Answer:
The sum is 4 i√2
Step-by-step explanation:
Both the numbers √-2 and √-18 are imaginary number and thus can be presented as
i√2 and i√18
On simplifying, the i√18 can be written as i√( 9 x 2)
Taking out square root of 9 we get-
3i√2
Thus the summation of i√2 and i√18 can be written as
i√2 + 3i√2
= 4 i√2
Answer:
The correct answer is (4 √2) i
Step-by-step explanation:
The sum we are looking is "x"
x= √-2+ √-18
By the Radical Properties of Multiplication ,
x=√-2 +√(-2*9)
x=√-2 +√-2* √9
Considering √-2= √((-1)*2)= √-1 *√2
According to the propriety of complex numbers , we can say
i=√-1
Replacing
x= i √2 + 3 i√2
The answer is x= (4 √2) i
What is the solution to the system of equations? X+3y=18 x+2y=14
Answer:
Solution to system is
x = 6 and y= 4
S.set={6,4}
Step-by-step explanation:
The given equations are
x + 3y = 18 ................(i)
x + 2y=14 .................(ii)
Subtracting both equation
(x+3y)-(x+2y)=18-14
x+3y-x-2y = 4
y = 4
put the value of y in equation (i)
the equation becomes
x + 3(4) = 18
x + 12 = 18
subtracting 12 from both sides
x + 12 -12 = 18-12
x =6
Solution to system is
x = 6 and y= 4
S.set={6,4}
Find missing part
Answer started below x=
Answer:
[tex]x=7.5[/tex]
Step-by-step explanation:
If you look at the large triangle, you will see that the side [tex]x[/tex] is opposite of 30° angle and the side 15 is opposite of 90° angle (side opposite of 90° angle is called the hypotenuse).
We have the angle, we have the side opposite and the hypotenuse. Which trigonometric ratio relates opposite side and hypotenuse? SINE!
So we use the sin ratio and cross multiply and solve for [tex]x[/tex]:
[tex]Sin(A)=\frac{Opposite}{Hypotenuse}\\Sin(30)=\frac{x}{15}\\x=15*Sin(30)\\x=15*(0.5)\\x=7.5[/tex]
Hence, [tex]x=7.5[/tex]
Answer:
a=3.75 un., b=11.25 un.
[tex]x=7.5\ un.[/tex]
[tex]y=\dfrac{15\sqrt{3}}{4}\ un.[/tex]
[tex]z=\dfrac{15\sqrt{3}}{2}\ un.[/tex]
Step-by-step explanation:
Given triangle is special 30°-60°-90° right triangle. The leg that is opposite to the angle of measure 30° is always equal to half of the hypotenuse. The hypotenuse is of length 15 units, the leg that is opposite to the 30° angle is leg with length of x units, then
[tex]x=\dfrac{15}{2}=7.5\ un.[/tex]
In right triangle with hypotenuse x and legs y and a, angle opposite to the leg a is 30°, then
[tex]a=\dfrac{x}{2}=\dfrac{7.5}{2}=3.75\ un.[/tex]
and
[tex]b=15-a=15-3.75=11.25\ un.[/tex]
By the Pythagorean theorem,
[tex]x^2=y^2+a^2,\\ \\7.5^2=3.75^2+y^2,\\ \\y^2=\left(\dfrac{15}{2}\right)^2-\left(\dfrac{15}{4}\right)^2=\dfrac{225}{4}-\dfrac{225}{16}=\dfrac{675}{16},\\ \\y=\dfrac{15\sqrt{3}}{4}\ un.[/tex]
In right triangle with legs y and b and hypotenuse z, leg y is opposite to 30° angle, then
[tex]z=2y=\dfrac{15\sqrt{3}}{2}\ un.[/tex]
The length of s and hypotenuse
Answer:
A
Step-by-step explanation:
this is a standard right triangle 30-60-90
with legs 1 and [tex]\sqrt{3}[/tex] and hypotenuse 2, hence
s = [tex]\sqrt{3}[/tex] and h = 2
Answer:
A. [tex]\sqrt{3}[/tex] ; 2
Step-by-step explanation:
Since We have all the angles of the triangle and one side we can use SIN, COS, and TAN to find the missing side lengths. SIN which is [tex]sin(x) = \frac{opposite}{hypotenuse}[/tex] can be used to find the hypotenuse
[tex]sin(30) = \frac{1}{h}[/tex]
[tex]\frac{1}{sin(30)} = \frac{h}{1}[/tex] ..... inverse both sides
[tex]\frac{1}{sin(30)} = h[/tex]
[tex]2 = h[/tex]
Now we can use the Pythagorean theorem to find the missing length. The Pythagorean Theorem is [tex]a^{2} +s^{2} = h^{2}[/tex]. So we just plug in the values we already have and solve for s.
[tex]1^{2} +x^{2} = 2^{2}[/tex]
[tex]1+s^{2} = 4[/tex]
[tex]s^{2} = 3[/tex]
[tex]s = \sqrt{3}[/tex]
In Conclusion, s = [tex]\sqrt{3}[/tex] and h = 2
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Which is the largest decimal? 0.0688 0.667 0.68 0.6
The largest decimal is :
0.68
Because: In the tenths place, 6 is the biggest number. Now we go to the hundredths to see which one is the biggest. 8 Is the largest one out of them. But what about the 0's? The 0's at the end don't really matter. They are there to confuze you or to add more extra 0's. The 0 at the front of the decimal is also smaller then the 6. For example: 0.0175 < 0.68
Hope helps!-Aparri
The largest decimal among 0.0688, 0.667, 0.68, and 0.6 is 0.68. This can be determined by comparing each digit from left to right in the numbers. Hence, 0.68 is the highest.
To determine which is the largest decimal among 0.0688, 0.667, 0.68, and 0.6, we compare each decimal value:
0.06880.6670.680.6We start from the leftmost digit and compare:
First, look at the integer part left of the decimal point. All numbers are less than 1.Next, compare the tenths place: 0.0688 (0), 0.667 (6), 0.68 (6), 0.6 (6). So, 0.0688 is the smallest.For 0.667, 0.68, and 0.6: compare the hundredths place. Here, 0.6 (60), 0.667 (66), 0.68 (68). The largest is 0.68.Therefore, the largest decimal among the given numbers is 0.68.
Casey buys a bracelet. She pays for the bracelet and pays \$0.72$0.72 in sales tax. The sales tax rate is 6\%6%. What is the original price of the bracelet, before tax?
Answer:
$12.00
Step-by-step explanation:
If they paid $0.72 in tax and tax is 6% or .06 then you could create an equation like this: x * .06 = .72 with x representing the original cost of the bracelet. Now you can just solve for x like so:
x * .06 = .72
÷.06 ÷.06
x = 12
Answer:
$12.00
Step-by-step explanation:
create a real life example using either temperature or money to compare -3 and -5
Example with temperature:
The temperature -3 degrees is warmer than -5 degrees. This applies to celsius or fahrenheit. You might also write "negative 3 degrees" as "3 degrees below zero"; the same applies for -5. The absolute difference between the two temperatures is 2 degrees.
=================================================
Example with money:
If your bank balance is -3 dollars and your friend's bank balance is -5 dollars, then your friend owes more money to the bank (s/he owes $2 more than you do).
Negative balances mean you are in debt. Another way to look at this is to consider you want to buy an item worth $10 but you only have $7. If the store owner lends you the difference, which you pay back later, then 7-10 = -3 is the amount of money on your balance sheet indicating you are in debt $3. The order of subtraction is important. Saying 10-7 = 3 shows a positive bank balance and you wouldn't be in debt (and still have $3 in your pocket).
=================================================
In either example, the value -3 is to the right of -5 on the number line so we would write the inequality -3 > -5 to say that -3 is larger than -5. Have a look at the image attached below.
The Gonzalez family has three children.on summer break they went to an amusement park.they bought 3 child tickets for $18.50 and 2 adult tickets.If they spent a total of $104.50, how much was the price of each adult ticket?
Answer:
43
Step-by-step explanation:
104.50 - 18.50 basically then you get 86 then divided by 2 and get 43
Which decimal is equivalent to 76/9?
Answer:
8.4444...
Step-by-step explanation:
So it's easier if we can write it first in mixed fractions. 9 x 8 is 72 and th is the highest we can go. So it becomes [tex]8\frac{4}{9}[/tex]. Then, if you just long divide 4 by 9 you get .44444.... So it is 8.4 repeating.
8.444 decimal is equivalent to fraction 76/9.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given a fraction of 76/9
Simplifying the above fraction,
=> 76/9
=> (72 + 4)/9
=> 8 + 4/9
=> 8 + 0.444
=> 8.444
Therefore, 8.444 decimal is equivalent to fraction 76/9.
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Which equation represents this situation? Five less than a number is equal to three times the sum of the number and two? Question 2 options: 5 - x = 3x + 2 x - 5 = 2x + 3 x - 5 = 3(x + 2) 5 - x = 3(2x)
Answer:
C) X - 5 = 3 (X + 2)
Step-by-step explanation:
X - 5 = 3 (X + 2)
- Write It Out -
5 Less Than A Number:
X is the anonymous number
X - 5
This is equal to three times the sum of the number and two:
Sum = addition
Sum of a number and two
X + 2
Three times this:
3 (X + 2)
X - 5 is the same as this:
X - 5 = 3 (X + 2)
- I.A. -
A school treasurer purchased jackets for the school store. She used the system of equations below to determine the price for each student jacket, x , and the price for each adult jacket , y. Write a system of equations that has the same solution set as the system of equations
Answer:
A: [tex]7x+y=801[/tex]
B: [tex]18x+3y=1949[/tex]
Step-by-step explanation:
we are given system of equations as
[tex]84x+12y=9612[/tex]
[tex]126x+21y=13643[/tex]
We can simplify each system of equations
[tex]84x+12y=9612[/tex]
we can factor out common terms
[tex]12\times 7x+12\times y=12\times 801[/tex]
[tex]12(7x+y)=12\times 801[/tex]
we can divide both sides by 12
[tex]7x+y=801[/tex]
now, we can simplify second system of equation
[tex]126x+21y=13643[/tex]
Firstly, we can factor
[tex]7\times 18x+7\times 3y=7\times1949[/tex]
[tex]7(18x+3y)=7\times1949[/tex]
we can divide both sides by 7
[tex]18x+3y=1949[/tex]
so, we get
A: [tex]7x+y=801[/tex]
B: [tex]18x+3y=1949[/tex]
Graph the functions and approximate an x-value in which the exponential function surpasses the polynomial function. In your final answer, include a copy of the graph. y = 2x2 + 7 y = 5(x-4)
Answer:
x-value is 6.87
Step-by-step explanation:
we are given
Polynomial as
[tex]y=2x^2+7[/tex]
Exponential as
[tex]y=5^{x-4}[/tex]
Firstly, we can draw graph
We can see that intersection point is (6.87,101.392)
so, x=6.87
At (6.97, 101.392) the exponential function surpasses the polynomial function.
What is the graphical solution of a system of equations?Graphical solutions of a system of equations are way of finding the intersection points of all the equations given.
A system with two or more than two equations has a solution only when they have a common intersection point.
Given, A system of equation y = 2x² + 7 and y = 5^(x - 4).
Now by graphing these two equations we observe that at 6.87 the exponential function surpasses the polynomial function.
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All these answers I need help
Cindy bought 5 dresses for $20 each and 3 pairs of shoes for $20 each. She used this expression to calculate the total amount she spent.
(5 × 20) + (3 × 20)
What is another expression to calculate the total amount spent?
A) (5 + 3) × 20
B) 5 × (20 + 3)
Eliminate
C) 5 × 20 × 3
D) (5 + 20) × (3 + 20)
The A) (5 + 3) × 20 is another expression to calculate the total amount spent
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that Cindy bought 5 dresses for $20 each and 3 pairs of shoes for $20 each. She used this expression to calculate the total amount she spent.
(5 × 20) + (3 × 20)
Multiply in the parentheses first
100 + 60
Now Add
= $160 total
Thus She spent $160 total
The A) (5 + 3) × 20 is another expression to calculate the total amount spent.
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3.a volunteer has 12 pounds of birdseed to put in bird feeders in all of the city parks. there are 3 ¼ Cups of birdseed in pounds, and each bird feeder holds about ¾ cups of birdseed.how many birds feeders can the volunteer fills completely?
Answer:
4 Bird Feeders
Step-by-step explanation:
3 1/4 ALSO is 13/4
13/4 dived by 3/4 or 13/3 witch is 4 and some extra so it can only fill four feeders fully
Answer:
52 bird feeders
Step-by-step explanation:
First, you must determine how much birdseed the volunteer has in cups. To do this, multiply the 12 pounds by the 3 1/4 cups, as there are 3 1/4 cups in one pound. This means the volunteer has 39 cups of birdseed.
Then you must divide the amount of birdseed the volunteer has (39 cups) by the amount of birdseed needed to fill a bird feeder (3/4 cups), which will give you the amount of bird feeders the volunteer can fill (52 bird feeders).
What is the area in square inches 3/8 inch 2/3 inch
Answer:
0.25 in²
Step-by-step explanation:
This is all basic stuff of conversion and multiplication
Option D, The area of the rectangle is 6/24 square inches.
The area of a rectangle is calculated by multiplying its length and width. Given a rectangle with a length of 3/8 inch and a width of 2/3 inch, we can find the area using the formula:
Area = Length × Width
Substitute the given values:
Area = (3/8) × (2/3)
To multiply these fractions, multiply their numerators and their denominators:
Area = (3 × 2) / (8 × 3) = 6 / 24
After simplifying the fraction 6/24, we get 1/4.
Therefore, the area of the rectangle is 1/4 square inches. Among the answer choices, Option D (6/24) is equivalent to 1/4, so the correct answer is Option D.
Complete Question :
What is the area, in square inches, of the rectangle below?
3/8 inch
2/3 inch
Answer choices:
A square 16/9inches
B 25/24 square inches
C 5/11 square inches
D 6/24 square inches
Sally needs 6 gallons of water, but she only has a 2 quart pitcher. How many times does she need to fill it up to make 6 gallons? A) 3 times B) 8 times C) 12 times D) 24 times E) 36 times
Answer: E
Step-by-step explanation: 1 gallon is equal to 4 quarts. If Sally needs to fill and refill a 2 quart pitcher with 6 gallons of water, multiply 6 by 4 to get 24.
Approximate: log 1/2 5
Answer:
-2.32193...
Step-by-step explanation:
log.5 (5)
Answer:
[tex]\log_{\frac{1}{2}} 5=-2.32193[/tex]
Step-by-step explanation:
Given : Expression [tex]\log_{\frac{1}{2}} 5[/tex]
To find : The solution of the given expression ?
Solution :
We have given expression [tex]\log_{\frac{1}{2}} 5[/tex]
Applying logarithmic property,
[tex]\log_b a=\frac{\log_e a}{\log_e b}=\frac{\ln a}{\ln b}[/tex]
Where, [tex]\log _e[/tex] is the natural logarithm indicated as [tex]\ln[/tex]
[tex]\log_{\frac{1}{2}} 5=\frac{\ln (5)}{\ln {\frac{1}{2}}}[/tex]
[tex]\frac{\ln (5)}{\ln {\frac{1}{2}}}=\frac{1.60943}{ -0.69315}[/tex]
[tex]\frac{\ln (5)}{\ln {\frac{1}{2}}}=-2.32193[/tex]
Therefore, [tex]\log_{\frac{1}{2}} 5=-2.32193[/tex]
What is the premium for $75000 for a 30 year old male for a 10 year policy ?
Answer: $286.50
If the AP (Annual Premium) $1000 for 30 yr male with 10 yr policy; $3.82...
75000/1000 = 75
75 x $3.83 = $286.50 AP
The premium for a 10-year, $75000 life insurance policy for a healthy 30-year-old male typically ranges from $10 to $20 per month. Actual pricing can vary based on health status, lifestyle, occupation and the specific insurance company's underwriting process. To get the most accurate premium, it's beneficial to shop around and compare quotes.
Explanation:The premium for a life insurance policy varies based on several factors including the age of the individual, the amount of coverage, policy term, and the individual's health status. The question doesn't provide enough information for an exact calculation as we do not know the general health status of the 30-year-old male, his occupation, lifestyle factors or the premium rates of the specific insurance company. However, we can give a general idea.
Assuming this individual is in good health, for a 30-year-old male, a $75000, 10-year term life insurance policy would typically cost between $10 to $20 per month. This is an average and the actual cost can vary greatly based on the factors mentioned.
Also, each insurance company has different pricing and underwriting processes, so it's important to shop around and compare quotes from different companies to ensure you're getting the best rate.
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Linda has $9.00 in her wallet. she buys a card for $1.17. she wants to buy some pens that cost $2.65. what is the maximum number of pens can she buy
Answer:
2 pens
Step-by-step explanation:
Let x represent the number of pens Linda buys. Since they cost $2.65 each, this gives us the expression 2.65x.
Adding the cost of the card to this gives us the expression 2.65x+1.17.
She has a total of $9.00; this gives us the equation
2.65x+1.17 = 9.00
Subtract 1.17 from each side:
2.65x+1.17-1.17 = 9.00-1.17
2.65x = 7.83
Divide both sides by 2.65:
2.65x/2.65 = 7.83/2.65
x = 2.95
We cannot buy a portion of a pen, so the most she can buy is 2 pens.
Answer:
The answer is 2 pens.
Step-by-step explanation:
Total amount Linda has in her wallet = $9
Amount spent on buying a card = $1.17
So, amount left with Linda = [tex]9-1.17=7.83[/tex]
Now, she wants to buy pens that cost $2.65, so the maximum number of pens she can buy are = [tex]\frac{7.83}{2.65}= 2.9[/tex]
But, pens cannot be in decimal, so the maximum pens she can buy are 2.
You open a lemonade stand in your neighborhood and start off charging $1 per glass of lemonade. After two weeks, you decide that business is doing so well and the demand for lemonade is high so you raise your prices to $1.75. What was your percent increase in price?
Answer:
75% increase in price
Explanation:
75% of $1 is 75 cents
find slop for 7x-2y=0.2
Answer:
M=3.5
Step-by-step explanation:
7x-2y=0.2
-7x -7x
-2y = -7x + .02
/-2 /-2 /-2
y= 3.5x+ 0.01
slope is 3.5
Jackson used the process of completing the square to solve the equation 2x2−12x=−6.
Answer:
[tex]x=3-\sqrt{6},x=3+\sqrt{6}[/tex]
Step-by-step explanation:
we are given equation as
[tex]2x^2-12x=-6[/tex]
Since, we have to solve it by using complete square
so, firstly we will complete square
and then we can solve for x
step-1:
Factor 2 from both sides
[tex]2(x^2-6x)=-3\times 2[/tex]
step-2:
Simplify it
[tex]x^2-6x=-3[/tex]
step-3:
Add both sides 3^2
[tex]x^2-6x+3^2=-3+3^2[/tex]
now, we can complete square
[tex](x-3)^2=6[/tex]
step-4:
Take sqrt both sides
[tex](x-3)=-\sqrt{6},(x-3)=\sqrt{6}[/tex]
step-5:
Add both sides by 3
we get
[tex]x=3-\sqrt{6},x=3+\sqrt{6}[/tex]
what's the answer to this
4 (w+1)-4w
I nee help!
Question
what's the answer to this
4 (w+1)-4w
Answer:
4Step-by-step explanation:
4 (w+1)-4w =
4w + 4 - 4w =
4
help how do I solve for 2^3x+1=9?
Answer:
No solution
Step-by-step explanation:
20 Points!!! Need Help ASAP!!! Will mark Brainliest!!!
Given: AB || CD, m
MA. 15
B. 33
C. 87
D. 93
Answer:
The answer is A
Step-by-step explanation:
5x + 18 = 7x - 12
Subtract 7x from both sides
5x + 18 - 7x = 7x - 12 - 7x
-2x + 18 = -12
Subtract 18 from both sides
-2x + 18 - 18 = -12 - 18
-2x = -30
Divide both sides by -2
-2x/-2 = -30/-2
x = 15
How can you tell by looking at the coordinates of the two triangles that a’b’c’ is a 180 degrees rotation of abc
Answer:
D
Step-by-step explanation:
Under a rotation about the origin of 180°
a point (x, y ) → (- x, - y) → D
Note this only happens if the rotation is about the origin
if r=7 what is the circumference?
The formula of a circumference of a circle:
[tex]C=2\pi r[/tex]
We have r = 7. Substitute:
[tex]C=2\pi(7)=\boxed{14\pi}[/tex]
Bowl A contains 6 apples and 3 mangoes this can be written as, Bowl B contain 8 apples and 2 mangoes this can be written as. What is the difference between the bowls.
Answer:
Bowl B contains 2 apples more than Bowl A and Bowl A contains 1 mango more than Bowl B.
Step-by-step explanation:
Number of apples in Bowl A = 6
Number of mangoes in Bowl B = 8
Difference in apples = 8 - 6 = 2
So, Bowl B contains 2 apples more than Bowl A.
Number of mangoes in Bowl A = 3
Number of mangoes in Bowl B =2
Difference in mangoes = 3 - 2 = 1
So, Bowl A contains 1 mango more than Bowl B.
Bowl B has 2 more apples and 1 fewer mango compared to Bowl A. Thus, the primary differences are in the quantities of apples and mangoes in each bowl.
Step by Step Solution:
To understand the differences between Bowl A and Bowl B, let's break down the contents of each bowl:
Bowl A contains 6 apples and 3 mangoes.
Bowl B contains 8 apples and 2 mangoes.
Now, let's find the differences in the number of apples and mangoes between the two bowls:
Difference in Apples: Bowl B has 8 apples, and Bowl A has 6 apples. Therefore, the difference is 8 - 6 = 2 apples. Bowl B has 2 more apples than Bowl A.
Difference in Mangoes: Bowl A has 3 mangoes, and Bowl B has 2 mangoes. Therefore, the difference is 3 - 2 = 1 mango. Bowl A has 1 more mango than Bowl B.
In summary, Bowl B has 2 more apples and 1 fewer mango compared to Bowl A.
a quadrilateral has interior angles 85, 105 and 120 what is the measure of the 4th angle?
__________________
Answer: [tex]50^{\circ}[/tex]
Step-by-step explanation:
By the definition of quadrilateral,
A quadrilateral has four interior angles and the sum of all interior angle of a quadrilateral is always equal to [tex]360^{\circ}[/tex]
Here the measurements of three interior angles are [tex]85^{\circ}[/tex], [tex]105^{\circ}[/tex] and [tex]120^{\circ}[/tex]
Let the measurement of fourth angle is x degree.
Thus, [tex]85^{\circ}+105^{\circ}+120^{\circ}+x=360^{\circ}[/tex]
[tex]310^{\circ}+x=360^{\circ}[/tex]
[tex]x = 360^{\circ}-310^{\circ}=50^{\circ}[/tex]
Thus, the measure of fourth angle is [tex]50^{\circ}[/tex]
The measure of the 4th angle is 50 degrees.
Explanation:To find the measure of the fourth angle of a quadrilateral, we need to know that the sum of all the interior angles of a quadrilateral is always 360 degrees. Therefore, to find the measure of the fourth angle, we can subtract the sum of the other three angles from 360. In this case, the given angles are 85, 105, and 120 degrees, so the sum of these three angles is 85 + 105 + 120 = 310 degrees. To find the measure of the fourth angle, we subtract 310 from 360: 360 - 310 = 50 degrees.
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When using pi, do you use 3.14 or 3.141592653?
i always use 3.1415 but just to be safe use the pi symbol :)