To find the smallest poster area with a fixed printed area of 388 square centimeters, calculate optimized values for the width and height of the printed area, considering the margins, and derive the poster's dimensions by adding the margins to these values.
Explanation:To find the dimensions of the poster with the smallest area given a fixed printed area, we should first determine the dimensions of the printed area. We know that the printed area is 388 square centimeters and that the margins do not change. Let's denote the width of the printed area as w and the height as h.
The area of the printed material is given by Area = w × h = 388 cm². The total width of the poster would be w + 2×(8 cm) (since there are two side margins), and the total height would be h + 2×(4 cm) (since there are top and bottom margins).
To minimize the area of the poster, we need to minimize the function for the total area of the poster A(w,h) = (w + 16)(h + 8). As the printed area is fixed, we can express h in terms of w using h = 388/w and substitute this into the function to get A(w) = (w + 16)((388/w) + 8).
Taking the derivative dA/dw and setting it to zero, we find the optimal value for w, and consequently, we calculate h. The dimensions of the poster that minimize the total area can then be determined by adding the margins to these optimized values of w and h.
Divide. Write your answer in simplest form.
eight divided by seven sixths
Graph the solution set to the inequality.
A.
B.
C.
D.
Answer:
this is the question from edgenunity i bet
alright first the question is
4(8-2y)4y+ less than or equal to 32 -8
we'll solve for Y by Isolating the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
y ≥ 2
the correct answer for me was A,
Step-by-step explanation:
Five times the sum of a number and seven is thirty. find the number.
Two vertices of an isosceles triangle in the coordinate plane have coordinates (0,0) and (2a,0). Where might the third vertex be located?
A quadrilateral has three angles that measure 80°, 110°, and 75°. Which is the measure of the fourth angle
To burn 1 molecule of c7h16 to form co2 and h2o (complete combustion), how many molecules of o2 are required?
Eleven molecules of O2 are required to completely combust one molecule of C7H16, producing CO2 and H2O. The balanced chemical reaction of this process is: C7H16 + 11O2 → 7CO2 + 8H2O.
Explanation:Combustion of one molecule of C7H16 (heptane) to produce CO2 (carbon dioxide) and H2O (water) requires 11 molecules of O2 (oxygen). The balanced chemical equation of this reaction is:
C7H16 + 11O2 → 7CO2 + 8H2O
The equation shows that for every one molecule (or mole) of C7H16, 11 molecules (or 11 moles) of oxygen are needed. An analogy can be seen in the combustion of methane where one methane molecule and two oxygen molecules react to yield one carbon dioxide molecule and two water molecules.
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how to find what numbers a number is divisible by
The sum that represents the number of tickets sold if 35 tickets were sold on monday, half of the remaining tickets were sold on tuesday , and 14 ticket were sold on wenesday
which one has the same value as 1 hundred 7 tens
A theorem is a statement that can be easily prove using a corollary
Answer:
false
Step-by-step explanation:
Ohhhh I have a math Brainliest!
The Greenville Art Museum had 12 sculptures on display that were made by students. The museum received 3 more student sculptures. After two weeks they loaned 4 of the sculptures to another museum. How many student sculptures are at the Greenville Art Museum now?
The Greenville Art Museum currently has 11 sculptures on display after receiving 3 more sculptures and then loaning out 4 sculptures.
Explanation:The Greenville Art Museum initially had 12 sculptures on display. They added 3 more sculptures to their collection, which increased the total number of sculptures to 15. Afterwards, they loaned out 4 sculptures to another museum. To find out how many sculptures are still at the Greenville Art Museum, we subtract the number of sculptures loaned out from the total.
Starting with 15 sculptures, after loaning out 4, we do the following calculation:
15 - 4 = 11 sculptures
Therefore, the Greenville Art Museum now has 11 sculptures on display.
If -4 is added to a number and them sum is doubled, the result is -16 less than the number. find the number.
Final answer:
By setting up an equation based on the given problem (2(n - 4) = n - 16) and solving for n, we find that the number in question is – 8.
Explanation:
To find the number in question, let's represent the unknown number as n. According to the problem, if -4 is added to a number and then the sum is doubled, it equals the number decreased by 16. So the equation based on the problem is:
2(n - 4) = n - 16
Expand the left side of the equation:
2n - 8 = n - 16
Now we want to get all the n terms on one side and the constants on the other. To do this, we subtract n from both sides:
n - 8 = -16
Next, we add 8 to both sides to solve for n:
n = -16 + 8
n = -8
So the number in question is -8.
A tennis ball hit from the ground level into the air. Its height above the ground at the time can be modeled by the function h(t) = -16t² +160t. The height, h, is measured in feet above the ground and the time, t, is measured in seconds after the ball is hit. How long is the ball in the air?
Answer:
a
Step-by-step explanation:
Which postulate or theorem can be used to prove that angle abc is congruent to angle def?
If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
The ratio of men to women working for a company is 7 to 4 . if there are 133 men working for the company, what is the total number of employees?
Where would an imaginary line need to be drawn to reflect across an axis of symmetry so that a regular pentagon can carry onto itself? A) any angle to any angle B) any angle to the farthest angle C) any angle to the next closest angle D) any angle to the center of the side opposite the angle
Answer:
Any angle to the center of the side opposite the angle
Step-by-step explanation:
The prefix milli- means one thousandth, or 10–3. how many milliseconds (ms) are in 6.7 seconds? 6.7 × 10–3 ms 2.0 × 104 ms 6.7 × 102 ms 6.7 × 103 ms
You know that the prefix mili means one thousandth or 1/100.
Numerically speaking, one thousandth is equals to 10 to the power of negative 3.
Solving seconds to milliseconds:
6.7 seconds x 1000 milliseconds / 1 second
Cancelling out the unit seconds. Then multiplying 6.7 to 1000 milliseconds.
The answer is 6,700 milliseconds or 6.7 x 10^3 ms
Can someone solve these for me? I have no idea what I'm doing wrong. 19 points.
Caitlin says the difference in their ages is 24 years. In two or more complete sentences, explain whether or not Caitlin is correct. In your explanation, include the equations and calculations necessary to support or contradict Caitlin's answer.
What are the discontinuities of the function f(x) = x^2+2x-8/12x+24?
A peer is having difficulty finding angle measures using trigonometric ratios in a right triangle. Create an example to demonstrate how to do this and be sure to address using the reciprocal relationships (cosecant, secant, cotangent too)
Final answer:
To find angle measures using trigonometric ratios, such as sine, cosine, and tangent, as well as their reciprocals (cosecant, secant, and cotangent), use SOHCAHTOA to relate the sides of the triangle to the angle. Utilize the inverse trigonometric functions (like arccos) on your calculator to find the angle's measure from the ratio you have calculated with sides of the triangle.
Explanation:
To find angle measures using trigonometric ratios in a right triangle, we can use the mnemonic SOHCAHTOA, which stands for Sine equals Opposite over Hypotenuse, Cosine equals Adjacent over Hypotenuse, and Tangent equals Opposite over Adjacent. Let's create an example:
Suppose we have a right triangle with a hypotenuse (h) of 10 units and an adjacent side (x) to angle theta of 8 units.
To find the cosine of angle theta, we use the ratio Cos(theta) = x/h. Thus, Cos(theta) = 8/10 = 0.8.
To determine the actual measure of angle theta, we use the inverse cosine function: theta = arccos(0.8), which gives us the angle's measure in degrees or radians.
For the reciprocal, secant (Sec) is simply the inverse of cosine: Sec(theta) = 1/Cos(theta) = 10/8 = 1.25.
If we needed to use the cotangent, which is the reciprocal of the tangent, we would first need to find the opposite side (y) using the Pythagorean theorem and then use the ratio Cot(theta) = x/y.
It's essential to understand these relationships and how to use the inverse functions to find the angle measures in a right triangle. Reciprocal relationships involve the use of cosecant (Csc), which is 1/Sin(theta), secant (Sec), and cotangent (Cot), which is 1/Tan(theta). Always make sure your calculator is set to the correct unit (degrees or radians) before calculating the angle.
Why must eye protection be worn at all times in welding shop?
At green deli employees earn double time for any hours worked in addition to their usual 40-hour week. Ester Klein worked 43 hours this week. Klein's regular hourly rate is $9.00 an hour. What is her total pay this week?
Answer:
$414.00
Step-by-step explanation:
At green deli employees earn double time for their over time.
Klein's regular hourly rate = $9.00
So, her overtime rate = $9 × 2 = $18.00
Ester Klein worked 43 hours this week.
40 hours regular work + 3 hours overtime
Her total pay this week = (40 × 9) + (3 × 18)
= 360 + 54
= $414.00
Her total pay this week is $414.00
Find the square numbers between 50 and 100
Name the set(s) of numbers to which 1.18 belongs.
a. rational numbers
b. rational numbers, irrational numbers
c. natural numbers, whole numbers, integers, rational numbers
Answer:
a. rational numbers
Step-by-step explanation:
The number is between integers, so it can't be an integer or a whole number.
In general, 1.18 belongs to three sets of numbers.
Firstly, it is a rational number because it can be written in the form p/q where p and q are integers and q is not equal to zero.
1.18=[tex]\frac{118}{100}[/tex]
Secondly, all rational numbers are also real numbers and all real numbers are complex numbers.
But we have been given to choose from only rational numbers, irrational numbers, natural numbers or whole numbers.
So, the only answer is rational number.
Find the equation of the line perpendicular to x−5y=15 that passes through the point (−2,5).
1. Solve the given equation for y.
x - 5y = 15
-5y = -x + 15
y = (-x + 15)/-5
y = (x/5) - 3
y = (1/5)(x) - 3
The slope is 1/5. See it?
The equation we are looking for has a slope which is the negative inverse of the slope in the equation we just solved for y.
The slope for the equation we want is -5 which is the negative inverse of 1/5. Undetstand?
We have the slope of the new equation and one point is given.
Plot BOTH into the point-slope formula and solve for y. To solve for a variable means to isolate the variable ALONE on one side of the equation.
y - y_1 = m(x - x_1)...This is the point-slope formula. Our given point is (5,-2)
y - 5 = -5(x - (-2))
y - 5 = -5(x + 2)
We now solve for y and that's it.
y - 5 = -5x - 10
y = -5x - 10 + 5
The equation we want is y = -5x - 5.
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The scale on a map of Virginia shows that 1 centimeter represents 30 miles. The actual distance from Richmond, VA to Washington, DC is 110 miles. On the map, how many centimeters are between the two cities? Round your answer to the tenth.
Answer:
3.7 cm
Step-by-step explanation:
Simplify negative 7 and one over 8 minus negative 9 and one half
Of a group of students, 5/8 of them are boys. the girls are put into groups so that each group has 1/16 of the total number of students. how many groups of girls are there?