Answer:
2i
Step-by-step explanation:
The square root of -4 is equal to 2i.
The square root of -4 can be simplified using the imaginary number i. Since the square root of a negative number is not defined in the set of real numbers, we use i to express it, where i is defined as the square root of -1. Thus, the square root of -4 is calculated as follows:
√-4 = √(-1*4)
= √(-1) * √(4)
= i * 2
= 2i
This result shows that 2i is the simplified form of the square root of -4 using the imaginary number i.
At a certain time of the day, a tree that is x meters tall casts a shadow that is x-49 meters long. If the distance from the top of the tree to the end of the shadow is x+1 meters, what is the height , x of the tree ?
The height of the tree is 60 meters.
Explanation:
Let the height of the tree be x. The tree casts a shadow of [tex]x-49[/tex] meters and the distance from the top of the tree to the end of the shadow is [tex]x+1[/tex] meters.
The sides of the triangle are attached in the image below:
Using pythagoras theorem,
[tex]x^{2}+(x-49)^{2}=(x+1)^{2}[/tex]
Expanding, we get,
[tex]2 x^{2}-98 x+2401=x^{2}+2 x+1[/tex]
[tex]2 x^{2}-98 x+2400=x^{2}+2 x[/tex]
[tex]2 x^{2}-100 x+2400=x^{2}[/tex]
[tex]x^{2}-100 x+2400=0[/tex]
Solving the equation using the quadratic formula [tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex], we get,
[tex]x=\frac{-(-100)\pm\sqrt{(-100)^{2}-4 \cdot 1 \cdot 2400}}{2 \cdot 1}[/tex]
Simplifying, we have,
[tex]x=\frac{100\pm\sqrt{10000-9600}}{2}[/tex]
[tex]x=\frac{100\pm\sqrt{400}}{2}[/tex]
[tex]x=\frac{100\pm{20}}{2}[/tex]
Thus,
[tex]x=\frac{100+20}{2} \\x=\frac{120}{2} \\x=60[/tex] and [tex]x=\frac{100-20}{2} \\x=\frac{80}{2} \\x=40[/tex]
where the value [tex]x=40[/tex] is not possible because substituting the value [tex]x=40[/tex] in [tex]x-49[/tex] results in negative solution. Which is not possible.
Hence, the value of x is 60.
Thus, The height of the tree is 60 meters.
If the area of a square is 121cm2 what is it’s side length
Answer:
Step-by-step explanation:
Area of a square
Area = l*l
121=l^2
l=√121
L=11cm
What is the problem answer for 25% of 450
Answer:
112.5
Step-by-step explanation:
25/100 x450/1 =
11250/100=112.5
here u go these are the notes
A cellphone company charges $60 for a cellphone and a monthly rate to use the phone.Regina will pay $1,140 for a 24-month cellphone plan.What is the monthly rate,m,for this cellphone plan?
The monthly rate is $45 for this cellphone plan.
Step-by-step explanation:
Given,
Amount charged for cell phone = $60
Amount paid by Regina for 24 month plan = $1140
Number of months = 24
Let,
m be the monthly rate for cellphone plan
Number of months * Monthly rate + cellphone charges = Amount paid
[tex]24m+60=1140\\24m=1140-60\\24m=1080[/tex]
Dividing both sides by 24
[tex]\frac{24m}{24}=\frac{1080}{24}\\m=45[/tex]
The monthly rate is $45 for this cellphone plan.
Keywords: subtraction, division
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Susy had 2/3 as much money as Mary at first. After receiving 1/2 of Mary's money, Susy had $210. How much money did Susy have at first?
Answer:
$120
Step-by-step explanation:
2/3 of Mary's money + 1/2 of Mary's money is equal to 7/6 of Mary's money
7/6 of Mary's money = $210
Mary's money = m
210 = 7/6*x
180 = x
Mary's money = $180
Suzy's original money = 2/3 of 180
2/3 * 180 = 120
Decompose -6x/(x-6)(x+3)
into partial fractions.
Answer:
B
Step-by-step explanation:
Answer: B
Step-by-step explanation:
There are 19 animals , total of legs are 54 and the animals are pigs and ducks. How many pigs and ducks are there?
Final answer:
Using a system of equations, we established that there are 8 pigs and 11 ducks among the 19 animals with a total of 54 legs.
Explanation:
To solve the problem of determining how many pigs and ducks there are when there are 19 animals in total and 54 legs, we set up two equations. Let's assume the number of pigs is x and the number of ducks is y. Pigs have 4 legs, and ducks have 2 legs. We can summarize this information in the following system of equations:
Equation 1: x + y = 19 (because there are 19 animals total)
Equation 2: 4x + 2y = 54 (because the total number of legs is 54)
We can solve this system using the substitution or elimination method. Simplifying Equation 2 by dividing every term by 2 gives us 2x + y = 27, which we'll call Equation 3.
Equation 3: 2x + y = 27
We can now subtract Equation 1 from Equation 3 to find the value of x:
(2x + y) - (x + y) = 27 - 19
(2x - x) + (y - y) = 8
x = 8 (number of pigs)
Substitute x back into Equation 1:
x + y = 19
8 + y = 19
y = 19 - 8
y = 11 (number of ducks)
Therefore, there are 8 pigs and 11 ducks among the 19 animals.
If Talia’s old bedroom measured 1 feet by 10 feet how much larger or smaller will her new bedroom be ?
Expression: [tex]\((x - 3)(x + 5)\)[/tex]. If original is 10 × 10, new is 105 sq ft. New is 5 sq ft larger.
1. **Expression representing the two binomials for the area of Talia's new bedroom:**
Let [tex]\( x \)[/tex] represent the original length of the square bedroom.
The original bedroom's dimensions: [tex]\( x \times x \)[/tex]
The new bedroom's dimensions: [tex]\( (x - 3) \times (x + 5) \)[/tex]
So, the expression representing the two binomials would be: [tex]\((x - 3)(x + 5)\)[/tex]
2. **Finding the difference in size between old and new bedrooms:**
If the original bedroom measured 10 feet by 10 feet, then [tex]\( x = 10 \)[/tex] (since it's a square).
Substituting into the expression: [tex]\( (10 - 3)(10 + 5) = (7)(15) = 105 \)[/tex] square feet.
So, the new bedroom's area is 105 square feet.
The original bedroom's area is [tex]\( 10 \times 10 = 100 \)[/tex] square feet.
The difference is: [tex]\( 105 - 100 = 5 \)[/tex] square feet.
Therefore, her new bedroom will be 5 square feet larger than her old bedroom.
The complete question is here:
Talia has a square bedroom. Her family is moving and her bedroom in her new apartment will be 3 feet shorter in one direction and 5 feet longer in the other direction. Write an expression that represents the two binomials you would multiply together to find the area of Talia's new bedroom.
2nd Part
If Talia's old bedroom measured 10 feet by 10 feet, how much larger or smaller will her new bedroom be?
3/8 of the seventh grade students were taking advanced math at the beginning of the year, but seven dropped out by the end of the year. If there were 140 students taking advanced math at the end of the year, how many seventh grade students are there?
Answer:
392 students
Step-by-step explanation:
Given: 3/8 of the seventh grade students were taking advanced math at the beginning of the year.
Seven dropped out by the end of the year.
There are 140 students taking advanced math at the end of the year.
Lets assume total number of students of seventh grade be "x".
As given, 3/8 of the seventh grade students were taking advanced math at the beginning of the year.
∴ Number of student took advanced maths at the beginning= [tex]\frac{3}{8} \times x= \frac{3x}{8}[/tex]
We know, 7 student dropped out of advanced math by the end of the year.
Now, forming an equation to determine number of students taking advanced math at the end of the year.
⇒ [tex]\frac{3x}{8} -7= 140[/tex]
Solving the equation to find number of student in seventh grade.
⇒ [tex]\frac{3x}{8} -7= 140[/tex]
Adding both side by 7
⇒ [tex]\frac{3x}{8} = 140+7[/tex]
Multiplying both side by 8
⇒[tex]3x= 147\times 8[/tex]
Dividing both side by 3
⇒[tex]x= \frac{147\times 8}{3}[/tex]
∴ [tex]x= 392[/tex]
Hence, there are 392 students in seventh grade.
Arrange the following measurement in order from smallest to largest. 2000 milititers 4.1 liters 0.7 liters
answer is
o.7 liters 2000 milliliters and 4.1 liters
Step-by-step explanation:
1 / 5
1 \text{ liter} ={1{,}000}\text{ milliliters}1 liter=1,000 milliliters1, start text, space, l, i, t, e, r, end text, equals, 1, comma, 000, start text, space, m, i, l, l, i, l, i, t, e, r, s, end text
So, 1 \text{ milliliter} = \dfrac1{1{,}000}\text{ liter}1 milliliter=
1,000
1
liter1, start text, space, m, i, l, l, i, l, i, t, e, r, end text, equals, start fraction, 1, divided by, 1, comma, 000, end fraction, start text, space, l, i, t, e, r, end text
Hint #22 / 5
We know \maroonD{0.7}0.7start color #ca337c, 0, point, 7, end color #ca337c liters is less than \greenD{4.1}4.1start color #1fab54, 4, point, 1, end color #1fab54 liters. But where does \blueD{2{,}000}2,000start color #11accd, 2, comma, 000, end color #11accd milliliters fit?
We need to convert \blueD{2{,}000}2,000start color #11accd, 2, comma, 000, end color #11accd milliliters to liters before we can compare.
Hint #33 / 5
\begin {aligned}{\blueD{2{,}000} \text{ mL}}&= {\blueD{2{,}000} \text{ mL}}\times \dfrac{1 \text{ L}}{{1{,}000 \text{ mL}}} \\\\ &= {\dfrac{\blueD{2{,}000} \cancel{\text{ mL}}}{1}}\times \dfrac{1 \text{ L}}{{1{,}000 \cancel{\text{ mL}}}} \\\\ &=\dfrac{\blueD{2{,}000}\text{ L} }{1{,}000}\\\\ &=\blueD{2{,}000}\text{ L}\div1{,}000\\\\ &=\blueD{2}\text{ L} \end{aligned}
2,000 mL
=2,000 mL×
1,000 mL
1 L
=
1
2,000
mL
×
1,000
mL
1 L
=
1,000
2,000 L
=2,000 L÷1,000
=2 L
Ignore the stuff around it ,could someone explain me this?
Answer:
The lines blue and green are perpendicular
Step-by-step explanation:
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
step 1
Find the slope of the blue line
we have the points
(-1,-3) and (0,3)
substitute
[tex]m=\frac{3+3}{0+1}[/tex]
[tex]m=\frac{6}{1}=6[/tex]
step 2
Find the slope of the red line
we have the points
(3,-3) and (4,2)
substitute
[tex]m=\frac{2+3}{4-3}[/tex]
[tex]m=\frac{5}{1}=5[/tex]
step 3
Find the slope of the green line
we have the points
(-4,-1) and (2,-2)
substitute
[tex]m=\frac{-2+1}{2+4}[/tex]
[tex]m=-\frac{1}{6}[/tex]
step 4
Compare the slopes
Blue line ----> [tex]m=6[/tex]
Red line ----. [tex]m=5[/tex]
Green line ---> [tex]m=-\frac{1}{6}[/tex]
so
The slope of the blue line and the green line are opposite reciprocal ( their product is equal to -1)
therefore
The lines blue and green are perpendicular
You throw two darts at a dartboard.
Let event A = The first dart hits the center.
Let event B = The second dart hits the center
What does P(BA) represent?
O
A. The probability that either the first dart or the second dart hits the
center
O
B. The probability that the second dart hits the center given that the
first dart hits the center
C. The probability that the second dart doesn't hit the center
D. The probability that the first dart hits the center given that the
second dart hits the center
Answer:
B. The probability that the second dart hits the center given that the
first dart hits the center
Step-by-step explanation:
P(BA) is also called the "Conditional Probability" of B given A.
B. The probability that the second dart hits the center given that the first dart hits the center
The following information should be considered;
Here we assume event A be the first dart hits the center.And, event B be the second dart hits the center.Now P(BA) should represent that the second dart should hit the center.Also, P(BA) is known as the "Conditional Probability" of B given A.Learn more: https://brainly.com/question/6789603?referrer=searchResults
Which length is longer 64 inches or 5 feet
what type of triangle is this?
Mikhail saved $1 of his paycheck the first week. He saved $2 the second week. He saved $4 the third week. He saved $8 the fourth week. If this pattern continues, how much will he save the sixth week
Answer:32
Step-by-step explanation:
The pattern seems to double each time there is a new week. By the fourth week he saved $8, and it asks how much he saved by the sixth week. We know $8 x 2 = 16 and 16 x 2 = 32, SO, by the sixth week Mikhail saved $32!
Are all squares proportional?
Answer:
Yes each side will always be of the same size unless you are purposely trying to make an uneven shape
Step-by-step explanation:
Polynomial functions with an even degree have y-axis symmetry
Polynomial functions with an even degree have y-axis symmetry is a true statement.
Explanation:
A function symmetrical with respect to the y-axis is called an even function. A function that is symmetrical with respect to the origin is called an odd function. f(x). Since f(−x) = f(x), this function is symmetrical with respect to the y-axis.
So a function that has an even degree in it, be it a polynomial function, has a y-axis symmetry always. The equations with odd degrees may or may not have a y axis symmetry.
Which of the following is not a perfect square (a) 2025 (b) 3210 (c) 4900 (d) 7744
Answer:
the right answer is b
Step-by-step explanation:
since its square root does not result in an integer
how can you describe pi?
Step-by-step explanation:
The number π is a mathematical constant. Originally defined as the ratio of a circle's circumference to its diameter.
It is an irrational number
[tex]\pi = 3.14159265359...[/tex]
A certain number was multiplied by 7.4 was then taken away from the product. Finally that difference was then divided by 9, resulting in 5. Find the initial number.
The initial number is 7.
Step-by-step explanation:
Let the initial number be 'x'.
The number was multiplied by 7 ⇒ 7x4 was then taken away from the product ⇒ 7x-4That difference was then divided by 9 resulting in 5 ⇒ (7x-4)/9 = 5⇒ 7x-4 = 45
⇒ 7x = 49
⇒ x = 7
The initial number is 300. Multiply by 7.4 to get 2220, subtract 2220, then divide by 9 to get 247. Confirming: 7.4(300) - 2220 = 247(9) = 5.
Let's denote the initial number as ( x ). According to the given information:
1. Multiply by 7.4: ( 7.4x )
2. Take away from the product: ( 7.4x - (7.4x) )
3. Finally, divide by 9:[tex]\( \frac{{7.4x - 7.4x}}{9} \)[/tex]
We know that this resulting expression equals 5:
[tex]\[ \frac{{7.4x - 7.4x}}{9} = 5 \][/tex]
Now, let's solve for ( x ):
[tex]\[ \frac{{0}}{9} = 5 \][/tex]
As ( 7.4x ) cancels out, we are left with ( 0 = 5 ), which is not a valid equation.
On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 118 and a standard deviation of 18. Suppose one individual is randomly chosen. Let X = IQ of an individual.
b. Find the probability that a randomly selected person's IQ is over 115.
Answer:
0.5675
Step-by-step explanation:
We have that, the IQ of the ruling species is normally distributed with a mean of 118 and a standard deviation of 18.
We want to find the probability that a randomly selected person's IQ is over 115.
We need to find the z-score of 115
using
[tex]z = \frac{x - \mu}{ \sigma} [/tex]
We substitute x=115 to get:
[tex]z = \frac{115 - 118}{18} [/tex]
This implies that:
[tex]z = \frac{ - 3}{18} = - \frac{1}{6} = - 0.17[/tex]
We read from the normal distribution table to get;
P(X>115)=0.5675
By converting the IQ score of 115 into a Z score and finding the area to the right of this Z score in a standard normal distribution, we find that the probability of a randomly selected individual's IQ being over 115 is approximately 0.57 or 57%.
Explanation:To answer this question, we need to understand how a normal distribution works. A random variable X, such as an individual's IQ, that is normally distributed can be converted into a standard normal variable Z, using the formula Z = (X - mean) / standard deviation.
In our case, the mean IQ is 118 and the standard deviation is 18. Therefore, to find the probability that a randomly selected individual's IQ is over 115, we convert 115 into a Z score using the aforementioned formula: Z = (115 - 118) / 18 = -0.167. This is the Z score for an IQ of 115.
To find the probability that a randomly selected individual's IQ is more than 115, we find the area to the right of Z = -0.167. From standard normal tables, we know that the area to the left of Z = -0.167 is approximately 0.4332. Therefore, the area to the right (which is the probability we want) is 1 - 0.4332 = 0.5668.
So, the probability that a randomly selected individual's IQ is over 115 is approximately 0.57 (or 57% when expressed as a percentage).
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Marlie will be starting college next month. She was approved for a 10-year, Federal Unsubsidized student
loan in the amount of $18,800 at 4.29%. She knows she has the option of beginning repayment of the loan
in 4.5 years. She also knows that during this non-payment time, interest will accrue at 4.29%.
How much interest will Marlie accrue during the 4.5-year non-payment period?
Marlie's federal unsubsidized student loan will accrue $3,627.34 in interest over a 4.5-year non-payment period, given a 4.29% annual interest rate.
Explanation:The subject of this problem is calculating interest accrued on an unsubsidized student loan. First, we need to understand that the 4.29% interest is an annual rate. So, for 4.5 years, the rate would become: 4.29% * 4.5 = 19.305%.
To calculate the amount of interest that will accrue during this period, we simply multiply this by the principal loan amount ($18,800). So, $18,800 * 19.305% = $3,627.34. Therefore, Marlie will accrue $3,627.34 in interest over this 4.5-year period.
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Marlie, who took a Federal Unsubsidized student loan that accumulates interest over time, will accrue $3,628.83 in interest during her 4.5 years of non-payment.
Explanation:The subject of this question is about interest calculation on a Federal Unsubsidized student loan. Interest on an unsubsidized loan like Marlie's accumulates from the time the loan is disbursed until it's paid in full, including during the non-payment period. The interest that will accrue can be calculated using the formula I = PRT, where 'I' is the interest, 'P' is the principal amount (the initial amount of loan), 'R' is the annual interest rate in decimal, and 'T' is the time the money is borrowed for in years.
In Marlie's case, P = $18,800, R = 4.29/100 = 0.0429, and T = 4.5. Therefore, the interest accrued will be I = 18800 * 0.0429 * 4.5. After performing the calculation, the total interest that Marlie will accrue over the non-payment period is $3,628.83.
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The next model a sports car will cost 4.9% less than the current model the current model cost for the $2000 how much will the price decrease in dollars what will be the price of the next model
Answer:
$98.00
Step-by-step explanation:
$2000.00 x .049=$98.00
Evaluate the function for x=-2
Y=2(4)x
Answer:
= -16
Step-by-step explanation:
If x= -2, then replace it on Y=2(4)X
Y=2x(4)x(-2)
Y=-16
Note:
2 multiplied by 4 = 8
8 multiplied by -2 = -16
Answer:
Step-by-step explanation:
y= 2(4)(-2)
y = 8(-2)
y =-16
if 150 microliters of a solution and serum contains 90 microliters of saline what is the dilution ratio of a solution
Final answer:
The dilution ratio of a solution when 150 microliters of it contains 90 microliters of saline is 3:5. This means there are 3 parts saline to every 5 parts of the total solution.
Explanation:
If 150 microliters of a solution contains 90 microliters of saline, the dilution ratio of the solution can be described as the volume of saline to the total volume of the solution. To find this ratio, divide the volume of saline by the total solution volume:
Ratio = Volume of Saline / Total Volume of Solution
Ratio = 90 µL / 150 µL
By dividing the two volumes, you get a ratio of 0.6, which can also be expressed as 3:5 after multiplying both numerator and denominator by 10 to eliminate the decimal. This means there are 3 parts of saline to every 5 parts of the total solution.
The dilution ratio is therefore 3:5.
The human appendix has no known function
Which term applied to structures like this?
O adaxial
O homologous
O obligatory
O vestigial
Answer:
Vestigial.
Step-by-step explanation:
It might have had a use in the past and man's evolution has rendered it of no known use.
Substitution and to solve
Answer:
x=1 y=2, there are your answers. Have a good dayStep-by-step explanation:
y=−3x+5;5x−4y=−3
Step: Solve: y=−3x+5for y:
Step: Substitute: −3x+5foryin5x−4y=−3:
5x−4y=−3
5x−4(−3x+5)=−3
17x−20=−3 (you have to simplify both sides of the equation)
17x−20+20=−3+20(then add 20 to both sides)
17x=17
17x
17
=
17
17
(Divide both sides by 17)
x=1
Step: Substitute1forxiny=−3x+5:
y=−3x+5
y=(−3)(1)+5
y=2( again Simplify both sides of the equation)
The Answer Is:
x=1 and y=2
Am I incorrect?
Mia's workout routine is to swim for 100 minutes 3 times a week, jump rope for 1 minute 7 days a week, and run for 10
minutes 2 times a week. What is the total time that Mia's workout routine takes each week?
Which of the following are examples of rational numbers? Select all that apply
Answer:
1.5,
Step-by-step explanation:
The examples of rational numbers are: a, d, and e.
A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.
Let's evaluate each option:
a. [tex]\( \sqrt{4} + \sqrt{16} = 2 + 4 = 6 \)[/tex]
This is a rational number because it can be expressed as the integer 6.
b. [tex]\( \sqrt{5} + \sqrt{36} = \sqrt{5} + 6 \)[/tex]
This is not a rational number because it involves the irrational square root of 5.
c. [tex]\( \sqrt{9} + \sqrt{24} = 3 + 2\sqrt{6} \)[/tex]
This is not a rational number because it involves the irrational square root of 6.
d. [tex]\( 2 + \sqrt{4} = 2 + 2 = 4 \)[/tex]
This is a rational number because it can be expressed as the integer 4.
e. [tex]\( \sqrt{49} + \sqrt{81} = 7 + 9 = 16 \)[/tex]
This is a rational number because it can be expressed as the integer 16.
f. [tex]\( 3\sqrt{12} = 3 \times \sqrt{4 \times 3} = 3 \times 2\sqrt{3} = 6\sqrt{3} \)[/tex]
This is not a rational number because it involves the irrational square root of 3.
So, the examples of rational numbers are: a, d, and e.
The complete Question is given below:
Which of the following are examples of rational numbers? Select all that apply
a. √4+√16
b. √5+√36
c. √9+√24
d. 2+√4
e. √49+√81
f. 3√12