Answer: [tex]-i\sqrt{10}[/tex]
Step-by-step explanation:
Assuming that you need to simplify the expression, below is the explanation to do it.
Given the following expression:
[tex]-\frac{1}{3}\sqrt{-90}[/tex]
You need to decompose the radicand (The number inside the square root) into its prime factors:
[tex]90=2*3*3*5=2*3^2*5[/tex]
Knowing that, you can rewrite the expression in this form:
[tex]=-\frac{(1)(\sqrt{-2*3^2*5})}{3}=-\frac{\sqrt{-2*3^2*5}}{3}[/tex]
Since [tex]\sqrt{-1}=i[/tex], you must substitute it into the expression:
[tex]=-\frac{i\sqrt{2*3^2*5}}{3}[/tex]
Now you need to remember the following property:
[tex]\sqrt[n]{a^n}=a^{\frac{n}{n}}=a[/tex]
Then, applying that property, you get:i:
[tex]=-\frac{3i\sqrt{2*5}}{3}=-\frac{3i\sqrt{10}}{3}[/tex]
Finally, you must divide the numerator and the denominator by 3. So, you get:
[tex]=-\frac{i\sqrt{10}}{1}=-i\sqrt{10}[/tex]
if you add five to twice a number the results is fifteen. What is the number?
The number is 5.
Step-by-step explanation:
Let,
x represent the unknown number.
According to given statement;
add five to twice a number the results is fifteen
2x + 5 = 15
Subtracting 5 from both sides
[tex]2x+5-5=15-5\\2x=10[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{10}{2}\\x=5[/tex]
The number is 5.
Keywords: variable, addition
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What kind of number is the square root of 16
Answer:
4 is the square root of 16 :)
Step-by-step explanation:
Answer:
I think the answer you're looking for is four?
Amanda is choosing between two exercise routines.
In Routine #1, she does only running, 15.5 burning calories per minute.
In Routine #2, she burns 22 calories walking. She then runs at a rate that burns 12.75 calories per minute.
For what amounts of time spent running will Routine #1 burn more calories than Routine #2?
Use t for the number of minutes spent running, and solve your inequality for .
Answer:
1 hour and 30 maybe my math might be wrong
Step-by-step explanation:
I need help please and thank you
We have two lines intersected by a transversal. There is a relationship between <6 and <2. They are corresponding angles and are congruent. So if the m<6 = 75° then the m<2 = 75°.
answer: m<2 = 75°
Laura answered 27 questions correct on a test on her test and scored 90%. How many questions where on the test?
The number of questions in the test is 30
Step-by-step explanation:
Let's call the total number of questions in the test N.
We know that Laura answered 27 questions, and these 27 questions represent the 90% of the test.
Therefore, we can say that 27 is the 90% of N.
Re-writing the percentage as a fraction,
[tex]90\% = 0.90[/tex]
This means that:
[tex]0.90 N = 27[/tex]
And now we can solve for N to find the number of questions in the test:
[tex]N=\frac{27}{0.90}=30[/tex]
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Please answerrrrrrrrrrrrrr
Answer:
1. Using the Pythagorean theorem.
2. Using the ratio 1 : 1 : √2.
Step-by-step explanation:
There are two options to find the value of x:
1. Using the Pythagorean theorem:
Hypotenuse = 5√2 inches and legs are equal in a 90 - 45 - 45 triangle like this.
Hypotenuse² = Leg² + Leg²
(5√2)² = 2Leg²
50 = 2Leg²
50/2 = Leg²
Leg² = 25
√Leg² = √25
Leg = 5 inches ⇒ x = 5
2. Using the ratio 1 : 1 : √2, this way:
1 : 1 : √2
x : x : 5√2
x = 5√2/√2
x = 5 and let's recall that in a 90 - 45 - 45 triangle legs are equal, therefore. ratio is:
5 : 5 : 5√2
Ibuki factored 12 xZ as (4x) (3x4)
Melodie factored 12x7 as (2x (6x)
Who factored correctly?
Neither Ibuki nor Melodie factored 12x² correctly based on the expressions given. However, if Melodie's (2x)(6x) was meant for 12x², then her factorization would be correct.
Explanation:The students are attempting to factor the expression 12x². Factoring is the process of finding two or more expressions that multiply together to get the original expression. Ibuki's factorization of 12x² as (4x)(3x⁴) contains an error since 3x⁴ would imply raising x to the fourth power, which is not present in the original expression. Melodie's factorization of 12x² as (2x)(6x) is also incorrect since when you multiply 2x and 6x, you get 12x², not 12x⁷ as her expression suggests. The correct factorization of 12x² is (2x)(6x) since 2x multiplied by 6x equals 12x².
In summary, neither student has factored the expression correctly. However, if we take Melodie's answer as a typo and she meant (2x)(6x) for 12x², then her factored form would be correct.
the drama club at school sells $15.00
coupon books. Their profit is 35% of the
total sales. What is their profit on each
book?
The profit on each book is $ 5.25
Solution:
Given that, the drama club at school sells $ 15.00 coupon books
Their profit is 35% of the total sales
Therefore,
Cost of a coupon book = $ 15
Profit = 35% of the total sales
We have to find the profit on each book
If a book is sold for $ 15 and then profit will be 35 % of 15
Let us find 35 % of 15
[tex]Profit\ on\ each\ book = 35 \% \times 15\\\\Profit\ on\ each\ book = \frac{35}{100} \times 15\\\\Profit\ on\ each\ book = 0.35 \times 15\\\\Profit\ on\ each\ book = 5.25[/tex]
Thus profit on each book is $ 5.25
Add and simplify 7/8+1/6
Answer:
Step-by-step explanation:
Find the number z, if 1 4/11 of z is 45. (FIRST PERSON TO ANSWER CORRECTLY GETS 5 STARS AND A THANKS.)
The value of z in the equation [tex]1\frac{4}{11}[/tex] of z is 45 is 33.
Solution:
Given: [tex]1\frac{4}{11}[/tex] of z = 45
To find: The value of z
On solving the given equation,
[tex]1\frac{4}{11}\times z=45[/tex]
[tex]\Rightarrow\frac{1\times11+4}{11}\times z=45[/tex]
[tex]\Rightarrow\frac{15}{11}z=45[/tex]
On grouping the like terms in one side we get,
[tex]\Rightarrow z=45\times\frac{11}{15}[/tex]
On solving the values we get,
[tex]\Rightarrow z=3\times11\rightarrow33[/tex]
The required value of z is 33.
Steps to convert a mixed fraction into an improper fraction:
Step 1: Multiply the whole number part by the fraction's denominator.
Step 2: Add that to the numerator.
Step 3: Then write the result on top of the denominator.
The sales tax in your city is 4.4% and a item costs 3$ before tax. How much tax would you pay
Answer:
0.13 tax
Step-by-step explanation:
0.044*3=0.132
What should i do now please help me
Answer:
x=24
Step-by-step explanation:
Here, you need to make proportion and find x.
12:16=18:x
We multiply 12 by x and 16 by 18:
12x=288
Divide by 12 both sides :
x=24
What is the next number in the
pattern -3, 6, -9, 12,
Answer:
-15
Step-by-step explanation:
The pattern is adding 3 and adding a negative sign
Last night, 4 friends went out to dinner at a restaurant. They split the bill evenly. Each friend paid $12.75 for his or her meal and each left the same amount for a tip, t. The total dinner bill including the tip was $61. What equation could you use to describe the situation?
Final answer:
To create the equation representing the situation, calculate the total meal cost by multiplying each friend's share by four and then add four times the tip to equal the final bill of $61. The equation is 4 times $12.75 + 4 imes t = $61.
Explanation:
To solve the problem using an equation, we need to consider the cost of each meal and the tip each friend left. Four friends each paid $12.75 for their meal, which gives us the cost of the meals alone: 4 times $12.75 = $51. The tip, t, needs to be added four times (once for each friend) to the total cost of the meals to reach the final bill of $61.
Therefore, the equation to represent the situation would be: 4 times $12.75 + 4 times t = $61.
Once we have the equation, we can solve for the tip, t, to find out how much each friend left for the tip.
Express 40 as a percentage of 200
Answer:
20 %.
Step-by-step explanation:
(40/200) * 100
= (2/ 10) * 100
= 2 * 10
= 20.
Final answer:
To express 40 as a percentage of 200, you set up a proportion and solve for x, finding that 40 is 20% of 200.
Explanation:
To express 40 as a percentage of 200, we can set up a proportion where 40 is to 200 as x is to 100 (since percentages are out of 100). This gives us the proportion 40/200 = x/100. Solving for x, we multiply both sides by 100 to isolate x on one side of the equation. This gives us x = (40 × 100) / 200.
Next, we perform the multiplication and division: x = 4000 / 200. Simplifying that, we get x = 20. Therefore, 40 is 20% of 200.
To illustrate the importance of outliers, suppose you do not count the owner in the last problem. The data for the other
workers is:
$ US
5 people earn $25,000, 3 earn $27,000, and 1 earns $34,000
What is the mean salary and standard deviation (to the nearest dollar) of the workers?
Answer:
The mean is 26666.67 and the standard deviation is 372919430.33.Step-by-step explanation:
The mean means the average of the numbers.
The mean will be [tex]\frac{25000\times5 + 27000\times3 + 34000}{5 + 3 + 1} = \frac{240000}{9} = 26666.666666666[/tex].
The differences of the earnings from the mean are 1666.67, 26997.33, 33997.33.
Squaring the numbers we get, 2777788.89, 728855827.13, 1155818447.12.
We need to find the mean of the above numbers to get the standard deviation.
Thus, the standard deviation is [tex]\frac{2777788.89\times5 + 728855827.13\times3 + 1155818447.12}{9} = 372919430.33[/tex].
please show the steps for the given picture
Answer:
8000
Step-by-step explanation:
So n equals 0.00 and then in the parentheses 1.1 you would multiply those two numbers X 1300. and then you would ×that answer by 8000 and you get 8000 .
What is the simplest form of this expression?
-X(4x² - 6x+1)
0
0
A. 4x² - 6x² - x
B. 4x3 + 6x2 - x
OC. 4x² - 6x+1
0
D. -4x3 + 5x
Answer:
Step-by-step explanation:
-x (4x^2 - 6x + 1).....distribute the -x through the parenthesis
- 4x^3 + 6x^2 - x <===
Answer:
b
Step-by-step explanation:
144 is what percent of 260
2 and 1/3 plus 1 and 5/9
Answer:
35/9
Step-by-step explanation:
2 1/3=7/3
1 5/9=14/9
------------------
7/3+14/9=21/9+14/9=35/9
Answer: 2 1/3 + 1 5/9 = 3 8/9
Step-by-step explanation: You make the fractions the same so 3/9 is equal to 1/3 so you multiply both numbers in fraction #1 (1/3) by 3 & just add, not the denominators though
how many diagonals does the regular polygon have
Answer:3
Step-by-step explanation:
I need to know the answer
x2-3xy-5xy-7y2+4x2+8y2
For this case we must simplify the following expression:
[tex]x ^ 2-3xy-5xy-7y ^ 2 + 4x ^ 2 + 8y ^ 2[/tex]
We must add similar terms taking into account that:
Equal signs are added and the same sign is placed.Different signs are subtracted and the major sign is placed.[tex](x ^ 2 + 4x ^ 2) + (- 3xy-5xy) + (- 7y ^ 2 + 8y ^ 2) =\\5x ^ 2-8xy + y ^ 2[/tex]
Thus, the simplified expression is:
[tex]5x ^ 2-8xy + y ^ 2[/tex]
Answer:
[tex]5x ^ 2-8xy + y ^ 2[/tex]
How do you use substitution with the system of equations x+2y=14 and y=3x-14
Answer:
see attached picture.
10x - 9y + 5x - 4y - 5x + 4x
Answer:
14x-13y
Step-by-step explanation:
explain how to find the area of the triangle when x = 3 inches. then find the area
To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles.
Step-by-step explanation: To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles.
Use the Pythagorean theorem to find the unknown side of the right triangle.
15
36
A right triangle has a vertical side of length 15, a horizontal side of length 36, and an unlabeled hypotenuse.
Hypotenuse lengthequals=3 StartRoot 169 EndRoot3169
(Simplify your answer. Type exact answers, using radicals as needed.)
The length of hypotenuse is 39.
Step-by-step explanation:
Given,
Vertical side = a = 15
Horizontal side = b = 36
Hypotenuse = c
Using pythagorean theorem
[tex]a^2+b^2=c^2\\(15)^2+(36)^2=c^2\\225+1296=c^2\\1521=c^2\\c^2=1521[/tex]
Taking square root on both sides
[tex]\sqrt{c^2}=\sqrt{1521}\\c=39[/tex]
The length of hypotenuse is 39.
Keywords: square root, addition
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AE = EC and BF = FC. EF = 8 and DF = 10. AB = [?]
Answer:
Therefore AB is 16 units.
Step-by-step explanation:
Given:
AE = EC
BF = FC
EF = 8 and DF = 10
To Find:
AB = ?
Solution:
Mid Point Theorem:
The Midpoint Theorem states that "the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side".
AE = EC .....Given
Therefore E is the Mid Point of AC.
BF = FC .....Given
Therefore F is the Mid Point of BC.
Therefore,
EF || AB ........................Mid Point Theorem.
[tex]EF=\dfrac{1}{2}AB[/tex] ..............Mid Point Theorem.
Substituting the values we get
[tex]8=\dfrac{1}{2}AB\\\\AB=8\times 2=16\ units[/tex]
Therefore AB is 16 units.
Answer:
16
Step-by-step explanation:
To indicate that one's purpose for writing is to inform, an author would include clues such as
Answer:
Facts
Step-by-step explanation:
How do you solve this step by step?
Answer:
x = 41
Step-by-step explanation:
To solve this problem, we want to find the value of 'x' by isolating it (separating 'x' from all other numbers).
First, simplify the expression by using the distributive property, where you multiply the number outside the brackets with each term inside the brackets.
Then isolate 'x' by doing reverse operations (on both sides) for every number that is on the same side as 'x'. Reverse operations are opposites (addition and subtraction, multiplication and division) and "cancel out" a number, which "moves" it to the other side.
7(x - 5) = 252 Use the distributive property
7x - 35 = 252 Result of 7 times x and 7 times -5
7x - 35 + 35 = 252 + 35 Add 35 to both sides
7x = 252 + 35 -35+35 on the left side cancelled out. Simplify right side
7x = 287 Continue to isolate 'x'
7x/7 = 287/7 Divide both sides by 7
x = 287/7 Left side cancelled out to be 'x'. Simplify the right side
x = 41 Answer
Check your answer:
Substitute 'x' for 41 in the original equation. Then, make sure that the equation is still balanced. Keep in mind BEDMAS order (brackets, exponents, division, multiplication, addition, subtraction).
7(x - 5) = 252
7(41 - 5) = 252 Simplify inside the brackets first
7(36) = 252 Multiply
252 = 252 Same answer
LS = RS
Since left side (LS) equals (=) right side (RS), the equation is still balanced and we got the correct value for 'x'.