times longer than a sea cow can.how long can a sperm whale stay underwater?
The sperm whale's underwater duration is seven times that of the sea cow, showcasing remarkable breath-holding abilities, likely adapted for deep-sea foraging and hunting.
The relationship between the underwater durations of a sperm whale and a sea cow suggests that the sperm whale's capability is sevenfold that of the sea cow. Let's denote the sea cow's duration as "x." Accordingly, the sperm whale's underwater duration would be 7 times x.
In practical terms, if we assume the sea cow can stay submerged for 10 minutes (x = 10), then the sperm whale, being seven times more proficient, can stay underwater for 7 times 10, which is 70 minutes (7x = 7 * 10 = 70). This sevenfold difference implies a significant contrast in their breath-holding abilities.
The numerical representation extends universally; if the sea cow can endure underwater for "x" units of time, the sperm whale can endure for 7 times "x" units of time. This relationship showcases the remarkable adaptation of the sperm whale to extended submersion, likely linked to its deep-sea foraging behavior and hunting strategies.
In essence, the sperm whale can stay underwater for a duration that is seven times longer than that of the sea cow, highlighting its remarkable breath-holding capacity.
A sperm whale can stay underwater for 7 times longer than a sea cow, so it can stay underwater for 7 times the duration of a sea cow.
If a sperm whale can stay underwater 7 times longer than a sea cow, we can express this relationship as:
Time a sperm whale can stay underwater = 7 * Time a sea cow can stay underwater
So, if we let the time a sea cow can stay underwater be represented by 'x', then the time a sperm whale can stay underwater is:
7 * x
Therefore, a sperm whale can stay underwater for 7 times longer than a sea cow, which means it can stay underwater for 7x.
please someone help..
ill give brainliest if ur answer is correct
a square parking lot has an area of 225 yards.There is a sidewalk along one side of the parking lot.How long is the sidewalk
Answer: 56.25
Step-by-step explanation:
Since there are four sides to a square and the area is 225 yards you would -
225 yards/ 4 sides
= 56.25 yards per side
If you were solving a system of equations and you came to a statement like 4 = 4, what do you know about the solution to the system? (1 point) The solution is (4, 4) The solution is x = 4 and y = 4 There is no solution There are infinitely many solutions
Answer:
There are infinitely many solutions.
Step-by-step explanation:
While solving a system of equations, if we get a true statement like 1=1, then there will be "infinitely many solutions" and if we get a false statement like 1=2, then there will be "no solution".
Here the statement is 4=4, which is a true statement.
So, there are infinitely many solutions.
Adam and Kevin are standing 35 metres apart, on opposite sides of a flagpole. From Adam’s position, the angle of elevation of the top of the flagpole is 36°. From Kevin’s position, the angle of elevation is 50°. How high is the flagpole?
What is the area of this polygon?
Enter your answer in the box.
Batman is 4 times robins age. The sum has f their ages is equal to 45. How old is Batman and robin?
Answer:
Robin is 9 years old and Batman is 36 years old
Step-by-step explanation:
Batman: 4x
Robin: x
4x + x = 45
5x = 45
x= 9
PLEASE HELP ASAP
The solutions to a certain quadratic equation are x=-4 and x=3. Write the equation in standard form below.
First correct answer will receive brainiest !!
What is the slope of this skateboard ramp if it rises 1.2 meters above the ground and runs 4 meters horizontally at the base?
Final answer:
The slope of the skateboard ramp, calculated using the rise over run formula, is 0.3. This is found by dividing the rise of 1.2 meters by the run of 4 meters.
Explanation:
The slope of a ramp is calculated as the rise divided by the run. To find the slope of the skateboard ramp, which rises 1.2 meters above the ground and runs 4 meters horizontally at the base, you would use the formula:
Slope (m) = Rise / Run
Here, the rise is the height the ramp rises above the ground, which is 1.2 meters, and the run is the distance along the ground, which is 4 meters horizontally. By substituting the given rise and run into the formula, you obtain:
Slope (m) = 1.2 m / 4 m = 0.3
So, the slope of the skateboard ramp is 0.3.
Myron put $5000 in a 2-year CD paying 3% interest, compounded monthly. After 2 years, he withdrew all his money. What was the amount of the withdrawal?
Answer:
$5308.79
Step-by-step explanation:
The future value can be computed from ...
FV = P(1 +r/n)^(nt)
where P is the principal invested, r is the annual interest rate, n is the number of times per year it is compounded, and t is the number of years.
You have P = $5000, r = 0.03, n = 12 (months per year), t = 2.
Filling in the given numbers, we have ...
FV = $5000(1 +.03/12)^(12·2) ≈ $5000(1.0617570) ≈ $5308.79
The amount of the withdrawal will be $5308.79.
Final answer:
To find the withdrawal amount for Myron's CD, the compound interest formula is used with the respective values plugged in. After 2 years, with 3% interest compounded monthly on a principal of $5000, the withdrawal amount is approximately $5,304.91.
Explanation:
The question deals with the calculation of compound interest for a Certificate of Deposit (CD), specifically with different compounding periods.
To calculate the withdrawal amount for Myron's 2-year CD with a principal amount of $5000 at a 3% interest rate compounded monthly, the formula for compound interest is:
[tex]A = P (1 + r/n)^{nt[/tex]
Where:
A = the amount of money accumulated after n years, including interest.P = the principal amount (initial deposit).r = the annual interest rate (decimal).n = the number of times that interest is compounded per year.t = the time the money is invested for in years.By plugging in Myron's values, we get:
[tex]A = $5000 (1 + 0.03/12)^{12\times 2[/tex]
Calculating this we find that A, the withdrawal amount, is approximately $5,304.91.
what is y−2=−3(x−7) written in standard form?
Eliza paints a circle on her bedroom wall as part of a mural. After she paints it, she decides that she wants a much bigger circle. So, she multiplies her original radius by four and repaints the circle. Which statement best describes Eliza's solution?
a.) The area of the new circle is two times larger.
b.) The area of the new circle is four times larger.
c.) The area of the new circle is eight times larger.
d.) The area of the new circle is 16 times larger.
Answer: d.) The area of the new circle is 16 times larger.
Step-by-step explanation:
Let the radius of the original circle be r.
Then the area of the original circle will be :-
[tex]\text{A}_1=\pi r^2[/tex]
When she multiplies her original radius by four and repaints the circle.
The new radius = [tex]R=4r[/tex]
Then the area of the new circle will be :-
[tex]\text{Area}=\pi R^2\\\\\Rightarrow\ \text{Area}=\pi (4r)^2\\\\\Rightarrow\ \text{Area}=\pi (16r^2)\\\\\Rightarrow\ \text{Area}=16\pi r^2\\\\\Rightarrow\ \text{Area}=16(\pi r^2)\\\\\Rightarrow\ \text{Area}=16A_1[/tex]
Hence, The area of the new circle is 16 times larger.