The left-hand side of the equation represents the logarithm of 64 with base x, and it is not possible to find a real value of x that satisfies the equation.
solve the equation logₓ(64) + 5 = 2, we can follow these steps:
Step 1: Move the constant term to the other side of the equation:
logₓ(64) = 2 - 5
logₓ(64) = -3
Step 2: Rewrite the equation in exponential form:
x^(-3) = 64
Step 3: Rewrite 64 as a power of x:
x^(-3) = x^6
Step 4: Set the exponents equal to each other:
-3 = 6
The equation -3 = 6 is not true, which means there is no real solution to the given equation.
Therefore, the equation logₓ(64) + 5 = 2 has no solution in the real number system.
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a faster Buffet line lets people line up on other side of the buffet table that's doubling the rate now one person picks up a plate every 10 seconds two people / 20 seconds which reduces to one person / 10 seconds how many seconds will pass for 200 people
Answer: 1000
Step-by-step explanation:
If one person can pick up a plate every 10 seconds, then the rate of picking up plates can be represented as 1 plate/10 seconds.
When two people are picking up plates, the rate doubles, so it becomes 2 plates/10 seconds or 1 plate/5 seconds.
To find how long it will take for 200 people to pick up plates, we need to use the formula:
time = amount ÷ rate
where an amount is the number of plates needed (in this case, 200), and the rate is the rate at which plates are being picked up (1 plate/5 seconds).Plugging in the values, we get:
time = 200 plates ÷ (1 plate/5 seconds)
time = 200 plates × 5 seconds/plate
time = 1000 seconds
Therefore, it will take 1000 seconds for 200 people to pick up plates at a faster rate.
I hope that this answer has helped you!
Pls answer!! reward is a lot of points. Question is "7/4 - (- 1/6)"
Answer:1 11/12
Step-by-step explanation:
What is the equation of the line that passes through the point (-3, 7) and has a slope of -5/3?
The equation of the line that passes through the point (-3, 7) and has a slope of -5/3 is y - 7 = (-5/3)(x + 3).
We are given the point (-3, 7) and the slope of the line as -5/3.The slope-intercept form of a line is y = mx + b where m is the slope and b is the y-intercept.
To obtain the equation of the line, we need to substitute the values of slope and point in the slope-intercept form and solve for b.(7) = (-5/3)(-3) + b 21/3 = b.
Now we have the value of b, and we can substitute the values of m and b in the slope-intercept form.y = (-5/3)x + 21/3 is the equation of the line in slope-intercept form.
To obtain the equation in the standard form Ax + By = C, we multiply each term by 3.3y = -5x + 7Add 5x to both sides5x + 3y = 7.
This is the equation of the line in standard form.
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(36)^x+2= 6
Solve and round to the nearest 100th
Please help I am confused and need an explanation
As the given equation is (36)ˣ⁺² = 6 , then the solution for the given equation is x ≈ -1.54.
The given equation in the question is (36)ˣ⁺² = 6
according to the given equation , the goal is to solve the equation for x.
For solving this equation ,
we'll have to use logarithmic operations which is as follows:
log36(6) = x+2.
We will be further using a calculator to determine the logarithmic value: log36(6) ≈ 0.4607.
Now, By subtracting 2 from both sides, we will get the value of x as:
x ≈ -1.54.
When we round off this value to the nearest 100th, we will get -1.54.
Thus , the solution for the given equation is x ≈ -1.54.
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A group of students at a high school took a standardized test. The number of students who passed or failed the exam is broken down by gender in the following table.
Determine whether gender and passing the test are independent by filling out the blanks in the sentence below, rounding all probabilities to the nearest thousandth.
Answer:
Gender and passing the test appear to be ________, as the probability of each event occurring does not depend on the other. Both males and females pass or fail the test with similar likelihoods. To confirm this independence, you could perform a chi-square goodness-of-fit test comparing observed frequencies to expected frequencies under the null hypothesis of independence between gender and test outcome. If the calculated p-value from the test exceeds your chosen significance level, you can conclude that there is sufficient evidence to reject the null hypothesis, indicating that gender and passing the test are dependent.
which graft shows the solution set for 2x+3>-9
The solution above is graphed correctly in the last option choice is x > -6
We have been given the equation 2x + 3> -9
In order to graph the solution, we must find the value of x
2x + 3 > -9
Subtract three from both sides
-9 - 3 = -12
2x > -12
Divide both sides by 2
x > -6
Examine the inequality symbol to figure out how to graph the solution. If the sign is "greater than," graph the line to the left. If it was "less than," you would draw a straight line.
We have the "greater than" symbol in our issue, which implies we will graph our line to the right, and since we start our line at -6, we know the last choice is the correct solution.
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The following question may be like this:
Which graph shows the solution set for 2x+3>-9.
Which are the solutions of x2= -13x -4
Answer: D
Step-by-step explanation:
To solve this question, we need to change the equation to standard form.
[tex]x^2=-13x-4[/tex] [add both sides by 13x and 4]
[tex]x^2+13x+4=0[/tex] [use quadratic equation]
[tex]\frac{-13+\sqrt{13^2-4(4)}}{2} , \frac{-13-\sqrt{13^2-4(4)}}{2}[/tex] [simplify]
[tex]\frac{-13+\sqrt{13^2-16}}{2} , \frac{-13-\sqrt{13^2-16}}{2}[/tex]
[tex]\frac{-13+\sqrt{169-16}}{2} , \frac{-13-\sqrt{169-16}}{2}[/tex]
[tex]\frac{-13+\sqrt{153}}{2} , \frac{-13-\sqrt{153}}{2}[/tex]
Therefore, the answer is D.
The diameter of a circle is 7 fr find it’s circumference in the terms of pi
Answer:
7*pi
Step-by-step explanation:
If the diameter is 7, the radius is 7/2
Therefore, the circumference would be 2*pi*(7/2)=7*pi
iangle with sides of 8 cm, 8 cm, and 10 cm,
Find the area of each shaded region.
6. 7.
A swimming pool is 8 m long, 6 m wide and 1.5 m deep. The water-resistant paint needed for the pool costs 6 dollars per square meter. How much will it cost to paint all the interior surfaces of the pool?
It will cost $1080 to paint all the interior surfaces of the pool.
6. & 7. The triangles have sides of 8, 8, and 10 cm, and an area of 24 square cm. The remaining areas are 18 and 12 square cm, respectively.
Triangle with Sides 8, 8, and 10 cm: First, we must calculate the area of the whole triangle, which has sides of 8, 8, and 10 cm. Using the Heron's formula, we can find the area of a triangle given the lengths of its sides: A = √(s(s - a)(s - b)(s - c)), where s = (a + b + c)/2 is the semi perimeter of the triangle.
A = √(13(13 - 8)(13 - 8)(13 - 10)) = √(13(5)(5)(3)) = √(2925) = 15√(65) ≈ 59.17 square cm. Next, we can calculate the areas of the shaded regions as follows: Area of Shaded Region 1 = Area of Whole Triangle - Area of Small Triangle Area of Shaded Region 1 = 15√(65) - 18 = 15√(65) - 6√(65) = 9√(65) ≈ 27.94 square cm.
Area of Shaded Region 2 = Area of Whole Triangle - Area of Large Triangle Area of Shaded Region 2 = 15√(65) - 24 = 3√(65) ≈ 7.74 square cm.7.
A swimming pool has the dimensions 8 m (length), 6 m (width), and 1.5 m (depth). The total area to be painted is the sum of the areas of the floor, the ceiling, and the walls of the pool. Since the pool is rectangular in shape, we can break it down into six different parts: the top and bottom surfaces, and the four vertical surfaces.
Let's begin by calculating the area of the floor, which has dimensions of 8 m by 6 m:Area of Floor = length x width = 8 x 6 = 48 square meters.
Next, we can calculate the area of the ceiling, which has the same dimensions as the floor: Area of Ceiling = length x width = 48 square meters. Since the pool has a depth of 1.5 m, the total height of the vertical surfaces is 1.5 x 2 = 3 m (since there are two vertical surfaces on each side of the pool).
Thus, the total area of the four vertical surfaces is given by: Area of Walls = perimeter x height = 2(length + width) x height = 2(8 + 6) x 3 = 84 square meters.
Finally, we can calculate the total area to be painted by adding up the area of the floor, ceiling, and walls: Total Area = Area of Floor + Area of Ceiling + Area of Walls Total Area = 48 + 48 + 84 = 180 square meters.
The cost of paint is given as $6 per square meter, so we can calculate the total cost of painting the pool as follows: Cost = Total Area x Cost per Square Meter Cost = 180 x $6 = $1080. Therefore, it will cost $1080 to paint all the interior surfaces of the pool.
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Given that x^2-4x + 1 = (x-p)- q for all values of x, find the value of p and the value of q
The values of p and q are 1 and 3, respectively.
Given the equation x^2-4x + 1 = (x-p)- q, we can compare the coefficients of the corresponding terms on both sides of the equation.
We compared the coefficients of the x^2 terms on both sides of the equation. The coefficient of the x^2 term on the left-hand side is 1, and the coefficient of the x^2 term on the right-hand side is 1. This means that the two terms are equal, and therefore p = 1.
We compared the coefficients of the x terms on both sides of the equation. The coefficient of the x term on the left-hand side is -4, and the coefficient of the x term on the right-hand side is -1. This means that the two terms are equal, and therefore q = 3.
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Select the correct answer.
Which expression is equivalent to 107-8y +3? Assume that the denominator does not equal zero.
O A. y2 (10y³ - 8y² + 3)
О в.
10³ - 8y² + 3
V
O c.
y (10y³
OD. 10²¹ - $y² +3
8y² + 3)
Reset
Next
The correct answer is option B: 10³ - 8y² + 3.
To obtain the equivalent expression, we can simplify the given expression by combining like terms. We have 107 as a constant term, -8y as the coefficient of the y term, and 3 as another constant term.
So, combining these terms, we get 10³ - 8y² + 3, which is equivalent to the given expression.
Option A is incorrect because it introduces an additional y term in the form of y², which is not present in the original expression.
Option C is incorrect because it only includes the y term and its coefficients, without considering the constant terms.
Option D is unrelated to the original expression as it introduces unrelated numbers and symbols.
Therefore, the correct equivalent expression is 10³ - 8y² + 3, as stated in option B.
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The come shown in the diagram has a circular base with a radius of 6 inches perpendicular to the height. The cone is 414.7 cubic inches. What is the height,h, of the cone to the nearest whole inch? If the length of the radius is doubled and the height of the cone changed to 8 inches, find the volume of the new cone.
The volume of the new cone is 1,536π cubic inches.
To find the height of the cone, we can use the formula for the volume of a cone:
V = (1/3)πr²h
Given that the volume of the cone is 414.7 cubic inches and the radius is 6 inches, we can substitute these values into the formula and solve for h:
414.7 = (1/3)π(6)²h
414.7 = (1/3)π(36)h
414.7 = 12πh
h = 414.7 / (12π)
h ≈ 10.93 inches
Therefore, the height of the cone is approximately 10.93 inches when rounded to the nearest whole inch.
Next, let's calculate the volume of the new cone after doubling the radius to 12 inches and changing the height to 8 inches.
Using the same formula, we have:
V = (1/3)π(12)²(8)
V = (1/3)π(144)(8)
V = 1,536π
The redesigned cone has 1,536 cubic inches of capacity.
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Two numbers between 0 and 1 on a number line are to be chosen at random. What is the probability that the second number chosen will exceed the first number chosen by a distance greater than 1/4 unit on the number line? Express your answer as a common fraction.
The probability is 5/8 that the second number chosen will exceed the first number by a distance greater than 1/4 unit on the number line when two numbers are randomly chosen between 0 and 1.
To determine the probability that the second number chosen will exceed the first number by a distance greater than 1/4 unit on the number line, we need to consider the possible range of values for both numbers.
Since the two numbers are chosen randomly between 0 and 1, we can visualize this as a unit interval on the number line, where 0 represents the left endpoint and 1 represents the right endpoint.
Let's analyze the scenario where the first number is chosen and labeled as x. The probability that the second number chosen will exceed x by a distance greater than 1/4 unit can be represented by the shaded area on the number line.
To calculate this probability, we need to determine the length of the interval where the second number can be chosen, given that it exceeds x by more than 1/4 unit.
If the first number, x, is chosen between 0 and 3/4 (i.e., x < 3/4), the second number can be chosen in the range (x + 1/4, 1]. The length of this interval is 1 - (x + 1/4) = 3/4 - x.
If the first number, x, is chosen between 3/4 and 1 (i.e., 3/4 ≤ x < 1), the second number can be chosen in the range (3/4, 1]. The length of this interval is 1 - 3/4 = 1/4.
Since the probabilities of choosing a number within each interval are equally likely, we need to calculate the weighted average of these probabilities based on the lengths of the intervals.
The probability of choosing a number between 0 and 3/4 is (3/4 - 0) = 3/4, and the probability of choosing a number between 3/4 and 1 is (1/4 - 0) = 1/4.
Therefore, the overall probability is calculated as:
P = (3/4) * (3/4) + (1/4) * (1/4) = 9/16 + 1/16 = 10/16 = 5/8.
So, the probability that the second number chosen will exceed the first number by a distance greater than 1/4 unit on the number line is 5/8.
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which statement is true about quadrilateral QRST
The statement that is true about quadrilateral QRST is: d. Side TQ has a length of sq rt of 17 units
What is quadrilateral?
A quadrilateral is a polygon with four sides and four vertices. The term "quadrilateral" is derived from the Latin words "quadri" meaning "four" and "latus" meaning "side."
Quadrilaterals come in various shapes and sizes, and they can have different angles and side lengths. Some common examples of quadrilaterals include rectangles, squares, parallelograms, trapezoids, and rhombuses.
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The complete question is:
Which statement is true about quadrilateral QRST?
a. Side QR has a length of 5 units.
b. Side RS has a length of sq rt of 40 units.
c. Side ST has a length of 6 units.
d. Side TQ has a length of sq rt of 17 units
10 marbles 6 black 4 white what is the decimal probability of getting a white
Answer:
.6
Step-by-step explanation:
Find value of x in trapezoid
Answer:
x = 1
Step-by-step explanation:
You want to know the value of x in the trapezoid with adjacent angles (43x+2)° and 135°.
Supplementary anglesThe two marked angles can be considered "consecutive interior angles" where a transversal crosses parallel lines. As such, they are supplementary.
(43x +2)° +135° = 180°
43x = 43 . . . . . . . . . . . . . . divide by °, subtract 137
x = 1 . . . . . . . . . . . . . . . divide by 43
The value of x is 1.
__
Additional comment
Given that the figure is a trapezoid, we have to assume that the top and bottom horizontal lines are the parallel bases.
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please help! with algebra I question
Answer:
[tex]\frac{g^{125}}{2h^{8}}[/tex]
Step-by-step explanation:
[tex]2g^{5^{3}} =2g^{125}[/tex]
[tex]4h^{2^3} = 4h^{8}[/tex]
[tex]\frac{2g^{125}}{4h^8} = \frac{g^{125}}{2h^8}[/tex]
Please awnser asap I will brainlist
The roster method of the set A' = {14, 15, 20}
How to find sets using roster method?The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.
A typical example of the roster method is to write the set of numbers from 1 to 5 as {1, 2, 3, 4, 5}.
Therefore,
U = universal sets = {14, 15, 16, 17, 18, 19, 20}
A = {16, 17, 18, 19}
Therefore, let's find A' as follows:
A' is the value not in A. Hence, in roster method.
A' = {14, 15, 20}
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The members of the given set in this problem are given as follows:
X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}
How to obtain the union and intersection set of two sets?The union and intersection sets of multiple sets are defined as follows:
The union set is composed by the elements that belong to at least one of the sets.The intersection set is composed by the elements that belong to at all the sets.The intersection of the sets Y and Z for this problem is given as follows:
Y ∩ Z = {0, 6, 23, 26}
(which are the elements that belong to both of the sets).
The union of the above set with the set X is given as follows:
X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}
(elements that belong to at least one of the sets).
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4. The physician's order states: Add 60mEq of potassium chloride to 1000ml D5W and infuse at a rate of 42 ml per hour. Available are ampoules labeled potassium chloride 40 mEq = 20 ml. The infusion set has a drop factor of 60 gtt/ml. (a) How much potassium chloride should be added to the IV?
Using concentration-volume relationship, 30 ml of potassium chloride should be added to the IV solution.
How much potassium chloride should be added to the IV?To calculate the amount of potassium chloride to be added to the IV, we need to consider the concentration of the potassium chloride ampoules and the desired final concentration in the IV solution.
Given:
Physician's order: Add 60mEq of potassium chloride to 1000ml D5W
Potassium chloride concentration in ampoules: 40 mEq per 20 ml
Desired final concentration: Not specified
To determine the amount of potassium chloride to be added, we can set up a proportion based on the mEq (milliequivalents) of potassium chloride:
This is done using concentration-volume relationship
40 mEq / 20 ml = 60 mEq / x ml
Cross-multiplying, we have:
40 mEq * x ml = 60 mEq * 20 ml
Simplifying:
40x = 1200
Dividing both sides by 40:
x = 30 ml
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proportional relationships 7th grade
Answer/ Step-by-step explanation:
---
Proportional relationships are relationships between two variables where their ratios are equivalent.
---
Lets take a look at example one attached image:
The constant of proportionality is the value of y when x = 1 in a proportional relationship.
On which line does y = 1/2 when x = 1?
Only line C has a y- value less than 1 when x = 1, but how can we be sure that the constant of proportionality is exactly 1/2?
If the constant of proportionality of a proportional relationship is 1/2 then:
y = 1/2x (like rise over run (slope), rise up 1 unit, and run right 2 units)
We can try the point (2, 1), and plug in the values into the equation, where x = 2, y = 1.
(1) = 1/2(2)
1 = 1
Line C has a constant proportionality of 1/2 between x and y.
--------
Example 2, 3, and 4 is a worked out example on khan academy (attached images)
The diameter of a circle is 4ft , Find it’s circumference in terms of pi.
Step-by-step explanation:
The circumference of a circle can be found using the formula:
C = πd
where C represents the circumference and d represents the diameter of the circle.
Given that the diameter of the circle is 4 feet, we can substitute this value into the formula:
C = π * 4
Therefore, the circumference of the circle is 4π feet.
p: A square has 4 sides. q: A triangle has 5 sides. Determine the truth values of the statements
The truth values of the statements can be determined as follows:
Statement p: "A square has 4 sides."
This statement is true. A square is a polygon with four equal sides and four equal angles, so it has 4 sides.
Statement q: "A triangle has 5 sides."
This statement is false. A triangle is a polygon with three sides and three angles, not five. It is a fundamental geometric shape with specific characteristics, and one of those characteristics is having three sides.Therefore, the truth values of the statements are:
p is true.
q is false.
It's important to note that truth values are based on established definitions and properties of geometric shapes. The statement p aligns with the definition of a square, while the statement q contradicts the definition of a triangle.
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A college student realized that he was spending too much money on fast food. For the remaining 5 months of the year his goal is to spend a mean of $50 a month
towards fast food. How much can he spend in December, taking into consideration that in the other 4 months he spent $35, $90, $15, and $60, respectively? Round
your answer to two decimal places, if necessary.
Answer: 50$
Step-by-step explanation:
To calculate the amount the college student can spend on fast food in December, we need to find the total amount he can spend in 5 months, given that he wants to spend an average of $50 per month.
Let's start by finding the total amount he can spend in 5 months:
Total amount = 5 x $50 = $250
Now, we can subtract the amount he spent in the other 4 months from the total amount to find out how much he can spend in December:
The amount he can spend in December = Total amount - Amount spent in 4 months
Amount spent in 4 months = $35 + $90 + $15 + $60 = $200
Amount he can spend in December = $250 - $200 = $50
Therefore, the college student can spend $50 on fast food in December to meet his goal of spending an average of $50 per month on fast food for the remaining 5 months of the year.
Refer to photo please.
Answer:
-5/6
-2/3
Step-by-step explanation:
it's easiest to write the line in the following form:
y=mx+b
where m is the slope
and b is the y intercept
In other words, we want to get y by itself
5x+6y= -4
6y= -4-5x
y=(-4-5x)/6
y=(-5/6)x-4/6
Thus, -5/6 is the slope
and -4/6= -2/3 is the y intercept
Sample response: The product of two numbers with
different signs is negative, so 2(-12) = -24, not 24. Then
-24-(-30) = -24 + 30 = 6.
Select all the information you considered when writing
your response.
The product or quotient of two integers with
different signs is negative.
To subtract an integer, add its opposite.
To add integers with opposite signs, subtract the
absolute values. The sum has the same sign as the
integer with the greater absolute value.
By considering these rules and properties of integers, the correct result of 6 was obtained.
When writing the response, I considered the following information:
The product or quotient of two integers with different signs is negative. This rule was used to determine that 2(-12) equals -24, not 24.
To subtract an integer, add its opposite. This rule was applied when subtracting -30 from -24, resulting in -24 - (-30) = -24 + 30.
To add integers with opposite signs, subtract the absolute values. The sum has the same sign as the integer with the greater absolute value.
This rule was used to calculate -24 + 30 = 6, where the absolute value of 30 is greater than the absolute value of -24.
By considering these rules and properties of integers, the correct result of 6 was obtained.
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Use the image below to answer the following question. What relationship do the ratios of sin x° and cos y° share?
A right triangle is shown. The two angles that are not 90 degrees are marked x and y. The leg across from angle y measuring 4, another leg across from angle x measuring 3, and the hypotenuse measuring 5
The ratios are both identical (three fifths and three fifths).
The ratios are opposites (negative three fifths and three fifths).
The ratios are reciprocals (three fifths and five thirds).
The ratios are both negative (negative five thirds and negative three fifths).
The ratios are both identical (three fifths and three fifths). Option A
How to determine the ratiosThe ratios of sin x° and cos y° are given as;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
In the question given above, the value of adjacent is 5 and the value of perpendicular is 12.
By using Pythagoras theorem, we can find the value of the hypotenuse.
Hypotenuse² = Adjacent² + Perpendicular²
Hypotenuse² = 5² + 12²
Hypotenuse² = 25 + 144
Hypotenuse² = 169 = 13²
Hypotenuse = 13
The value of sin X° will be;
sin X = 5/13
cos Y = 5/13.
sin X° = cos Y° = 5/13
Therefore, both the ratios of sin x° and cos y° are equal and their value is 5/13.
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Complete question:
Use the image below to answer the following question. What relationship do the ratios of sin x° and cos y° share?
A right triangle is shown. The two angles that are not 90 degrees are marked x and y. The leg across from angle y measuring 4, another leg across from angle x measuring 3, and the hypotenuse measuring 5
The ratios are both identical (three fifths and three fifths).
The ratios are opposites (negative three fifths and three fifths).
The ratios are reciprocals (three fifths and five thirds).
The ratios are both negative (negative five thirds and negative three fifths).
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The roster method of the set X ∪ (Y ∩ Z) = {p, q, r, s, 21, 22, 23, 25}
How to find sets using roster method?The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.
A typical example of the roster method is to write the set of numbers from 1 to 5 as {1, 2, 3, 4, 5}.
Therefore,
X = {p, q, r, 21, 22, 23}
Y = {q, s, t, 21, 23, 25}
Z = {q, s, 22, 23, 25}
Therefore, let's find X ∪ (Y ∩ Z) as follows:
(Y ∩ Z) = {q, s, 23, 25}
X = {p, q, r, 21, 22, 23}
Therefore,
X ∪ (Y ∩ Z) = {p, q, r, s, 21, 22, 23, 25}
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Enter the number that belongs in the green box
The angle measure that belongs in the green box is given as follows:
70.67º.
What is the law of sines?We consider a triangle with side lengths and angles related as follows, as is the case for this problem:
Side length of a is opposite to angle A.Side length of b is opposite to angle B.Side length of c is opposite to angle C.Then the lengths and the sines of the angles are related as follows:
sin(A)/a = sin(B)/b = sin(C)/c.
The relation for this problem is given as follows:
sin(x)/12 = sin(76º)/12.34
Applying cross multiplication, the missing angle measure is given as follows:
sin(x) = 12 x sine of 76 degrees/12.34
sin(x) = 0.9436.
x = arcsin(0.9436)
x = 70.67º.
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NO LINKS!! URGENT HELP PLEASE!!!
For 6a and 6b., Write the equation for each graph below
6a. The equation for the graph is y = 2√(x + 5).
6b. The equation for the graph is y = -|x + 1| + 5
What is a square root function?In Mathematics and Geometry, the standard form of a square root function can be modeled as follows;
y = a√(x - h) + k
h and k represents the vertex of the graph.a represents the leading coefficient.Part 6a.
Next, we would determine value of a as follows;
4 = a√(-1 + 5) + 0
4 = a√4
4 = 2a
a = 2
Therefore, the required square root function is given by;
y = 2√(x + 5)
Part 6b.
Since the line representing the absolute value function has a y-intercept at (0, 4) and vertex at (-1, 5), the absolute value equation for the graph is given by:
y = a|x - h| + k
y = -|x + 1| + 5
Read more on absolute value function here: brainly.com/question/28308900
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