Final answer:
When Isaac uses 24cm of string to make rectangles, no matter the individual dimensions, the sum of the length and width of these rectangles must always be 12 cm. This is a direct result of the fixed perimeter, which requires that the combined measurements of length and width halves the total perimeter to maintain the consistent total string usage.
Explanation:
Isaac made all these rectangles with 24cm lengths of string, which implies that the perimeter of all these rectangles is equal. The observation about the sum of the length and the width of these rectangles is that regardless of the individual measurements of the length and width, their sum must always be half the total perimeter of the rectangle. Given a fixed perimeter of 24cm, the formula for the perimeter of a rectangle (P) is
P = 2(l + w),
where l is the length and w is the width. Since the perimeter is given as 24cm, this simplifies to
24 = 2(l + w), or 12 = l + w.
This equation means that the sum of the length and width of the rectangles must always equal 12 cm. This is because the total loop made by the string when forming the rectangle has to be divided into four edges, two lengths, and two widths, which totals the provided 24cm of string. Therefore, if we adjust either the length or the width, the other measurement must adjust in such a way that their sum remains constant at 12 cm to maintain the total perimeter as 24cm.
if xy=c^2, prove that x^2 dx/dy+c^2=0
the solutions to the inequality y>-3x+2 are shaded on the grap.which point is a solution?
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30 POINTS + BRAINLIEST.. PLEASE CHECK MY ANSWER
Answer:
you are correct good job
I will go to the mall if and only if I get paid today.
Determine the conditions that will make the biconditional true.
A. It is true if I go to the mall and I get paid. It is true if I go to the mall and I don’t get paid.
B. It is true if I go to the mall and I get paid. It is true if I don’t go to the mall and I don’t get paid.
C. It is true if I go to the mall and I don’t get paid. It is true if I don’t go to the mall and I don’t get paid.
D. It is true if I go to the mall and I get paid. It is true if I don’t go to the mall and I get paid.
Final answer:
The correct answer is Option B, covering both true-true and false-false scenarios.
Explanation:
To determine the conditions that make the biconditional statement true, let's analyze it step by step. The statement in question is: "I will go to the mall if and only if I get paid today." A biconditional statement is true in two scenarios: both parts are true or both parts are false.
Looking at the options provided:
Option A is incorrect because if the statement is true, I cannot go to the mall without getting paid.Option B is correct because it encompasses both scenarios where the biconditional statement holds true: If I go to the mall, then I must have gotten paid, and if I don’t go to the mall, then I must not have gotten paid.Option C is incorrect because according to the biconditional, I cannot go to the mall unless I have been paid.Option D is incorrect because if I don’t go to the mall, it must mean that I didn't get paid, which is not covered in this option.Therefore, the correct answer is Option B: It is true if I go to the mall and I get paid today. It is also true if I don't go to the mall and I don't get paid today. This matches the requirements of a biconditional statement where either both conditions are true or both are false.
A land mass is roughly in the shape of a rectangle whose perimeter is 1180 miles. the width is 110 miles less than the length. find the length and the width?
if a sample of 21 runners were taken from a population of 580 runners, μ could refer to the mean of how many runners times?
Answer:
the answers is 580
How was his payment
The dimensions of a triangle are shown below. If the height of the triangle is increased by a factor of 4, which statement will be true about the area of the triangle?
Answer:
The area will increase by a factor of 4
Step-by-step explanation:
4 * 4 = 16
IT'S UP THERE STEVE (Like on family feud)
what is the sum of (5xy + x - 8) and (13x + 2)
help:
quadrilateral ABCD is located at A(-2,2) B(-2,4) G(2,4) D(2,2). the quadrilateral is then transformed using the rule (x+2,y-3) to form the image A'B'C'D'. what are the new coordinates of of A'B'C'D'? describe what characteristics you would find if the corresponding vertices were connected with line segments.
The length of a rectangle is stored in a double variable named length, the width in one named width. write an expression whose value is the length of the diagonal of the rectangle. submit
Three times the number of blue marbles exceeds twice the number of red marbles by 18 also five times the number blue marbles is two less than six times number of red marbles how many of each are there
Solve and show steps. will award brainliest.
For the first question please find the attached diagram.
As per the diagram, P is the upstream point and Q is the downstream point. The distance between P and Q is 22.5 miles.
Let the speed of the boat in the still waters of the lake be represented by S.
Then, when the boat travels upstream, the net speed of the boat will be (S-6) miles per hour because the river flows downstream and thus the speed of the boat will have to be subtracted from the speed of the river.
Now, we know that the relationship between the net speed, distance and time of travel is give as:
Distance = Net Speed x Time of travel
For the upstream ride of the board we know that Distance is 22.5 miles and Net Speed is (S-6). Therefore, the above equation will become:
[tex] 22.5=(S-6)\times T_{1} [/tex] where [tex] T_{1} [/tex] represents the time taken to travel upstream.
We can rearrange the above equation to be:
[tex] T_{1}=\frac{22.5 }{S-6} [/tex]......................(Equation 1)
By similar arguments we know that the downstream speed of the boat is S+6 and the distance travelled is the same and so the time taken to travel downstream (represented by [tex] T_{2} [/tex]) will be:
[tex] T_{2}=\frac{22.5}{S+6} [/tex]................(Equation 2)
Now, we know that the total time of travel should be 9 hours.
This means that: [tex] T_{1}+T_{2}=9 [/tex]............(Equation 3)
Plugging in the values of [tex] T_{1} [/tex] and [tex] T_{2} [/tex] from (Equation 1) and (Equation 2) into (Equation 3), we get:
[tex] \frac{22.5 }{S-6} +\frac{22.5 }{S+6}=9 [/tex]
Simplifying the above we will get a quadratic equation:
[tex] 9S^2-45S-54=0 [/tex]
The roots of this quadratic equation are:
[tex] S=-1 [/tex] and [tex] S=6 [/tex]
Since, speed cannot be negative, [tex] S=-1 [/tex] is out of consideration.
The speed of the boat in the lake is thus [tex] S=6 [/tex] miles per hour.
But we have a problem with S=6 too. The problem is that if S=6, then the boat will not be able to move upstream.
Let us solve problem 2
We are given that: [tex] \frac{x-2}{x+3}+\frac{10x}{x^2-9} [/tex]
We can rewrite it as:
[tex] \frac{x-2}{x+3}+\frac{10x}{(x-3)(x+3)} [/tex]
[tex] \frac{(x-3)(x-2)+10x}{(x-3)(x+3)} =\frac{x^2-5x+6+10x}{(x-3)(x+3)} [/tex]
Now, the numerator can be simplified as:
[tex] \frac{x^2+10x+6}{(x-3)(x+3)} =\frac{(x+3)(x+2)}{(x-3)(x+3)} =\frac{x+2}{x-3} [/tex]
Thus, our final simplified answer is:
[tex] \frac{x+2}{x-3} [/tex]
The restriction on the variable x is that it cannot be equal to either +3 or -3 as that would make the denominator of the original question equal to zero.
Thus, the restriction is [tex] x\neq \pm 3 [/tex]
The graph of the function g(x) is shown on the coordinate plane below. For what value of x does g(x)=0
Answer:
the answer is 6 on algebra nation
Step-by-step explanation:
The average monthly amount Isabella has spent on gasoline since 1990 is shown in the table. Use the data in the table to complete the statements. Let x be the number of years since 1990. The year 2005 corresponds to an x-value of . The function that best models the data, with numerical values rounded to the nearest hundredth, is f(x) = x + 22.08. Models have their limitations. For which year would this model not make sense to use?
What is the y-intercept of the line that is the perpendicular bisector of the segment joining (-3,-4) and (5,10)? express you answer as a mixed number?
write an equation that represents the situation in the table?
x: y:
6 122
10 170
15 230
28 336
find the circumferences
Please guys help me with this question!
PLEASE HELP
Use the domain {½ , 1, 2, 4, 8} to plot the points on the graph for the given equation.
[tex]y=log_{2}x[/tex]
WILL MARK AS BRAINLIEST
Answer:
Warning the guy above is correct just make sure you count each line as 1,2,4,8. On the graph if you count the bold big lines for the domain you will run out of room for the last domain for 8. Like the person above did.
Step-by-step explanation:
Using the fafsa, you can apply for
Which equation is y = –6x2 + 3x + 2 rewritten in vertex form?
Answer:
c
Step-by-step explanation:
(20 points) Find AC, BC, m
Pleasee
A company's advertising budget is split between newspaper ads, magazine ads, television ads, and Internet ads. The company spends the same amount of money on newspaper and magazine ads. It spends 4 times the amount of money on television ads as it does on newspaper ads. It spends 2 times the amount of money on Internet ads as newspaper ads. If the budget is $22,000, how much money is spent on magazine ads?
Answer:
2,750+2750=
2750 x 4+2750 x 2=
22,000
Step-by-step explanation:
Look at the picture below // 99 points // PLEASEE HELPP
if a and b are independent events then it must be true that P(A|B)=P(A) TRUE OR FALE
Write the polynomial −11x^3 − 2 − 9x^5 − 4x^2 − 6x^4 − 14x in standard form. Then give the leading coefficient. HELP ASAP!
Adrien has 4 liters of milk. He drinks y liters each day. If Adrien has x liters of milk left after one week, express d in terms of y.
Dylan works 30 hours a week. His hours are decreased by 20%. How many hours does he now work each week?
Answer:
He now work 24 hours each week
Step-by-step explanation:
Dylan works 30 hours a week. His hours are decreased by 20%.
The number of work hours 30 is decreased by 20%
we need to find 20% of 30
[tex]30 \cdot \frac{20}{100} =6[/tex]
So number of hours should be decreased by 6
[tex]30-6= 24[/tex]
he now work 24 hours each week