Answer:
50%
Step-by-step explanation:
(new-old)/old × 100
(600 - 400)/400 × 100
(200)/400 × 100
0.5 × 100
50%
A 6-sided number cube is rolled twice. what is the probability of getting a 3 on the first roll and a 4 on the second roll?
The probability of getting a 3 on the first roll and a 4 on the second roll when a the probability of getting a 3 on the first roll and a 4 on the second roll is 1/36.
Therefore the answer is 1/36.
The probability of rolling a 3 on the first roll and a 4 on the second roll is the product of the probabilities of rolling each number separately.
Since the number cube is fair, the probability of rolling any number on a single roll is 1/6. Therefore, the probability of rolling a 3 on the first roll and a 4 on the second roll is
(1/6) × (1/6) = 1/36.
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The probability of rolling a 3 on the first roll and a 4 on the second roll is 1/36, or approximately 0.028.
This is because the probability of rolling any particular number on a 6-sided number cube is 1/6. Therefore, the probability of rolling a 3 on the first roll is 1/6, and the probability of rolling a 4 on the second roll is also 1/6. Since these events are independent (rolling a 3 on the first roll does not affect the probability of rolling a 4 on the second roll), you can multiply the probabilities of each event to find the probability of both events occurring.
Therefore, the probability of rolling a 3 on the first roll and a 4 on the second roll is (1/6) * (1/6) = 1/36. This can also be written as a decimal as 0.028.
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Last weekend, the movie theater in Wildgrove issued 8,060 tickets to comedies. This weekend, it issued 15,314 tickets to comedies. What is the percent of increase in the number of comedy ticket issued per weekend?
Answer:
The percent increase in amount of tickets sold is 90 %
Step-by-step explanation:
We need to calculate what what is the percentage of tickets sold the second weekend, in comparison to the first weekend:
[tex]\frac{15314}{8060} = 1,9[/tex]
Then we just subtract the 1 and we get 0.9 - which is 90%
What is SSS SAS ASA and AAS?
SSS - Side - Side - Side
SAS - Side - Angle - Side
ASA - Angle - Side - Angle
AAS - Angle - Angle - Side
The above theorems can be used to compare two triangles.
SSS, which stands for "side, side, side," represents two triangles having identical angles on each of their three sides. Two triangles are said to be congruent if their third sides coincide with those of another triangle.
That is what the SAS regulation says. The triangles are congruent if the two sides and included angle of one triangle match the two sides and included angle of the other triangle. Any angle that may be made by two particular sides is regarded as an included angle.
A triangle is comparable to another if its two matching angles are congruent, according to the AAA postulate of Euclidean geometry. The AAA postulate is derived from the observation that the total internal angle of a triangle is always equal to 180°.
While in case of ASA the angle - side and another angle of first triangle is equal to the corresponding angle - side - angle of other triangle.
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SSS, SAS, ASA, and AAS are four types of triangle congruence.
SSS (Side-Side-Side) is the congruence of three sides of a triangle. This means that all three sides of the triangle have the same length. To prove SSS congruence, you need to show that the corresponding sides of the two triangles have the same length. This can be done by calculating the length of each side and comparing them.
SAS (Side-Angle-Side) is the congruence of two sides and the included angle of a triangle. This means that the two sides of the triangles must have the same length, and the angles between those two sides must also be the same. To prove SAS congruence, you need to show that the corresponding sides of the two triangles have the same length, and that the angles between those two sides are also the same.
ASA (Angle-Side-Angle) is the congruence of two angles and the included side of a triangle. This means that the two angles of the triangles must have the same measure, and the side between those two angles must also be the same length. To prove ASA congruence, you need to show that the corresponding angles of the two triangles have the same measure and that the side between those two angles is also the same length.
AAS (Angle-Angle-Side) is the congruence of two angles and a non-included side of a triangle. This means that two angles of the triangles must have the same measure, and the side not included between those two angles must also be the same length. To prove AAS congruence, you need to show that the corresponding angles of the two triangles have the same measure, and that the side not included between those two angles is also the same length.
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Amazon Math Flow Questions • You have 30 associates who all work an 8 hour day, 5 days a week. 2 need to be indirect-they are not on the floor producing. Your direct rate is 150 units per hour but you have two 15 minute breaks during the day. How many units can your department produce in a 40 hour week? . If you need to produce an extra 10,000 units in a given week how many extra people will it require? Question: Each sandwich takes 10 minutes to make which means in the 10 hour shift there will be a... Each sandwich takes 10 minutes to make which means in the 10 hour shift there will be a total of 60 sandwiches. The deli wants an efficient way to increase the sandwich output using the same five workers and 10 hour shift (Don't Factor Break in) to produce 75 because of the 25% increase due to the expansion of the deli. What would you do to make the the process more efficient? Where each sandwich would take 8 minutes to make instead of 10 minutes. Please answer the question throughly.
Extra people required is 50.
Each of the five workers should increase their efficiency to a rate of 15 sandwiches per 10 hour shift.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Question 1 :
Number of associates = 30
Number of direct workers = 30 - 2 = 28
You work 8 hours a day and 5 days a week with two 15 minutes break or 30 minutes break per day.
Direct rate = 150 units per hour
Number of working hours in a week with break = 8 × 5 = 40 hours per week Number of working hours in a week = 7.5 hours per day × 5 days a week
= 37.5 hours per week
Units that department produce in a 40 hour week = 37.5 × 150 = 5625 units
28 people produce 5625 units in a week
Let x people produce 10,000 + 5625 = 15,625 units in a week
Using proportion,
28 : 5625 = x : 15,625
28 / 5625 = x / 15,625
x = (28 × 15,625) / 5625 = 77.78 ≈ 78
Extra people required = 78 - 28 = 50
Question 2 :
Number of sandwiches made in 10 minutes = 1
Number of sandwiches made in 10 hours = 60
5 workers are there. one worker makes 60/5 = 12 sandwiches
But Deli want number of sandwiches in 10 hours = 75
One worker should make 75/5 = 15 sandwiches instead of 12.
Number of sandwiches made in 8 minutes should be 1.
So the working efficiency on each worker should be increased and produce each one should produce 15 sandwiches in a 10 hour shift.
Hence extra people required in question 1 is 50 and efficiency of each worker in question 2 should be increased to 15 sandwiches in 10 hours shift.
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Process a has fixed costs of $1000 and variable costs of $5 per unit. Process b has fixed costs of $500 and variable costs of $7. 50 per unit. What is the crossover point between process a and process b?.
You must discover the point at which the total cost of each process is equal in order to identify the crossover point between processes a and b. The sum of the fixed cost and the variable cost per unit, multiplied by the number of units, is the cost of process A as a whole. The sum of the fixed cost and the variable cost per unit, multiplied by the quantity of units, is the cost of process b as a whole.
You can make the overall cost of each process equal to one another and solve for the number of units to determine the crossover point.
When x is the number of units, the total cost of process an is equal to $1000 + (5 * x).
Process B has a total cost of $500 plus (7.50 * x), where x is the number of units.
When we equalize these two expressions, we obtain:
$1000 + (5 * x) = $500 + (7.50 * x)
2.5 *x=500
x=200$
So, 200$ is the crossover point between a and b.
Therefore,200$ crossover point between process a and process b.
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Eduardo weighs 120 pounds and is gaining 5 pounds each month. Peta weighs 160 pounds and is losing 3 pounds each month. In how many months will they weigh the same?
It will take 5 months for Eduardo and Peta to weigh the same.
Eduardo weighs 120 pounds and is gaining 5 pounds each month, so after 1 month he will weigh 120 + 5 = 125 pounds.
After 2 months he will weigh 125 + 5 = 130 pounds.
This pattern continues, so after n months he will weigh 120 + 5n pounds.
Peta weighs 160 pounds and is losing 3 pounds each month, so after 1 month she will weigh 160 - 3 = 157 pounds.
After 2 months she will weigh 157 - 3 = 154 pounds.
This pattern continues, so after n months she will weigh 160 - 3n pounds.
We want to find the number of months it will take for Eduardo and Peta to weigh the same, so we set the expressions for their weights equal to each other and solve for n:
120 + 5n = 160 - 3n
8n = 40
n = 5
It will take 5 months for Eduardo and Peta to weigh the same.
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find the curvature k of the curve. r(t) = ti + t2j + t2 2 k
The curvature of the curve is k = [tex]\sqrt{\frac{5}{(1 \:+\: 5t^2)^3}}[/tex].
The complete question is in the attachment. The parameterized curve
r(t) = t i + t² j + t²/2 k
The velocity vectorThe curvature of the curve
k = |v(t) × a(t)| ÷ |v(t)|³
|v(t) × a(t)|k = |v(t) × a(t)| ÷ |v(t)|³
[tex]k \:=\: \frac{\sqrt{5}}{(\sqrt{1 \:+\: 5t^2})^3}[/tex]
[tex]k \:=\: \sqrt{\frac{5}{(1 \:+\: 5t^2)^3}}[/tex]
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for what value of v is a^v = 1, if a ≠ 0
By using properties for quotients we will see that:
a^v = 1
Only if v = 0.
For what value of v is a^v = 1?We need to remember two properties.
First, the quotient of two equal numbers is always equal to 1. So for any real number a different than zero, we can write:
a/a = 1
The second property is for the quotient of powers with the same base, we can write:
a^n/a^m = a^{n - m}
Now, notice that if we take the quotient of two numbers with the same exponent, we will get:
(a^n)/(a^n) = a^{n - n} = a^0
And that is the quotient between two equal numbers, then that is equal to 1, so:
a^0 = 1
For any real number a different than zero.
Then the value of v such that:
a^v = 1
must be v = 0.
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Probability sampling is when individuals are picked through random selection from a larger population. Which probability sampling method involves selecting large, broad groups rather than individuals
Systematic Sampling is the probability sampling method involves selecting large, broad groups rather than individuals.
Systematic sampling is a type of probabilistic sampling technique that selects sample members from a larger population according to random starting points, but with regular periodic intervals. This interval, called the sampling interval, is calculated by dividing the population size by the desired sample size.
Systematic sampling is a type of probabilistic sampling technique that selects sample members from a larger population at regular periodic intervals according to random starting points. This interval, called the sampling interval, is calculated by dividing the population size by the desired sample size. Systematic sampling is considered random if the regular intervals are predetermined and the starting point is random, even though it preselects the sample population.
Systematic sampling, when performed correctly on large populations of a defined size, allows researchers, including marketing and sales professionals, to obtain representative results on large groups of people. without having to contact each individual. Example, if we select a random group of 1,000 people from a population of 50,000 by systematic sampling, we should list all potential participants and choose a starting point. When the list is created, every 50th of her on the list (starting counting from the starting point you chose) will be selected as participants because 50,000 ÷ 1,000 = 50.
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An ice cream truck sells ice cream between 2 p.m. and 10 p.m. each night in the summer. At the end of the night, the driver calculates his profits and makes a graph to analyze the data. What is the average rate of change for the data from the 5th hour to the 8th hour? Be sure to include the correct units of measurement.
a scatter plot with x axis labeled Hour and y axis labeled Money Earned in Dollars per Hour with points at 1 comma 54 and 2 comma 58 and 3 comma 64 and 4 comma 78 and 5 comma 96 and 6 comma 126 and 7 comma 99 and 8 comma 75
7 hours
−7 dollars per hour per hour
21 dollars
−21 dollars per hour per hour
The requried average rate of change is given as -7 dollars per hour. Option D is correct.
What is a scatter plot?The association between two numerical variables measured for the same individuals is displayed in a scatterplot. One variable's values are displayed on the horizontal axis, and the other variable's values are displayed on the vertical axis.
here,
The average rate of change for the data from the 5th hour to the 8th hour is given as,
m = (y₂ - y₁) / (x₂ - x₁)
m = 75 - 96 / 8 - 5
m = -21/3
m = -7 dollars per hour.
Thus, the requried average rate of change is given as -7 dollars per hour. Option D is correct.
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Larry needed 3- bags of mulch for his rose garden. He is only ready to put mulch on three fourths of his rose garden. How much will Larry spend on mulch if each bag costs $3.25?
Since Larry needs 3 bags of mulch and each bag costs $3.25, the total cost of the mulch will be 3 × $3.25 = 9.75$
Larry is only ready to put mulch on 3/4 of his rose garden, so he will need 3/4 × $9.75 = 7.31$
answer: 7.31$
The sum of the measures of the interior angles of a convex polygon is 720°. Classify the polygon by the number of sides.
Answer:angles of 720˚ has 1+5=6 sides.
Step-by-step explanation:
7 dollar because I don't know
The measures of the exterior angles of a triangle are 3x, 8x, and 9x. Find
the measure of the smallest exterior angle.
=========================================================
Explanation:
Method 1
The exterior angles of any polygon always add to 360 degrees.
3x+8x+9x = 360
20x = 360
x = 360/20
x = 18
Then,
3x = 3*18 = 548x = 8*18 = 1449x = 9*18 = 162which represent the exterior angles of this triangle.
As a check: 54+144+162 = 360 which confirms we have the correct values.
The smallest exterior angle is therefore 54 degrees
---------------------
Method 2
The exterior angles 3x, 8x, and 9x have the corresponding interior angles of 180-3x, 180-8x, and 180-9x in that order.
For any triangle, the interior angles always add to 180 degrees.
angle1+angle2+angle3 = 180
(180-3x)+(180-8x)+(180-9x) = 180
540-20x = 180
-20x = 180-540
-20x = -360
x = -360/(-20)
x = 18
This then leads to 3x = 3*18 = 54 degrees as the final answer.
 Which function depicts f (x)
Picture included ( example of question, shifted up five units)
On solving the provided question, we can say that -- the value of the function will be f(x) = [tex]x^{-2}[/tex]
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
here,
we have the function
x^2 + 37xy + y^5
the answer is = [tex]x^{-2}[/tex]
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What is the period of the function f(x) = cos 2x?
02
05/20
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The period of the function f(x) = cos 2x is π
What is a function?A function is defined as a relation between a set of inputs having one output each.
Given is a function, f(x) = cos 2x
If we express the cosine function in the following way :
y = a cos(bx+c)+d
Then:
∣a∣ = the amplitude
2π/|b| = the period
-c/b = the phase shift
d = the vertical shift
For given function we have :
∣b∣=2
So period is :
2π/2 = π
Hence, The period is π
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What is the image of the point (6, 9) after a rotation of 270° counterclockwise about
the origin?
After the rotation of 270° counter-clockwise about the origin, the coordinates become A'(6, - 9).
What is image rotation?A rotation is a type of transformation which is a turn. A figure can be turned clockwise or counterclockwise on the coordinate plane. In both transformations the size and shape of the figure stays exactly the same.Given is the coordinate of point as (6, 9). It is rotated by 270° counter clockwise about the origin.
After the rotation of 270° counterclockwise about the origin, the coordinates will become -
A(x, y) → A'(y, - x)
So, the coordinates will become -
A(6, 9) → A'(6, - 9)
Therefore, after the rotation of 270° counter-clockwise about the origin, the coordinates become A'(6, - 9).
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In each of the following intervals, find the value of such that sin(0*) = √2/2
a. 900 270
b. 2700< 450
c. -270 <0-90
The values of angles for the intervals given are obtained as 135°, 405° and -135° respectively.
What are trigonometric ratios?The trigonometric ratios are defined for a right angled triangle.
The example of these ratios are sin, cos, tan, cosec, sec and cot.
The trigonometric ratios are useful in determining the heights and distances of the large objects.
The given trigonometric equation is sin(θ) = √2/2.
It can be written as,
sin(θ) = √2/2
⇒ sin(θ) = 1/√2
⇒ θ = 45°
(a) The value of the angle in interval 90° < θ < 270° is given as,
⇒ 180°- θ = 180° - 45° = 135°
(b) The value of the angle in interval 270° < θ < 450° is given as,
⇒ 360°+ θ = 360°+ 45° = 405°
(c) The value of the angle in interval -270° < θ < -90° is given as,
⇒ -180° + θ = -180° + 45° = -135°
Hence, the required values of angles for the given interval are 135°, 405° and -135° respectively.
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A. (×+4)2-exponent
B. (7×+5y)2- exponent
C. (4×+5y)2-eponent
Pls answer and explain
The value of (x + 4)² will be x² + 8x + 16
The value of (7x + 5y)² will be 49x² + 70xy + 25y²
The value of (4x + 5y)² will be 16x² + 40xy + 25y²
How to illustrate the exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.
The value of (x + 4)² will be:
(x + 4)²
= (x + 4)(x + 4)
= x² + 4x + 4x + 16
= x² + 8x + 16
(7x + 5y)² will be:
= (7x + 5y)(7x + 5y)
= 49x² + 35xy + 35xy + 25y²
= 49x² + 70xy + 25y²
(4x + 5y)² will be:
= (4x + 5y)(4x + 5y)
= 16x² + 20xy + 20xy + 25y²
= 16x² + 40xy + 25y²
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Consider the two functions below. Which one of these functions is linear? What is its equation? Enter any answers to two decimal places X y 3 6 LO 5 Function A 9 10 15 Function 8 ts equation is y = 12 20 15 25 is linear. X+ 9 8 6 4 3 2 1 0 y 0 1 2 3 Function B 4 5 6 7 8 9 X
Answer:
98
Step-by-step explanation:
B456789X+235575336
The first sequence rule is subtract 8 starting from 72. The second sequence rule is subtract 6 starting from 58. What is the first number that appears in both sequences
The first number or term that appears in both sequences is equals to the sixteen.
We have two sequences, for first sequence rule is subtract 8 starting from 72. The second sequence rule is subtract 6 starting from 58. We can see that both are arithmetic sequence, which defined as a sequence (list of numbers) that has a common difference (a positive or negative constant) between the consecutive terms. Now, First number in sequence 1ˢᵗ , a₁
= 72
common difference, d₁ = 8
Similarly, for 2ⁿᵈ sequence, aₙ = 58 - 6n
First number in sequence, b₁ = 58
common difference, d₂ = 6
We have to locate the number which appears in both sequences.
The nᵗʰ term of the 1ˢᵗ sequence,aₙ = a₁+ (n-1)d₁
The nᵗʰ term of 2ⁿᵈ sequence, bₙ = b₁ +(n−1)d₂
For the same number to appear on both sequence, the nᵗʰ term must be equal, so
a₁ + (n-1)d₁ = b₁ +(n−1)d₂
=> 72 + (n-1)8 = 58 +(n-1)6
=> 8n - 8 + 72 = 58 + 6n - 6
=> 8n - 6n = 52 - 64 = - 12
=> n = -6
plugging the value of n ,
72 + (-6- 1)8 = 72 - 56 = 16
58 +(-7)6 = 58 - 42 = 16
Therefore, 16 is the first common term/ number appears in both sequences.
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how do you put 6.009, -4, 0, 6.3,-5 in least to greatest
Answer:
-5, -4, 0, 6.009, 6.3
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A particle moves along a straight line with velocity given by v(t)=7-(1.01)-t^2 at time t>0. What is the acceleration of the particle at time t=3 ?
The sides of a triangle are formed by the x-axis, the line 3x-2y=3, and the line 5y+6x=60. Is the point (5, 6) a vertex of the triangle?
Yes, the point (5, 6) a vertex of the triangle.
What is a triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
Given that, the sides of a triangle are formed by the x-axis, the line 3x-2y=3, and the line 5y+6x=60.
Here, 3x-2y=3 -------(I) and 6x+5y=60 -------(II)
Multiply equation (I) by 2, we get
6x-4y=6 -------(III)
Subtract equation (III) from equation (II), we get
6x+5y-6x+4y=60-6
9y=54
y=6
Substitute y=6 in equation (I), we get
3x-2(6)=3
3x=15
x=5
So, the vertex is (5, 6)
Yes, the point (5, 6) a vertex of the triangle.
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If C(x) = 12000 + 400x − 3.8x2 + 0.004x3 is the cost function and p(x) = 4000 − 8x is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)
The production level that will maximize profit is 300 units
Given,
C(x) = 12000 + 400x − 3.8x^2 + 0.004x^3
P(x) = 4000-8x
First we need to find revenue function
R(x) = x.P(x) = x(4000-8x) = 4000x-8x^2
Now, we need to find marginal revenue
R'(x) = d/dx (4000x-8x^2) = 4000-16x
And now we'll find marginal cost
C'(x) = d/dx (12000+4000x-3.8x^2=0.004x^3) = 400-7.6x+0.012x^2
for maximum profit,
C'(x) = R'(x)
or, 4000-16x = 400-7.6x+0.012x^2
or, 0.012x^2+8.4x-3600 = 0
or, x^2+700x-300000=0
or, (x+1000) (x-300) = 0
so, x=-1000 or, x=300
Production level can not be negative.
So, the production level is 300 units
The production level that will maximize profit is 300 units
The production level that will maximize profit is 300 units
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find 9 f(x) dx 0 if f(x) = 5 for x < 5 x for x ≥ 5 .
9 f(x) dx of f(x) = 5 for x < 5 x for x ≥ 5 is 53 when x is between 0 and 9.
What is integration ?
Integration is a fundamental concept in calculus, which is used to find the area under a curve and the total change of a function. It is the reverse process of differentiation and can be used to find the original function, given its derivative.
For f(x) = 5 for x < 5, we have
∫(5dx) from 0 to 5 = 5*(5-0) = 25
For f(x) = x for x ≥ 5, we have
∫(x dx) from 5 to 9 = (1/2)x^2 from 5 to 9 = (1/2)(9^2 - 5^2) = (1/2)(81 - 25) = (1/2)(56) = 28
So the definite integral of the piecewise function is
∫(9 f(x) dx) from 0 to 9 = ∫(5dx) from 0 to 5 + ∫(x dx) from 5 to 9 = 25 + 28 = 53,
Therefore , 9 f(x) dx of f(x) = 5 for x < 5 x for x ≥ 5 is 53 when x is between 0 and 9.
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Verify the first special case of the chain rule for the composition f o c in each of the cases. (a) f(x, y) .xy, c(t) (e cos(t)) (f o c) (t) '(cos (t) sin t (f o c) (t) (e e Y 2t 2t (f o (c) (t) n e (d) f(x, y) x exp(x y c (t) (t, -t) (f o c) (t) 4t 1
The first special case of the chain rule for the composition f o c states that the derivative of f(c(t)) is equal to f'(c(t))c'(t).
For case (a):
(f o c) (t) = f(c(t)) = f(e cos(t)) = e cos(t) sin(t)
Therefore, (f o c)' (t) = f'(c(t))c'(t) = [e cos(t) sin(t)]' (e cos(t))' = e sin(t) cos(t) (e cos(t))' = e cos(t) (-sin(t)) = -e cos2(t)
For case (d):
(f o c) (t) = f(c(t)) = f(t, -t) = t exp(-t)
Therefore,
(f o c)' (t) = f'(c(t))c'(t) = [t exp(-t)]' (t, -t)' = exp(-t) (t, -t)' = exp(-t) (1, -1) = t exp(-t) (-1) = -t exp(-t)
The first special case of the chain rule for the composition f o c states that the derivative of f(c(t)) is equal to the product of f'(c(t)) and c'(t). This means that the derivative of the composition of two functions, f and c, is equal to the product of the derivative of the outermost function and the derivative of the innermost function. To verify this for each case, we need to calculate the derivatives of both f and c, then substitute them into the equation for the derivative of the composition. For example, in case (a), we have (f o c) (t) = f(c(t)) = e cos(t) sin(t). Therefore, (f o c)' (t) = f'(c(t))c'(t) = e sin(t) cos(t) (e cos(t))' = -e cos2(t). Similarly, for case (d), we have (f o c) (t) = f(c(t)) = t exp(-t). Therefore, (f o c)' (t) = f'(c(t))c'(t) = exp(-t) (t, -t)' = -t exp(-t).
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The complete question is
Verify the first special case of the chain rule for the composition f o c in each of the cases. (a) f(x, y) .xy, c(t) (e cos(t)) (f o c) (t) '(cos (t) sin t (f o c) (t) (e e Y 2t 2t (f o (c) (t) n e (d) f(x, y) x exp(x y c (t) (t, -t) (f o c) (t) 4t 1 exp(-t ) (f o c) (t) t exp(-t )
Finding the missing angle
We have found the missing angle x = 60° using the angle sum property.
What is angle sum property?The triangle's angle sum property states that the sum of its angles can equal 180 degrees. Since a triangle has three sides, each of its vertices has an angle. Regardless of whether a triangle is acute, obtuse, or right-angled, its interior angles always sum to 180 degrees.
The triangle's angle sum property is one of the geometry's most frequently used properties. The main application of this property is in the calculation of the unknown angles. The angle sum property is used to calculate the measure of an unknown interior angle when the values of the other two angles are known.
Here,
Given that
Let the angles be y, z and x
y = 80°
z = 40°
x = ?
Using the angle sum property
Sum of the interior angle of a triangle = 180°
x + y + z = 180°
x + 80 + 40 = 180
x + 120 = 180
x = 180 - 120
x = 60°
Thus, we have found the missing angle x = 60° using the angle sum property
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Your school is donating items to the local food pantry. Your homeroom is having a competition to see who will donate the most items. You have already donated 14 items and plan to donate 3 more each week. Your friend has already collected 8 items and plans to collect 5 more items each week. Write and solve a system of equations for the number of weeks (x) when you both donate the same number of items (y).
The number of weeks (x) when you both donate the same number of items (y) is equal to 3 weeks.
How to write and solve a system of linear equations?In order to write and solve a system of linear equations to describe this situation, we would assign variables to the number of weeks and number of items respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of weeks.Let the variable D represent the donations.Let the variable y represent the number of items.Since you have already donated 14 items and plan to donate 3 more each week, a linear equation which represents this situation is given by;
D = 3x + 14 ........equation 1.
Since you have already donated 8 items and plan to donate 5 more each week, a linear equation which represents this situation is given by;
D = 5x + 8 ........equation 2.
Equating equation 1 and equation 2, we have:
3x + 14 = 5x + 8
5x - 3x = 14 - 8
2x = 6
x = 6/2
x = 3 weeks.
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How do you solve SSS theorem?
A SSS (side-side-side) theorem is kind of Congruence rule where two triangles with three congruent sides. So, we can solve it by showing the congruency between two triangles.
Statement: Side-Side-Side (SSS) ,the congruence theorem states that two triangles are congruent if three of their sides are equal to the corresponding sides of the other triangle.
Proof: Given, AB = DE, BC = EF, AC = DF.
To prove: ΔABC ≅ ΔDEF.
We know that the three sides of both triangles are equal in size and length. With both triangles superimposed, DE is placed on AB, EF is placed on BC, and DF is placed on AC. That is, AB = DE, BC = EF, AC = DF. Therefore, we can say that ΔABC ≅ ΔDEF.
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Find the inverse of the function.
ƒ(x) = 4x², x ≤0
whats the inverse?
Answer:
To find the inverse of a function, you need to switch the roles of the x and y variables. So the inverse of ƒ(x) = 4x² for x ≤ 0 is written as ƒ^(-1)(y) = ?.
To find the inverse function, we can solve for x in terms of y:
4x² = y
x² = y/4
x = √(y/4)
So the inverse of ƒ(x) = 4x² for x ≤ 0 is ƒ^(-1)(y) = √(y/4). Note that this inverse function is only defined for y ≤ 0, since the original function is only defined for x ≤ 0.
