Answer:
Using the identity rule:
[tex](a-b)^2 = a^2-2ab+b^2[/tex]
Given the equation:
[tex]x^2-12x+36 = 90[/tex]
Rewrite the above equation as:
[tex]x^2-2 \cdot x \cdot 6+6^2 = 90[/tex]
Apply the identity rule:
[tex](x-6)^2 = 90[/tex]
Take square root to both sides we have;
[tex]x-6 = \pm \sqrt{90}[/tex]
Add 6 to both sides we have;
[tex]x = 6\pm \sqrt{90}[/tex]
or
[tex]x = 6 \pm 3\sqrt{10}[/tex]
Therefore, the value of x are:
[tex]6+3\sqrt{10}[/tex] and [tex]6-3\sqrt{10}[/tex]
Pablo randomly picks three marbles from a bag of eight marbles (four red ones, two green ones, and two yellow ones).
How many outcomes are there in the sample space?
The sample space for drawing 3 marbles from a bag of 8 marbles is 56. This is determined using the combinations formula in statistics and probability, which takes into account the number of items and the number of draws.
Explanation:The question you're asking relates to the concept of combinations in probability and statistics. When Pablo picks three marbles from a bag of eight marbles without replacement, he changes the number of possibilities with each draw. The sample space of his experiment consists of all possible outcomes he could get when drawing the three marbles.
The number of outcomes is determined by calculating the combination of 8 items taken 3 at a time. The formula for combinations is:
C(n, r) = n! / r!(n - r)!
Substituting the given values:
C(8, 3) = 8! / 3!(8 - 3)!
C(8, 3) = 8! / 3!5! = (8 x 7 x 6) / (3 x 2 x 1) = 56
So, the sample space for this experiment contains 56 possible outcomes.
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The question is about calculating combinations in combinatorics, a topic in mathematics. For a bag containing 8 marbles and picking 3 at a time, there are 56 possible outcomes or ways in which the marbles can be drawn from the bag.
Explanation:The number of outcomes in the sample space can be found by multiplying the number of choices for each marble. In this case, Pablo is picking three marbles from a bag of eight marbles. The number of outcomes is determined by the combination formula: nCr = n! / (r! * (n - r)!). So, for Pablo picking three marbles from eight marbles, the number of outcomes in the sample space is:
nCr = 8! / (3! * (8 - 3)!)
nCr = 8! / (3! * 5!)
nCr = 8 * 7 * 6 / (3 * 2 * 1) = 56.
Therefore, there are 56 outcomes in the sample space.
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What is the quadratic function with the given vertex and through the given point? Write the equation of the parabola in vertex form and describe how the function was transformed from the parent function y = x2.
vertex (0, 0), point (−2, 2)
The quadratic function with vertex (0, 0) and passing through the point (-2, 2) is y = 0.5x^2. This is a transformation of the parent quadratic function y = x^2 with a vertical stretch by a factor of 0.5.
Explanation:The quadratic function with the given vertex (0, 0) and going through the point (-2, 2) can be written in the form of the vertex form of a quadratic function i.e. y = a(x - h)² + k, where (h, k) is the vertex of the parabola. Since the vertex given is (0,0), the function becomes y = ax².
Now, to find the value of 'a', we can substitute the x and y coordinates of the given point (-2,2) into the equation. So, 2 = a(-2)², this simplifies to 2 = 4a. Solving for 'a', we get a = 0.5. So, the function is y = 0.5x².
This function is a transformation of the parent function y=x². The 0.5 in front of x² means that the graph of the function stretches vertically by a factor of 0.5. Thus, the parabola opens upwards and is narrower than the parent function.
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Which of the following options represeWrite the point-slope form of the equation of the line that passes through the points (6, 6) and (-6, 1). Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.nts the form of a linear equation that should be used to write the equation of a line when the slope and a point on the line are given? general form standard form factored form point-slope form
which of the following is the converse of the statement "If it is my birthday, then it is September"?
what integer and 9 have the product of -135
Can you please help me with this math problem
This question is nasty. It sounds like you should be finding area of the figure you see. I'll do that first, although I don't think it's the right answer. (But it might be).
Area Trapezoid = (b1 + b2) * h / 2
b1 = 8
b2 = 12
h = 5
Area Trapezoid = (8 + 12 ) * 5 / 2
Area Trapezoid = 20 * 5/2
Area = 50 square feet.
The problem is that no lumber yard will cut that for you without charging you. The practical answer is 12 * 5 = 60 square feet is what you will have to buy. Then you cut out the triangles for yourself.
Suppose a weather forecaster says the probability that it will rain on saturday is 2929% and the probability that it will rain on sunday is 4040%. from this information, is it possible to find the probability that it will rain on saturday or sunday (or both)? why or why not?
the angle of the first hill of a roller coaster is 55 degrees. if the length of the track from the beginning of the ascent to the highest point is 98 feet, what is the height if the roller coaster when it reaches the top of the first hill?
How many fluid ounces in 8 ounces and 5 cups?
Cross section of a metal ingot is a trapezoid the cross section has an area of 39 square cm the top base of the cross section is 12 CM the length of the bottom base is 2 cm greater than the top base how tall is the Metal Ingot explain
you are painting a room that is 18 ft long, 14 ft wide and 8 ft high. find the area of the four walls that you are going to paint.
Final answer:
The total area to be painted is 512 square feet, calculated by summing up the areas of the two longer walls (288 sq ft) and the two shorter walls (224 sq ft). For time estimation, the linear equation would be t = 4 + (512/1000), resulting in approximately 4.51 hours of painting time.
Explanation:
To calculate the area of the four walls in a room for painting, you will be finding the surface area of the sides not including the floor or ceiling. First, you need to calculate the area of the two longer walls and the two shorter walls separately.
For the longer walls, the area for one wall is 18 ft (length) times 8 ft (height), which gives you 144 square feet for one long wall. There are two such walls, so multiply by 2, which equals 288 square feet for both long walls.
For the shorter walls, the calculation is similar. The area for one short wall is 14 ft (width) times 8 ft (height), which gives 112 square feet for one short wall. With two short walls, the total is 224 square feet.
Add the area of the long walls and the area of the short walls together to get the total painting area: 288 sq ft + 224 sq ft = 512 square feet.
To express this as part of a linear equation for time estimation given in the scenario, if it takes one hour per 1,000 square feet, we would use the equation t = 4 + (A/1000), where t is the total time in hours and A is the area in square feet. Since the painting area is 512 square feet, the painting time is t = 4 + (512/1000), giving 4.512 hours, which rounds up to approximately 4.51 hours.
how does the division look for 8.43206 ÷ 26
Determine the number of solutions the following system of equations will have: 1/3 y - 5 = 2x y = 15 + 6x
Q and R are not mutually exclusive events. p (q) = 3/5 p(r) = 1/3 and p ( q and r)= 1/5 find P(Q or R).
The answer to this item is 23/32.
What is probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.
Given that the events are not mutually exclusive the union of the probability of the events is calculated through the equation,
P(Q or R) = P(Q) + P(R) - P(Q and R)
Substituting the known values,
P(Q or R) = 3/5 + 1/3 - 1/5
Simplifying,
P(Q or R) = 11/15
Hence the answer to this item is 23/32.
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HELP FAST!! What is the volume of a right rectangular prism with a base that measures 4 in by 6 in. and a height of 7 in? A) 17 in.3. B) 51 in.3. C) 84 in.3. D) 168 in.3.
Answer:
d
Step-by-step explanation:
If p ( x ) = 8 + 6 x − 4 x 2 p(x)=8+6x-4x2 represents the profit in selling x x thousand boombotix speakers, how many speakers should be sold to maximize profit?
Final answer:
To maximize the profit from selling Boombotix speakers, the company should sell 0.75 thousand speakers, or 750 speakers, which is determined by finding the vertex of the profit function p(x) = 8 + 6x - 4x2.
Explanation:
The function p(x) = 8 + 6x - 4x^2 represents the profit from selling x thousand Boombotix speakers. To find the number of speakers that should be sold to maximize profit, we need to find the vertex of the parabola represented by this quadratic function, which is a downwards opening parabola because the coefficient of x^2 is negative (-4).
The vertex form of a quadratic function is p(x) = a(x-h)2 + k, where (h, k) is the vertex of the parabola. The x-coordinate of the vertex (h) can also be found using the formula h = -b/(2a) where a is the coefficient of x2 and b is the coefficient of x in the standard form of the quadratic function. In this case, a = -4 and b = 6. Applying the formula:
h = -b/(2a) = -6/(2 * -4) = -6 / -8 = 0.75
Hence, the company should sell 0.75 thousand speakers, or 750 speakers, to maximize profit.
julie will build a rectangular pen for her dog against a barn. A wall from the barn will from one side of the pen. She has 32m of fencing to form the other three sides. She plans to build the pen so that it has its maximum possible area. What will be the dimensions of julie's pen?
the answer is 8 and 16
Solve the systems x ≡ 1 (mod 2), x ≡ 2 (mod 3). x ≡ 2 (mod 5), 2x ≡ 3 (mod 7), 3x ≡ 4 (mod 11). x ≡ 31 (mod 41), x ≡ 59 (mod 26).
The sum of Andy and Brett's ages is 44. Andy's age is 8 more than twice Bret's age. Find the solution.
The ages of Andy and Brett can be determined by setting up two equations from the given information and solving for their ages. Andy is 32 years old, and Brett is 12 years old.
Explanation:The subject of this question is Mathematics. The question falls under algebraic problem-solving typically taught in middle school. To find Andy and Brett's ages, we can set up two equations based on the given information.
Let A represent Andy's age, and B represent Brett's age. According to the problem, we have:
A + B = 44 (since the sum of their ages is 44)A = 2B + 8 (since Andy's age is 8 more than twice Brett's age)We can substitute the second equation into the first:
(2B + 8) + B = 443B + 8 = 443B = 36B = 12Brett is 12 years old. Now, we can find Andy's age using the second equation:
A = 2(12) + 8A = 24 + 8A = 32 years oldSo, Andy is 32 years old, and Brett is 12 years old.
The sum of Andy and Brett's ages can be found using a system of equations. We can solve the equations to find Andy's age is 32 and Brett's age is 12.
Explanation:The problem can be solved using a system of equations.
Let's assume Andy's age is 'x' and Brett's age is 'y'.
We are given that the sum of their ages is 44, so the equation is: x + y = 44.
Additionally, Andy's age is 8 more than twice Brett's age, so we have another equation: x = 2y + 8.
Now we can solve this system of equations to find the values of x and y.
Substituting the value of x from the second equation into the first equation, we get (2y + 8) + y = 44. Simplifying this equation gives us 3y + 8 = 44. Subtracting 8 from both sides, we have 3y = 36. Dividing both sides by 3, we get y = 12. Substituting this value back into the first equation, we find x = 32.
Therefore, Andy is 32 years old and Brett is 12 years old.
Find an equation of the line described. Write the equation in slope-intercept form when possible. Slope 1, through (-4,3)
Is a cubic inch is the space taken by a cube whose sides are 1 inch long?
Anyone care to help with this please
Use the given information to find the indicated probability. a and b are mutually exclusive. p(a) = .8, p(b) = .1. find p((a ∪ b)').
Given that P = (-5, 5) and Q = (-13, 6), find the component form and magnitude of 2vector PQ
ANSWER
Component form:
[tex]\binom{ - 16}{2} [/tex]
2. Magnitude
[tex]2\sqrt{65} [/tex]
EXPLANATION
Given that P = (-5, 5) and Q = (-13, 6),
Vector PQ
[tex] = \binom{ - 13}{6} - \binom{ - 5}{5} [/tex]
[tex] = \binom{ - 13 + 5}{6 - 5} [/tex]
[tex] = \binom{ - 8}{1} [/tex]
2 vector PQ
[tex] = 2 \binom{ - 8}{1} [/tex]
[tex] = \binom{ - 16}{2} [/tex]
This is the component form.
The magnitude is given by
[tex] = \sqrt{ {x}^{2} + {y}^{2} } [/tex]
[tex] = \sqrt{ {( - 16)}^{2} + {2}^{2} } [/tex]
[tex] = \sqrt{256 + 4} [/tex]
[tex] = \sqrt{260} [/tex]
[tex] = 2\sqrt{65} [/tex]
use the product-to-sum identities to rewrite the following expression
sin 14° cos50°
Need help with hw, willing to give $$
Given the following sets:
A={ 2, 4, 6, 8, 10}
B={ 3, 5, 7, 9}
C={ 2, 3, 5, 7}
N={ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Match the following Unions and intersections to the correct set.
1.
What is A U C?
2.
What is A ∩ B?
3.
What is A ∩ N?
4.
What is B ∩ N?
5.
What is B U C?
{2, 3, 4, 5, 6, 7, 8, 10}
{2, 3, 5, 7, 9}
{ }
{3, 5, 7, 9}
{2, 4, 6, 8, 10}
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A college cafeteria pays student cashiers $10.20 per hour. Cashiers earn an additional $1.30 per hour for each hour worked over 35 hours per week. A cashier worked 40 hours one week and 38 hours the second week. How much did this cashier earn in this two-week period?
Answer:
$806
Step-by-step explanation:
The regular earning of a cashier = $10.20 per hour
over 35 hours per week he gets = $10.20 + $1.30 per hour
= $11.50 per hour
He worked 40 hours in first week and 38 hours the second week.
His earnings in first week = (35 × 10.20) + (5 × 11.50)
= $357 + $57.5
= $414.50
His earnings in second week = (35 × 10.20) + (3 × 11.50)
= $357 + $34.50
= $391.50
His total earnings in this two weeks = $391.50 + $414.50
= $806
His total earning was $806.
What is the height of a triangle that has an area of 60 yd squared and a base with a length of 12 yd