How do I solve by multiplying Imaginary Numbers? (10√-6) (√42)
Select the correct answer.
If Georgia and Farrah work together, it takes them 8 minutes to clean the espresso machine at their coffee shop. Alone, Farrah takes 12 minutes less than Georgia to clean the machine. If x is the number of minutes it takes Georgia to clean the machine by herself, the situation can be represented by this equation
Georgia takes 24 minutes to clean the espresso machine by herself.
The correct answer is an option D.
The equation for the situation is:
[tex]\frac{1}{x} +\frac{1}{x-12} =\frac{1}{8}[/tex]
here, x is the number of minutes it takes Georgia to clean the machine by herself.
We need to find the value of x.
Consider the equation,
[tex]\frac{1}{x} +\frac{1}{x-12} =\frac{1}{8} \\\\\frac{(x -12)+x}{x(x-12)}=\frac{1}{8}\\\\\frac{x -12+x}{x^2-12x}=\frac{1}{8}[/tex]
(2x - 12) × 8 = x² - 12x
16x - 96 = x² - 12x
x² - 12x -16x + 96 = 0
x² - 28x + 96 = 0
x²-24x-4x+96 = 0
(x - 24)(x - 4) = 0
x = 24 or x = 4
If x = 4, then x - 12 would be negative which is not possible.
Thus, it takes 24 minutes for Georgia.
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Find the complete question below.
Find the indicated real nth root(s) of a. n=2, a= -49
As, a = -49 is a negative number, so there is no real root for the integer.
What is square root?
A number's square root is a value that, when multiplied by itself, yields the original number. The other way to square an integer is to find its square root.
The expression is given as - a = -49
The value for n is n = 2
Find the nth root value for the expression a.
Since a = -49 is a negative number there is no real square root for the number.
If it would have been a = 49, then there would have been one real square root.
n=2 which generates √49.
This gives the value as 7.
Therefore, there are no roots for -49.
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3. A unit cube is shown below. Which of these can best be measured by using unit
cubes?
Unit Cube
A. Weight
B. Area
C. Volume
D. Temperature
I unit
unif
1. Circle C is centered at the origin. Is point (5, 5) on the circle? -8 -6 -4 -2 8 6 4 2 101 -2 -4 -6 -8 2 4 6 ++ 8
Answer: d
Step-by-step explanation:
put some clothes on
if JKLM is a parallelogram what is measure angle K
PLEASE HELP
JKLM is a parallelogram with four sides and four angles, meaning its measure of angle K is equal to the measure of angle M.
What is a parallelogram?A parallelogram is a quadrilateral having four equal-length sides and opposing sides that are parallel. It is a two-dimensional form with two pairs of parallel sides and equal angles on all sides.
JKLM has four sides and four angles if it is a parallelogram. Because it is a parallelogram, the opposite sides of the figure will be parallel, as will the opposite angles. This signifies that the angle K measure is equal to the angle M measure. As a result, if the measure of angle M is known, the measure of angle K may be calculated.
For example, if angle M is 70 degrees, then angle K is also 70 degrees. In general, if the measure of angle M is x, the measure of angle K must be x as well.
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i need to know how to find the gcf
The greatest positive integer that completely divides both of the numbers is known as the greatest common factor, or GCF. The GCF or HCF is composed of two or more non-zero integers.
In other words, the greatest common factor (GCF) among all the factors of the provided numbers is the case when there are two or more numbers. The Highest Common Factor of the Given Numbers is another name for it.
The approaches that are utilized to discover the GCF are listed below.
citing common elements:
Here, we list the common components of the given numbers and highlight those that are most frequently occurring.
main determinants:
In order to determine the highest common factors from both prime factor lists, we must write the given numbers as the product of prime numbers.
division strategy
Here, we must use the long division method to divide the greatest integer by the lowest number until the result is zero. The GCF of the given integers will make up the rest of the divisor when we reach the point where we have zero.
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magine you are painting a series of towers built from cubes. You are going to paint only the exposed faces of the cubes. If the tower you paint has 25 exposed faces, how many cubes are in the tower?
Answer: 6
Step-by-step explanation:
4x + 1 = 25
4x = 24
x = 6
PLS HELP IF SOMEONE KNOWS THE ANSWER!!!!!!!!!!
Answer:
see below.
Step-by-step explanation:
1. g(x) = 2^(x-5) +3
2. g(x)= 1/3 * 2^x
3. f(x) was vertically stretched by 3. K value is 3. The Y intercept became augmented by 3 folds.
4. k value = 5, the curve basically got "lifted" up by 5 units.
Please helppp please now ASAP
Answer:
Step-by-step explanation:
ok so with triangle sum theorem the equation we use for this is n-2•180 (n equals number of sides, for 3*180 is 540, 540-all non variable numbers leave us with 165, divide 165 by 13 and that’s your answer, if anything round. Please lmk if this is wrong
a) if a leaf completes the color transformation, what is the probability that it will complete the textural transformation?
the probability that it will complete the textural transformation
is 0.90334.
Let A be the event that a leaf completes the color transformation and B be the event that a leaf completes the textural transformation.
n(A) = 243 + 26 = 269
n(B) = 243 + 13 = 256
n (A∩ B) = 243
n(S) = 243 +26+13+18 = 300
Finding the Probability of the event that the leaf completes the color transformation by using the Probability of an event formula
P(A)= 269 / 300
= 0.89667
p(A∩ B) = 243/300
= 0.81
By using the conditional probability of a leaf completing textural transformation given a leaf completing color transformation
P(B/A) = p(A∩ B) / P(A)
= 0.81/0.89667
= 0.90334
The conditional probability of a leaf completing textural transformation given a leaf completing color transformation is 0.90334
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The complete question is :
The analysis of results from a leaf transmutation experiment (turning a leaf into a petal) is summarized by type of transformation completed:
(a) ) If a leaf completes the color transformation, what is the probability that it will complete the textural transformation?
[tex]\sqrt{45)[/tex]
The required solution to the given radical expression √45 is 3√5.
What are the radical expressions?Any expression that contains a radical symbol is considered a radical expression. To find the square roots, cubic roots, and higher, radical symbols are used. For example, √7, √6, and √11 are in the radial form.
The radical expression is given in the question
√45
As per the given question, the required solution would be as:
√45 = √(3 × 3 × 5)
√45 = 3√5
Thus, the solution to the given expression is 3√5.
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In a quadrilateral ABCD,if m(<A)=80,m(<B)=100° and m(<D)=110°,find m(<C).
In quadrilateral ABCD, m∠C = 70°.
What is quadrilateral?A quadrilateral in geometry is a four-sided polygon with four edges and four corners.
Given:
ABCD is a quadrilateral.
m∠A =80°, m∠B = 100° and m∠D = 110°.
The sum of all the interior angles is 360°.
m∠A + m∠B + m∠C + m∠D = 360°.
80 + 100 + 110 + m∠C = 360
m∠C = 360 - 290
m∠C = 70°
Therefore, m∠C = 70°
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Step-by-step explanation:
In a quadrilateral, the sum of the measures of the angles is 360 degrees. Therefore, if we know the measures of three of the angles in a quadrilateral, we can use this information to find the measure of the fourth angle.
In this case, we know that:
m(<A) = 80 degrees
m(<B) = 100 degrees
m(<D) = 110 degrees
So, to find m(<C), we can use the equation:
m(<A) + m(<B) + m(<C) + m(<D) = 360
Substituting in the known values, we get:
80 + 100 + m(<C) + 110 = 360
Solving for m(<C), we get:
m(<C) = 360 - (80 + 100 + 110) = 360 - 290 = 70 degrees
So the measure of angle C is 70 degrees.
The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 246.7 and a standard
deviation of 62.5. (All units are 1000 cells/μL.) Using the empirical rule, find each approximate percentage below.
a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or
between 59.2 and 434.2?
b. What is the approximate percentage of women with platelet counts between 184.2 and 309.2?
a) The approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 59.2 and 434.2 is of 99.7%.
b) The approximate percentage of women with platelet counts between 184.2 and 309.2 is of 68%.
What is defined by the Empirical Rule?These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:
68% of the measures within one standard deviation of the mean.95% of the measures within two standard deviation of the mean.99.7% of the measures within three standard deviation of the mean.Hence the percentages are given as follows:
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May I have help on this math question please? thank you if you do!
The rate of change of the function is: 2.
The y-intercept/initial value is: 3.
How to Find the Rate of Change and Initial Value of Linear Function?The rate of change is also the slope of a function, which is calculated as, m = change in y / change in x.
Given the points, (0, 3) and (2, 7):
Rate of change/slope (m) = (7 - 3) / (2 - 0)
m = 4/2
m = 2
To find the initial value/y-intercept (b), substitute m = 2 and (x, y) = (0, 3) into y = mx + b:
3 = 2(0) + b
3 = 0 + b
3 = b
b = 3
y-intercept = 3.
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Nora hired a plumber to come to her house. The equation
y = 35x + 50 represents the costs in dollars, y, of hiring the plumber for x hours. Interpret the y-intercept.
The meaning of the y-intercept is that Nora paid her plumber an initial fee of $50.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:
y = mx + c
Where:
x and y represents the data points.m represents the slope of a line.c represents the y-intercept of a line.What is y-intercept?In Mathematics, the y-intercept is sometimes referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
In this scenario, the y-intercept of this equation is 50 and it represents the initial fee being charged by the plumber.
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Jeffrey wants to make jam. He needs a combination of raspberries and blackberries totaling six pounds. Blueberries cost $1.00 per pound, and raspberries cost $2.00 per pound. If Jeffrey can afford $11.60, how many pounds of each berry should he buy?
The amount for each berry are 5.60 and 1.60 respectively.
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =
Given that, Jeffrey wants to make jam. He needs a combination of raspberries and blackberries totaling six pounds. Blueberries cost $1.00 per pound, and raspberries cost $2.00 per pound. If Jeffrey can afford $11.60,
We will set a system of linear equations, to solve this,
Establishing the equation,
Let the amount of raspberries be x and that of blueberries be y,
x + y = 6
y = 6-x...(i)
2x + y = 11.60
y = 11.60 - 2x...(ii)
Equating eq(i) and eq(ii)
6-x = 11.60 -2x
x = 5.60
Put x = 5.60 in eq(i)
y = 6-5.60
y = 1.60
Hence, the amount for each berry are 5.60 and 1.60 respectively.
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Jasmine gets paid $96 for 3 hours, how many dimes is she making an hour? How many nickels is she making an hour? how many quarters is she making an hour? how many pennies is she making an hour? use the problem.
[tex]x = [/tex]
Answer:
Step-by-step explanation:
I DON'T KNOW
suppose in mathlandia 11 peak dollars is equivalent to 22 sal dollars if a hamburger is 45 peak dollars what is the cost of the hamburger in sal dollars
The cost of the hamburger in sal dollars will be 90
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
Suppose in Mathlandia 11 peak dollars is equivalent to 22 sal dollars. Then the ratio of the sal dollar to the peak dollar will be constant. Then the ratio is given as,
Ratio = 22 / 11
Ratio = 2
If a hamburger is 45 peak dollars. Then the number of sal dollars is given as,
⇒ 2 x 45
⇒ 90
The cost of the hamburger in sal dollars will be 90
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Lucia opened a savings account and deposited $600.00 as principal. The account earns 13% interest, compounded annually. What is the balance after 5 years?
Use the formula A=P1+
r
n
nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
The amount of money in Lucia's account after 5 years will be $1,105.5.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Lucia opened a savings account and deposited $600.00 as principal. The account earns 13% interest, compounded annually. Then the amount of money after 5 years will be given as,
A = $600 × (1 + 0.13)⁵
A = $600 × (1.13)⁵
A = $600 × 1.84
A = $1,105.5
The amount of money in Lucia's account after 5 years will be $1,105.5.
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Solve 3x − 2 = 37. a 2 b 5 c 7 d 9
Answer: x = 13
Step-by-step explanation:
To solve, we will isolate the variable.
Given:
3x − 2 = 37
Add 2 to both sides equation:
3x = 39
Divide both sides of the equation by 3"
x = 13
Given ; WV is parallel to YZ, X is the midpoint of VY
Prove : Triangle VWX is congruent to Triangle YZX
Statement Given
1. X is the midpoint of VY 1. Given
2. WV ║ YZ 2. Given
3. VX = XY 3. X is midpoint
4. ∠WXY = ∠YXZ 4. Corresponding Angle Theorem
5. ∠WVX = ∠XYZ 5. Vertical Angle Theorem
6. △YXZ = △VWZ 6. AA Similarity
7. WV ≅ YZ 7. Prove
We know that WV ║ YZ, X is the midpoint of VY.
If X is the midpoint of VY. So VX = XY
The corresponding angles in the two regions of intersection are congruent when a line intersects two parallel lines.
From the Corresponding Angle Theorem
∠WXY = ∠YXZ
When two straight lines cross, the Vertical Angle Theorem states that they create two sets of linear pairings with congruent angles.
From the Vertical Angle Theorem
∠WVX = ∠XYZ
According to the AA similarity theorem, two triangles are similar if two of their triangles' triangles are congruent with two of their other triangles' angles.
By AA Similarity
△YXZ = △VWZ
Hence, WV ≅ YZ
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The complete question is given below:
Are true lines y= -1 and X =1 parallel, perpendicular, or neither? Explain
The lines, y = -1 and x = 1 are perpendicular lines.
What are Perpendicular Lines?If two lines are perpendicular to each other, it means they form right angle at the point of intersection, and also, they have slopes that are negative reciprocals to each other.
Also, vertical and horizontal lines are perpendicular to each other because horizontal line has a slope that is zero while vertical line has an undefined slope.
y = -1 is a horizontal line, while x = 1 is a vertical line. Therefore, we can concluded that, they are perpendicular to each other.
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Explain how you can model 3x2/4
You can model 3x2/4 as the mathematical expression that represents the division of the product of 3 and 2 by 4. The result of this expression is 3/2.
What is division of a product in mathematics?In mathematics, division is an arithmetic operation that is the inverse of multiplication. Given two numbers, the quotient is the number of times the second number "fits into" the first number.
The product is the result of multiplying two or more numbers together. Dividing a product is the process of finding out how many times one of the factors in the product can be taken to equal the product.
For example, if the product is 12 and the divisor is 3, then the quotient is 4, because 3 x 4 = 12
So, in the example 3x2/4, the product of 3 and 2 is 6 and we divide it by 4 to get the quotient of 3/2.
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based on the healthy people 2030 initiative, what is one change that should be made in school cafeterias? a. reducing the number of protein choices b. frying potatoes in saturated fats for shorter periods of time c. removing soda pop from the lunchroom d. adding candy to vending machines e. increasing the size of vegetable servings on lunch choices
The Healthy People 2030 initiative goals of reducing obesity and promoting a healthy lifestyle.
One change that should be made in school cafeterias is to reduce the number of protein choices. This can be done by decreasing the amount of red meat, poultry, and fish in the cafeteria by at least 50%. The number of vegetarian and vegan options should also be increased. This would reduce the amount of saturated fat and cholesterol that students are consuming and help them to make healthier food choices. It would also help to reduce the environmental impact of the cafeteria by reducing the amount of animal products being consumed. This change would help schools to meet the Healthy People 2030 initiative goals of reducing obesity and promoting a healthy lifestyle.
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Explain how rectangles are related to squares.
Enter rectangles or squares in the answer boxes. Words may be used more than once.
Answer:
Rectangles
Squares
A square is a special type of rectangle. All squares are rectangles, but not all rectangles are squares. In a square, all four sides are equal in length (congruent), making it a special case of a rectangle where all angles are right angles and all four sides have the same length. In contrast, a rectangle can have sides of different lengths.
How do I find the perpendicular line of y = -3x + 2. The perpendicular line passes through the point 6, 8 (please break down into steps)
Answer:
y = [tex]\frac{1}{3}[/tex]x + 6
Step-by-step explanation:
The equation we currently have right now is y = -3x+2. Since we know that the line equation is y = mx + b, let's take out m to find the slope of a perpendicular line. M will be -3.
To convert a regular slope to a perpendicular one, we have to:
- reciprocal/flip it (this means that if m = 3, the perpendicular will be [tex]\frac{1}{3}[/tex])
- swap the signs (this will mean that if a number is positive, then it will become negative)
Therefore, if m = -3, the perpendicular slope will be [tex]\frac{1}{3}[/tex] (we flipped and changed signs)
Now, we are also given that this line passes through the point (6,8), so we can use this formula: [tex]y - y1 = m(x-x1)[/tex]
What do we know right now?
- y1 = 8 (from (6,8))
- x1 = 6 (from (6,8))
- m = [tex]\frac{1}{3}[/tex]
Let's plug in what we know:
y - 8 = [tex]\frac{1}{3}[/tex](x - 6)
y = [tex]\frac{1}{3}[/tex](x-6) + 8
y = [tex]\frac{1}{3}[/tex]x - 2 + 8
y = [tex]\frac{1}{3}[/tex]x + 6
Bob has 3/5 as many stamps as Barry. If Barry has 120 stamps, how many more stamps does he have than Bob?
If Barry has 120 stamps and Bob has 3/5 as many stamps as Barry, you can set up the proportion:
3/5 = x/120
Where x is the number of stamps Bob has. To solve for x, you can cross-multiply:
3 * 120 = 5 * x
Simplifying:
360 = 5x
x = 72
So, Bob has 72 stamps. To find out how many more stamps Barry has than Bob, you can subtract the number of stamps Bob has from the number of stamps Barry has:
120 - 72 = 48
Barry has 48 more stamps than Bob.
Answer: 72
Multiply 120 by 3/5 to get Bob's amount of stamps.
Please only give answers
The y-intercept of the linear function 11x - 10y = 2 is given as follows:
y = -1/5.
How to obtain the y-intercept?The function for this problem is defined as follows:
11x - 10y = 2.
The y-intercept of a function is given by the value assumed by y when x assumes a value of 0.
Considering it's concept, the y-intercept of the function in this problem is obtained as follows:
-10y = 2
10y = -2
y = -2/10
y = -1/5.
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groups of 20 and more receive a 20% discount to the zoo. tickets range in price from $10.00 to $15.00 depending on your age. what is the range of the ticket prices after the discount is used
In a case whereby groups of 20 and more receive a 20% discount to the zoo. tickets range in price from $10.00 to $15.00 depending on your age. the range of the ticket prices after the discount is used is $8 to $12.
How can the Discounted ticket range be calculated?The concept that will be used is discount. Discount is the term used to describe a sum or a percentage subtracted from an item's usual selling price.
Since the ticket prices are been seen from the range from $10 to $15 so then we can say that the new range can have two figures reduced by 20%.
Then we can calculate the $10 after the discount as :
= [10 * (1 - 20%)]
= $8
Then we can calculate the $15 after the discount as :
=[ 15 * ( 1 - 20%)]
= $12
The we can calaculate the Discounted ticket range as
= $8 to $12
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complete question:
Groups of 20 or more receive a 20% discount at the LA Zoo. Tickets range from $10 to $15, depending on age. What is the range in ticket price after the 20% discount?