a + b = 88
ab = y
a = 88 - b
y = (88 - b)*b
y = -b^2 + 88b
Take the derivative and set equal to 0
y' = -2b + 88 = 0
2b = 88
b = 44
a=44
both numbers are 44
To find two positive numbers a and b whose sum is 88 and whose product is maximized, we can use the concept of quadratic equations. By taking the derivative of the product function and setting it equal to zero, we can find the maximum value. Plugging that value back into the product function will give us the maximum product.
Explanation:To find two positive numbers a and b whose sum is 88 and whose product is maximized, we need to use the concept of quadratic equations. Let's assume a as x and b as 88-x. The product of the two numbers can be expressed as the quadratic equation P(x) = x(88-x). To maximize the product, we need to find the maximum value of P(x). We can use calculus to find the maximum value by taking the derivative of P(x) and setting it equal to zero. Solving that equation will give us the value of x, and plugging it back into P(x) will give us the maximum product.
Let's go through the steps:
Write the quadratic equation: P(x) = x(88-x).Take the derivative of P(x) and set it equal to zero: P'(x) = 88-2x = 0.Solve for x: x = 44.Plug x back into P(x) to find the maximum product: P(44) = 44(88-44) = 1936.So, the two positive numbers a and b are 44 and 88-44, which is 44 as well. Their sum is 88 and their product is maximized at 1936.
How do scientists communicate the results of investigations? A. by publishing articles in scientific journals B. by giving talks at scientific conferences C. by exchanging e-mails D. all of the above
The proof that ΔQPT ≅ ΔQRT is shown. Given: SP ≅ SR Prove: ΔQPT ≅ ΔQRT What is the missing reason in the proof? Statements Reasons 1. SP ≅ SR 1. given 2. ST ⊥ PR 2. converse of the perpendicular bisector theorem 3. PT ≅ RT 3. ? 4. QT ⊥ PR 4. ST and QT name the same line. 5. QP ≅ QR 5. perpendicular bisector theorem 6. ΔQPT ≅ ΔQRT 6. HL theorem definition of perpendicular bisector definition of congruence reflexive property substitution property
Answer:
A. definition of perpendicular bisector
Step-by-step explanation:
I JUST TOOK THE TEST!!!!!!
Answer:
The correct option is a) perpendicular bisector definition.
Step-by-step explanation:
Given :
Triangle QPT is similar to triangle QRT.
[tex]\rm SP \cong SR[/tex]
To find : Why [tex]\rm PT \cong RT[/tex]
Solution :
According to perpendicular bisector definition -
Perpendicular Bisector is a line or a segment perpendicular to a segment that passes through the midpoint of the segment. Any point on the perpendicular bisector is equidistant from the endpoints of the line segment.
Therefore, [tex]\rm PT \cong RT[/tex]
Hence option a) is correct.
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Please Help!! Find the measure of angle 2. Image Attached
opposite angles have to equal 180
so 180-111 = 69
angle 2 is 69 degrees
Which of the following is a simpler form of the expression sin (theta)sec(theta)÷ cos(theta)tan(theta)
Answer: [tex]sec \theta[/tex].
Step-by-step explanation: Given expression : [tex]\frac{sin \theta \ sec \theta }{cos \theta \ tan \theta} .[/tex]
We know,
[tex]sec \theta = \frac{1}{cos \theta}[/tex]
[tex]tan \theta = \frac{sin \theta}{cos \theta}[/tex]
Substituting those values in given expression, we get
[tex]\frac{sin \theta \ sec \theta }{cos \theta \ tan \theta} .[/tex] =[tex]\frac{sin \theta\ \frac{1}{cos \theta} } {cos \theta\ \frac{sin \theta}{cos \theta} }[/tex]
= [tex]\frac{sin \theta \ cos \theta}{cos \theta \ cos \theta \ sin \theta}[/tex]
Crossing out [tex]sin \theta \ cos \theta[/tex] from top and bottom, we get
=[tex]\frac{1}{cos \theta }[/tex]
= [tex]sec \theta[/tex].
Answer:
The simplified form of the given expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex] is [tex]\sec\theta[/tex]
Step-by-step explanation:
Given: Expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex]
We have to writ the given expression in simplified form.
Consider , The given expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex]
Since, we know,
[tex]\sec\theta=\frac{1}{\cos\theta}[/tex]
and [tex]\tan\theta=\frac{\sin\theta}{\cos\theta}[/tex]
Substitute, we have,
[tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}=\frac{\sin\theta \cdot\frac{1}{\cos\theta}} {\cos\theta\cdot \frac{\sin\theta}{\cos\theta} }[/tex]
Simplify, we have,
[tex]=\frac{\frac{1}{\cos\theta}} {\cos\theta\cdot \frac{1}{\cos\theta} }[/tex]
Simplify further, we get,
[tex]=\frac{1}{\cos\theta}=\sec\theta[/tex]
Thus, The simplified form of the given expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex] is [tex]\sec\theta[/tex]
A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing 200 pounds requires 250 milligrams of medicine. What is the weight of a patient who requires 220 milligrams of medicine?
Look at the figure. What is the next step in this construction of a line parallel to AC passing through point B.
A. use a protractor to measure ∠BAC
B. Draw a line through point B that intersects arc 2.
C. Measure the distance between AB and AC along arc 1 with a ruler.
D. Measure the distance between AB and AC along arc 1 with a compass.
Answer:
Option A is correct
Step-by-step explanation:
In the given figure to draw the parallel line to AC passing through B we have to tell the next step.
As lines AC and AB given and we know if lines are parallel then alternate angles are equal.
Hence, if line through B parallel to AC drawn then alternate angles ∠BAC and ∠ABD equal.
∴ To draw parallel lines our next step is to use a protractor to measure ∠BAC so that the same angle through B is drawn results in equal alternate interior angles.
Hence, Option A is correct.
I NEED THIS ASAP Are two regular hexagons always congruent? Explain your answer
In the triangle below, what ratio is sin θ?
Answer: The required ratio is [tex]\dfrac{12}{13}.[/tex]
Step-by-step explanation: In the given triangle, we are to find the ratio of sinθ.
We know that
in a right-angled triangle, the ratio sine of an angle is given by the length of the perpendicular divided by the length of the hypotenuse.
For the given right-angled triangle, we get
[tex]\sin\theta=\dfrac{perpendicular}{hypotenuse}\\\\\\\Rightarrow \sin\theta=\dfrac{36}{39}\\\\\\\Rightarrow \sin\theta=\dfrac{12}{13}.[/tex]
Thus, the required ratio is [tex]\dfrac{12}{13}.[/tex]
To take a taxi, it costs $3.00 point plus an additional $2.00 per mile traveled. You spent exactly $20 on a taxi, which includes the $1 tip you left. How many miles did you travel?
If the average price of four pairs of shoes is $50, and three of those pairs of shoes are priced at $35, $40 and $55, what is the price of the fourth pair of shoes?
X+y=13and x-y=2 what is the value of x^2-y^2
Evaluate | 4t+n | if t=-2 and n=5
Will give brainliest to correct and best explained answer.
How many hours are in 2 weeks?
In triangle KLM LM = 7 and angle k equals 45 Find KL.
In this problem, the student can use the properties of a 45°-45°-90° triangle to determine that the hypotenuse KL is 7 * √2 which is approximately equal to 9.9.
Explanation:In a triangle where you know one angle (45°) and one side (7 units) across from the right angle, it is a typical example of a situation where trigonometry can be used. In this case, you're dealing with a 45°-45°-90° triangle, also known as an isosceles right triangle. In such a triangle, the sides are in a specific ratio. The sides opposite the 45° angles are the same length (let's call it 'a'), and the hypotenuse is a√2.
Given that LM = 7 and angle K is 45°, triangle KLM is therefore an isosceles right triangle and KL (the hypotenuse) is equal to LM multiplied by √2. So, KL = 7 * √2 which approximately equals to 9.9.
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Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 240 b = 123 c = 207
What are all the possible 3 digit number combinations 0-9?
A blue billiard ball with mass m crashes into a red billiard ball with the same mass that is at rest. The collision results in the blue billiard ball traveling with a velocity of v and the red billiard ball travelling with a velocity of 3v. In terms of v and m, determine the blue billiard ball’s velocity before the collision...
Your computer monitor has a width of 13.93 inches and a height of 10.45 inches. what is the area of the monitor display in square meters
The area of a computer monitor with dimensions of 13.93 inches by 10.45 inches is approximately 0.09381 square meters.
Explanation:To calculate the area of your computer monitor, you first need to convert the dimensions from inches to meters because the area is asked for in square meters. There are approximately 0.0254 meters in an inch. So the width is 13.93 inches * 0.0254 m/inch equals to approximately 0.354 meters, and the height is 10.45 inches * 0.0254 m/inch equals to approximately 0.265 meters.
Then, we can calculate the area using the formula: Area = width * height. Substituting the converted measurements into the formula: Area = 0.354 m * 0.265 m which equals to approximately 0.09381 square meters.
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In a random sample of 2121 people, the mean commute time to work was 30.130.1 minutes and the standard deviation was 7.17.1 minutes. assume the population is normally distributed and use a t-distribution to construct a 8080% confidence interval for the population mean muμ. what is the margin of error of muμ? interpret the results.
The margin of error can be calculated using the t statistic. The formula for margin of error is given as:
Margin of error = t * s / sqrt (n) ---> 1
Where,
t = the t score based on the given confidence level and degrees of freedom
n = number of samples = 21
s = standard deviation = 7.1
Degrees of freedom = n – 1 = 21 – 1 = 20
Based on the standard probability tables for t, the t score is:
t = 0.860
Substituting into equation 1:
margin of error = 0.860 * 7.1 / sqrt (21)
margin of error = 1.33
The range is:
range = 30.1 ± 1.33
range = 28.77, 31.43
Therefore the commute time to work is between 28.77 minutes and 31.43 minutes.
Difference between algebra 1 and pre-algebra
Answer:
Step-by-step explanation:
The prefix Pre stands for before and algebra is math so pre algebra is informing you about what you will be learning before it actually happens.
Algebra is math for ninth graders that if you fail makes you have to take it until you pass it.
Regression and modeling with functions
The roots of the equation are 3 + 8i and 3 – 8i.
What is the value of c?
x2 – 6x + c = 0
c = [1]
If a wheel with a radius of 70 inches spins at a rate of 600 revolutions per minute, find the approximate linear velocity in miles per hour. use pi= 3.14
What is the solution to the following system of equations? X-2y=2, x-2y=-2
The given system of equations, x - 2y = 2 and x - 2y = -2, are parallel lines and do not intersect, thus there is no common solution to the system.
Explanation:In mathematics, to find the solution to a system of equations, we generally try to find the values of variables that satisfy all the equations in the system. When looking at the given equations: x - 2y = 2 and x - 2y = -2, we can see that there is something strange. These two equations are equivalent to each other, meaning they represent the same line. This is due to the fact that both equations have the same coefficients for the x and y variables (1 and -2 respectively). So, if two lines are equivalent, they are essentially the same line. This means there are infinitely many solutions which satisfy this system of equations, since all points on the line satisfy both equations. However, if two lines have the same coefficients but different constants (the numbers without the variables), as in our case, then they are parallel and do not intersect, indicating that there's no solution for the system of equations. Therefore, this system of equations has no solution.
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Factor the difference of two perfect squares using the X method. What are the two binomial factors for x2 – 25?
(x – 5)(x – 5)
(x + 5)(x + 5)
(x – 20)(x + 5)
(x – 5)(x + 5)
Answer:
its D
Step-by-step explanation:
angie andKenny play online video games angie buys 1 software package and 3 months of game play. Kenny buys 1 software package and 4 months of game play. each software package costs $20. if there total cost is $117 what is the cost of one month game play
At 2:00 Tony rented a mountain bike from the slick rock cyclery. He returned the bike at 5:00 after cycling 18 mi.Tony paid 24 for the rental. Find the rental rate in dollars per mile. Take the number of dollars and divide by the number rate mile
Kenji buys 3 yard of fabric for 7.47 then he relizes that he need 2 more yard how much fbric will he need
Identify the volume and surface area of the sphere
volume = 4/3 x PI x r^3
in terms of pi. multiply r^3 x 4/3 = 18432PI
surface area = 4pir^2
in terms of pi multiply r^2 x 4 = 2304PI