The dimensions of the one whose area is largest is 39 by 39
The formula for calculating the perimeter of a rectangle is expressed as:
P = 2(L + W)
L is the length of the rectangle
W is the width
Given that the perimeter is 156, hence;
2(L + W) = 156
2L + 2W = 156
L + W = 78
W = 78 - L
The area of the rectangle is expressed as:
A = LW
A = L(78-L)
A = 78L - L^2
To get the dimensions of the one whose area is largest, dA/dL = 0
dA/dL = 78 - 2L
0 = 78 - 2L
2L = 78
L = 78/2
L = 39
Recall that 2(L+W) = 156
2(39 + W) = 156
39 + W = 78
W = 78 - 39
W = 39
Hence the dimensions of the one whose area is largest is 39 by 39
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why does the sum of -4 and 3 complain more than the sum of -3 and 5
Final answer:
The sum of -4 and 3 is -1 because we subtract the smaller number from the larger and keep the sign of the larger absolute value number. The sum of -3 and 5 is positive 2 for the same reason.
Explanation:
The question seems to be asking about the rules for adding numbers with different signs. When adding -4 and 3, which have opposite signs, you subtract the smaller number from the larger number, and the sign of the answer is the same as the sign of the larger absolute value number.
So the sum is -1, because 4 is larger than 3, and the sign is negative. In contrast, when adding -3 and 5, you also subtract the smaller number from the larger, but since 5 is greater than 3, the sum is 2, and it has a positive sign because 5 has a positive sign.
Examples demonstrate the rules of addition:
When two positive numbers are added, like 3 + 2, the result is a positive 5.If two negative numbers are added, for example, -4 + (-2), the result is a negative -6.Mixing a negative and a positive number, such as -5 + 3, the result is -2, mirroring the sign of the larger absolute value number.These basic rules ensure clarity in arithmetic operations and provide a foundation for more complex math problems. The 'complaints' likely refer to the unexpected results when dealing with negative numbers, which can seem counterintuitive but follow consistent mathematical rules.
Numbers mr. wahl is thinking of two numbers. the sum of the numbers is 27. the product of the numbers is 180. what two numbers is mr. wahl thinking of?
On each coordinate plane,the parent function f(x)=|x| is represented by a dash line translation is represented by a solid line. Which graph represents the The translation g(x)=|x+2| as a solid line?
Answer:
Refer the attached graph.
Step-by-step explanation:
Given : On each coordinate plane,the parent function [tex]f(x)=|x|[/tex] is represented by a dash line translation is represented by a solid line.
To find : Which graph represents the the translation [tex]g(x)=|x+2|[/tex] as a solid line?
Solution :
The parent function [tex]f(x)=|x|[/tex]
with the vertex (0,0)
And the graph of [tex]g(x)=|x+2|[/tex]
with the vertex (-2,0)
The graph of g(x) is the translation of f(x)
The parent function is translated towards left.
Transformation to the left,
f(x)→f(x+b) , the graph of f(x) is shifted towards left by b unit.
Same as the graph f(x) is shifted towards left by 2 unit and form graph of g(x).
We plot the graph of both the equations in which translation is shown.
Refer the attached graph below.
3(x+y)=y, if (x,y) is a solution to the equation above and y cannot equal to zero what is the ratio x/y
The ratio, x/y in the equation, if y ≠ 0 is: x/y = -2/3.
What is the Solution of an Equation?Solution of an equation is the value of a variable or two variables that makes an equation true.
Given:
3(x+y)=y
We are required to find the ratio, x/y if y ≠ 0.
Thus:
3(x+y)=y
Open bracket
3x + 3y = y
Subtract 3y from both sides
3x = y - 3y
3x = -2y
Divide both sides by 3
x = -2y/3
Divide both sides by y
x/y = -2/3
Therefore, the ratio, x/y in the equation, if y ≠ 0 is: x/y = -2/3.
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The function y = -0.017x^2 + 0.55x models the height y, in feet, of your pet frog's jump, where x is the horizontal distance, in feet, from the start of the jump. How far did the frog jump? How high did it go? Round your answer to the nearest hundredth. Be sure to show work / explain your reasoning.
The frog jumped approximately 16.18 feet horizontally. The maximum height it jumped was approximately 4.65 feet.
Explanation:The function y = -0.017x^2 + 0.55x models the frog's jump, it represents a parabola where the highest point, the vertex, means the highest point the frog reached, and where it hits the x-axis indicates the horizontal distance the frog jumped. We can find the distance of the frog's jump by setting y to 0 and solving the equation for x, whereas, the maximum height of the frog's jump will be determined by the vertex of the parabola.
For a function in the form y = ax^2 + bx + c, the x-value of the vertex, which is the maximum height in this context, can be found by using the formula -b/2a.
Substituting the given values from the equation, -b/2a = -0.55/(-2*-0.017) = 16.18 feet approximately.
Substitute x = 16.18 feet into the given function to find the maximum height the frog jumped: y = -0.017*(16.18)^2 + 0.55*16.18 = 4.65 feet approximately.
So, the frog jumped approximately 16.18 feet horizontally and the maximum height it jumped was approximately 4.65 feet.
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The frog jumped approximately 32.35 feet in distance and reached a maximum height of about 4.71 feet. We found this by setting the quadratic function to zero and solving for the horizontal distance, and by calculating the vertex of the parabola for the maximum height of the jump.
The function y = -0.017x^2 + 0.55x models the height y, in feet, of your pet frog's jump, where x is the horizontal distance, in feet, from the start of the jump. To determine how far the frog jumped, we look for the value of x when y equals zero, which represents when the frog lands back on the ground. To find this, we set the equation equal to zero and solve for x:
0 = -0.017x^2 + 0.55x
This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = -0.017, b = 0.55, and c = 0. We can solve this by factoring or using the quadratic formula. The solutions to this equation represent the starting point (x=0) and the landing point of the jump. Ignoring the x=0 solution, we find that the frog lands at approximately x = 32.35 feet (after rounding to the nearest hundredth).
To determine how high the frog went, we need to find the vertex of the parabola because this represents the highest point of the jump. The x-coordinate of the vertex is given by -b/(2a), so we calculate:
x = -0.55 / (2 * -0.017) = 16.18 (rounded to the nearest hundredth)
We plug this value into the original equation to find the height:
y = -0.017(16.18)^2 + 0.55(16.18) = approximately 4.71 feet (after rounding to the nearest hundredth)
Therefore, the frog jumped approximately 32.35 feet in distance and reached a maximum height of about 4.71 feet.
Which number is equivalent to 0.45 repeating?
Answer:
5/11
Step-by-step explanation:
5/11 is the equivalent number because its the fraction of the repeating decimal ^^
Which professionals most directly use geometry in their work?
a.accountants
b.astronomers
c.judges
d.pharmacists
e.politicians
Answer:
The answer to the question: Which professionals most directly use geometry in their work?
b. Astronomers
Step-by-step explanation:
The astronomers are the professionals most directly use geometry in their work in this list options, some examples of the geometric in this profession are:
Orbits of planets around stars or orbits of satellites around planets behave like ellipses or hyperbolas; geometry is also used to find coordinates of celestial objects
the perimeter of a scalene triangle is 14.5 cm. the longest side is twice that of the shortest side. which equation can be used to find the side lengths if the longest side measures 6.2cm?
Answer:
9.3+b=14.5
Step-by-step explanation:
The number of males per 100 females in a country's population is called what?
What is the slope of the line through (-1,8) and (3,-4)?
Answer:
-3
Step-by-step explanation:
The slope of a line is the ratio of the vertical distance and horizontal distance between two points on a line.
Note that zero is tangible if the line is horizontal, and undefined if it is vertical.
Slope = ∆y / ∆x
Coordinates given: (-1,8) and (3,-4)?
Slope = -4 - 8 / 3 - (-1)
Slope = -12 / 4
= - 3
which function represents g(x) , a reflection of f(x)= 2/5 (10) x across the x-axis ?
Answer: The correct option is A.
Explanation:
The given function is,
[tex]f(x)=\frac{2}{5}(10)^x[/tex]
If a function is reflect across the x-axis, then the x-coordinate remains the same but the sign of y coordinate change.
[tex](x,y)\rightarrow(x,-y)[/tex]
[tex]g(x)=-f(x)[/tex]
[tex]g(x)=-\frac{2}{5}(10)^x[/tex]
The graph of f(x) and g(x) in shown in below figure.
Therefore option A is correct.
Find height of triangle given hypotenuse and angle
compare 6.51326 and the square root of 39. (show work)
After estimating and calculating, we find that 6.51326 is greater than the square root of 39, which is approximately 6.245.
To compare 6.51326 and the square root of 39, we first need to calculate the square root of 39 to see how it measures up against 6.51326. Since the exact square root of 39 is not easily found without a calculator, we can estimate it by finding the nearest perfect squares that surround 39.
36 and 49 are the nearest perfect squares to 39, and their square roots are 6 and 7, respectively. Since 39 is closer to 36 than to 49, we can estimate the square root of 39 to be slightly more than 6. Therefore, without performing the exact calculation, we can intuit that the square root of 39 will be between 6 and 7, but closer to 6.
Doing the exact calculation or using a calculator, we find that the square root of 39 is approximately 6.245, which means that 6.51326 is greater than the square root of 39.
A bowl contains 10 quarters, 20 dimes, 15 nickels, and 5 pennies. a coin is selected at random and kept and then a second coin is selected at random. which combination would have a probability of 6/49?
How to find the variance of a sample with only mean standard deviation size?
Can someone help me find DB TR and SR thank you :)
The function f(x)= 70x^3/4 power can be used to estimate the BMR (Basic Metabolic Rate) of mammals. In this function, x is the mass of the animal in kilograms, and f(x) is its BMR in kilocalories (kcal) per day. Note that one kcal is equal to one food calorie. The howler monkeys at a zoo are fed a diet that contains 3.35 kcal per gram. Write a function g(x) that gives the mass of food in grams that a howler monkey must eat to obtain x kilocalories of energy. Please help!
The Statement of Theorem should be in what form?
if-then
then-if
maybe-conclusion
does not matter
Answer: If/then.
Step-by-step explanation: A theorem is a statement that has been proven on the basis of other statements, for example other theorems, which are known to be true.
We use the pattern "If A...., then B..." when we known that "A" is a statement that is true and we want to declare that since A is true, B should also be true.
20! / 16! = a 24 b 11,628 c 116,280 d A number too big to compute
20! / 16! =
20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1
divided by
16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1
equals C. 116,280
george wants to save money for a car, he invests $700 into an account that pays 7.25 percent interest, how many years will it take to reach $14,300
A retailer has some skirts that cost $18 each. She wants to sell them at a profit of 40% of the selling price. What price should she charge for the skirts?
The selling price is $25.2.
Profit and lossIf the selling price is greater than the cost price, then the difference between the selling price and cost price is called profit.
If the selling price is less than the cost price, then the difference between the selling price and cost price is called loss.
Given
The cost of the skirt is $18
Profit is 40%
To findThe selling price of the skirt.
How to calculate the selling price?The selling price is given by
selling price = cost price + profit
Profit is given by
[tex]\begin{aligned} \rm Profit\ percent\ &= \rm \dfrac{Profit}{cost\ price} *100\\40 &= \rm \dfrac{Profit}{18} *100\\\rm profit &= 7.2 \end{aligned}[/tex]
Then the selling price = 18 + 7.2 = $25.2.
Thus, the selling price is $25.2.
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The solution to 2 x - 2 + 5 = 13 is___.
A cord is cut into two pieces of different lengths. the sum of the two lengths is 10 centimeters, and the difference between the two lengths is 4 centimeters. find the lengths of the two pieces of cord.
Answer:
Start with x+y=10 and x-y=4
Add the equations to eliminate y:
x+y=10
+ x-y=4
2x =14
So now solve for x:
2x=14 (Divide each side by 2 to get x by itself)
x=7
Now you have solved for x, but you still need to solve for y:
x+y=10
7+y=10 (Subtract 7 from both sides to get y by itself)
y=3
Now you have both x and y but to check it, just plug it into the original equations:
x+y=10 ----> 7+3=10 (That's correct)
x-y=4 ----> 7-3=4 (That's correct)
Step-by-step explanation:
Mattie,Joel,and Oscar each ate 325 calories at lunch each day for 18 days.About how many calories did they eat in all
5 with a negative exponent of 4 over 5 with a exponent of 3 simplified
A.) 5 with an exponent of 7
B.) 5 with a negative exponent of 1
C.) 1 over 5 (fraction)
D.) 1 over 5 with an exponent of 7
So turns out I’m not good at this math stuff. I someone help me with this monstrosity.?!
Identify each sequence below as geometric, arithmetic, or neither.
(a) 1, 3, 5, 7, 9, 11, 13, 15
(b) 21, 16, 12, 9, 7, 6
(c) .3, .03. .003, .0003, .00003
(d) -4, -12, -36, -108, -324
Sequence (a) is an arithmetic sequence because the common difference is constant. Sequence (d) is a geometric sequence because the common ratio is constant. Sequences (b) and (c) do not follow the patterns of arithmetic or geometric sequences and are neither.
Explanation:The question asks to identify each sequence as arithmetic, geometric, or neither.
Arithmetic sequence: In an arithmetic sequence, the difference between successive terms is constant. This difference is also called the common difference. For example, the sequence (a) 1, 3, 5, 7, 9, 11, 13, 15 is an arithmetic sequence because the common difference between the terms is 2.Geometric sequence: In a geometric sequence, the ratio of any two successive terms is constant. This ratio is also called the common ratio. For example, the sequence (d) -4, -12, -36, -108, -324 is a geometric sequence because the common ratio between the terms is 3.Neither: If a sequence is not arithmetic or geometric, it is classified as neither. For example, the sequence (b) 21, 16, 12, 9, 7, 6 and (c) .3, .03, .003, .0003, .00003 do not follow the patterns of arithmetic or geometric sequences and therefore are classified as neither.Learn more about Sequence Identification here:https://brainly.com/question/30531377
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Prove: The midsegment between sides Line segment AB and Line segment BC is parallel to side Line segment AC.
I need help with #22
Answer:
[tex]4 = y \\ 4 = x[/tex]
Step-by-step explanation:
The isosceles triangle containing the side of y + 12 is congruent to 3x² - 32 [base angles are congruent], and if you look closer, they are also equivalent to all three sides of the equilateral triangle adjacent to the isosceles triangle. So, we will be working with alot gadgets here, if you know what I mean. Anyway, this is how we start out:
[tex]5y - 4 = y + 12[/tex]
-5y - 5y
___________________
-4 = -4y + 12
-12 - 12
____________
-16 = -4y
___ ___
-4 -4
4 = y [Plug this back into both equations to get the value of 16.]
Next, you will set 3x² - 32 equal to 16:
[tex]16 = 3{x}^{2} - 32[/tex]
+32 + 32
_________________
48 = 3x²
__ ___
3 3
16 = x²
4 = x [In this case, we want the NON-NEGATIVE root because inputting a -4 for x will not give us identical answers.]
I am joyous to assist you anytime.
Is 770 x 6 = 77 x 6 x 100 true or false?
The equation 770 x 6 = 77 x 6 x 100 is false.
To determine if the equation 770 x 6 = 77 x 6 x 100 is true or false, let's evaluate both sides of the equation.
On the left side:
770 x 6 = 4,620
On the right side:
77 x 6 x 100 = 46,200
Since 4,620 is not equal to 46,200, the equation 770 x 6 = 77 x 6 x 100 is false.
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