Answer:
2cis(20°)
Step-by-step explanation:
we are given that
[tex] \displaystyle \rm z = 10cis ({30}^{ \circ} )[/tex]
[tex] \displaystyle \rm w = 5cis ({10}^{ \circ} )[/tex]
We want to find z/w . To do so, divide 10cis(30°) by w = 5cis(10°) which yields:
[tex] \displaystyle \rm \frac{ z}{w} = \frac{10cis ({30}^{ \circ} )}{5cis( {10}^{ \circ} )}[/tex]
recall that,
[tex] \displaystyle \rm \frac{ r_{1} cis ({ { \theta}_{1}} )}{ r_{2}cis( { \theta}_{2})} = \frac{ r_{1} }{ r_{2} } cis({ \theta}_{1} - { \theta}_{2})[/tex]
consider,
[tex]{ r}_{1} \implies 10[/tex][tex]{ r}_{2} \implies 5[/tex][tex]{ \theta}_{1} \implies {30}^{ \circ} [/tex][tex]{ \theta}_{2} \implies {10}^{ \circ} [/tex]Therefore, utilizing the formula yields:
[tex] \displaystyle \rm \frac{ z}{w} = \frac{10cis ({30}^{ \circ} )}{5cis( {10}^{ \circ} )} \\ \implies \rm\frac{ z}{w} = \dfrac{10}{5} cis( {30}^{ \circ} - {10}^{ \circ} ) \\ \implies \rm \dfrac{z}{w} = \boxed{ \rm2cis( {20}^{ \circ} )}[/tex]
and we're done!
NB: cis(x) is also known as cos(x)+i×sin(x)
Which inequality has no solution? 6 (x 2) greater-than x minus 3 3 4 x less-than-or-equal-to 2 (1 2x) negative 2 (x 6) less-than x minus 20 x minus 9 less-than 3 (x minus 3)
From the provided equations, the equation which has no solution is 3 4 x less-than-or-equal-to 2 +4x. Option 2 is correct.
What is the inequality equation?Inequality equation is the equation in which the two expressions are compared with greater than, less than or other inequality signs.
From the given equations, the equation which has no solution has to be found out. When the value, does not equate for the expression, then the expression has no solution.
The first equation given in the problem is,
[tex]6 (x +2) > x-3[/tex]
Solve it further,
[tex]6 x +12 > x-3\\6x-x > -3-12\\5x > -15\\x > -3[/tex]
The second equation given in the problem is,
[tex]3+ 4x \leq 2 (1 +2x)[/tex]
Solve it further,
[tex]3+ 4x \leq 2 +4x\\4x- 4x \leq 2-3\\0\leq-1[/tex]
The value of 0 is greater than the number -1. Thus, this inequality has no solution.
The option 3 and 4 has a solution. Hence, from the provided equations, the equation which has no solution is 3 4 x less-than-or-equal-to 2 +4x. Option 2 is correct.
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Which line most accurately represents the line of best fit for the scatter plot?
(I think its D, correct me if im wrong)
Line A
Line B
Line C
Line D
Answer:
Your right, it's D.
Step-by-step explanation:
I am trying to find the entire surface area of the entire shape. I got 306, but it is wrong.
Is it possible you could help?
Answer:
281
Step-by-step explanation:
12*4 rectangle 2 times because theres 2 of the same surfaces
5*4 rectangle 2 times
12*5 rectangle on the bottom surface 1 time
4 triangle surfaces of (5*5)/2
7*5 rectangle on top
add and you get 281
Say that romania puts a tariff of 6% on its exports and 21% on its imports. if romania has a trade deficit of (equivalent us dollars) $26.76 billion and gained tariff revenue of $18.9603 billion, how much are romania’s imports worth? a. $62.56 billion b. $64.29 billion c. $76.17 billion d. $97.04 billion please select the best answer from the choices provided a b c d
The amount of money that Romania’s imports are worth is equal to: C. $76.17 billion.
Given the following data:
Exports tariff = 6% = 0.06.
Imports tariff = 21% = 0.21.
Trade deficit = $26.76 billion.
Tariff revenue = $18.9603 billion.
How to calculate Romania’s imports?In order to determine how much Romania’s imports are worth, we would write a mathematical expression for the total tariff revenue and trade deficit as follows:
0.06E - 0.21I = 18.9603 .....total tariff revenue (eqn. 1).
I - E = 26.76 .....trade deficit (eqn. 2).
From eqn. 2, we have:
E = I - 26.76 ..equation 3.
Substituting eqn. 3 into eqn. 1, we have:
0.06(I - 26.76) - 0.21I = 18.9603
0.06I - 1.6056 - 0.21I = 18.9603
0.27I = 18.9603 + 1.6056
0.27I = 20.5659
I = 20.5659/0.27
I = $76.17 billion.
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help please it´s so hard
Answer:
9
Step-by-step explanation:
To solve this expression, we need to follow the BODMAS. The BODMAS states that to simplify the expression in the parenthesis first. Then, divide or multiply if possible. Lastly, add or subtract if possible.
The BODMAS states that:
B - BracketsO - OrderD - DivisionM - MultiplicationA - AddtionS - SubtractionExpression BODMAS
⇒ 6 ÷ 2(1 + 2) ⇒ 6 ÷ 2(3) B - Brackets (BODMAS)⇒ 6 ÷ 2 × 3⇒ 3 × 3 D - Division (BODMAS)⇒ 9 M - Multiplication (BODMAS)Therefore, the value of the expression is 9.
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Increase 31 kg by 100%.
helppppnmeeeeeee please
Answer:
? = 14.48
Step-by-step explanation:
This is a right triangle so you can use trigonometry.
since you know the opposite and hypotenuse sides, use sin.
sin(?) = opposite/hypotenuse = 4/16 = 1/4
? = arcsin(1/4)
? = 14.48
A dress that regularly costs $92 and has tax of
8%. How much is the tax charge for this dress?
Answer:
Tax = $7.36
Step-by-step explanation:
[tex]tax=92(\frac{8}{100} )=92(0.08)=7.36[/tex]
Hope this helps
Answer:
7.36$ tax.
When finding the whole amount of dollars to the percentage, multiply the whole number(92) by the tax percentage(0.08) which is a decimal for this case.
[tex]92 * 0.08 = 7.36\[/tex]
Optionally, find the tax plus the whole number.
[tex]92 + 7.36 = 99.36\[/tex]
__________________________________________________________
Questions or Suggestions?Ask in comments.
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP PLS PLS THANKS
Answer:
The answer is B. 1/2
Step-by-step explanation:
You want to role a number less than 4 so you want 1,2,3 at least.
A dice has 6 numbers, 1-6.
So 3/6 = 1/2 making it a 50% change of you getting either 1,2,3.
Pls help! It's due soon and I can't figure out the answer!
Answer:
9cm and 2cm
Step-by-step explanation:
∴ They're similar triangles.
∴ [tex]\frac{a}{3}[/tex]= [tex]\frac{6}{b}[/tex] = [tex]\frac{3}{1}[/tex]
∴ a = 9cm
∴ b = 2cm
What is the circumference of a circle with a diameter of 10 meters? (Use 3.14 for pi.)
13.14 m
31.4 m
15.7 m
314 m
Answer:
The answer is given in the picture
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECTAnswer:
31.4 m
Step-by-step explanation:
The formula for the circumference of a circle is c=dπ, so we can substitute our diameter and 3.14 for pi.
c=(10)(3.14)
c=31.4
So the diameter is 31.4 meters.
PLEASE HELP ME I NEED HELP RIGHT NOW..this is weird question...it is on a problem thingy please help
um im sorry,....wtf
Answer:
I don't think it would be called bias, it's just asking for an opinion if a state can kill a person if they break the law.
HELP! WILL GIVE BRAINLY
Today, the sum of Harper's age and Cadence's age is 61. 8 years ago Cadence was 4 times older than Harper.
Part A: Enter Harper's age today.
Part B: Enter Cadence's age today.
Answer:
Harper is 17 and Cadence is 44.
Step-by-step explanation:
First, we can set up an equation to displays the sum of both ages.
Let x = Harper's age and y = Cadence's age
x+y=61
8 years ago, this means the sum will decrease by a total of 16 as we have to subtract 8 from both variables
The equation to represent 8 years ago is: x+y=45
Now we can write another equation to represent Cadence being 4 times older than Harper (8 years ago)
y=4x
We can substitute this back into the equation we had for the ages 8 years ago.
x+(4x) = 45
5x=45
x=9
Now, Harper's age 8 years ago is 9 years old. We add 8 to this number to determine that Harper is currently 17 years old.
We can insert this into the original equation to determine Cadence's age.
17+y=61
y=44
Thus, Cadence is currently 44 years old
An investor buys in a company and in the twelve months after she invests the value of the stock decreases by 30% , bu what amount will the value of the stock need to go up from there in order that the price of the stock will be equal to what the investor first paid for it ?
a:30%
b:37,5%
c:42. 9
d:45
e:46. 7
Answer:
B 37.5%
Step-by-step explanation:
If I get paid 8 dollars a hour, and I worked 180 hours how much money will I recive
Answer:
$1440
Step-by-step explanation:
It's kind of obvious, 8 x 180 = 1440
If the ball leaves her hand 6 feet above the ground at 65 feet/second: a) what is the maximum height of the ball
[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&65\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&6\\ \qquad \textit{of the object}\\ h=\textit{object's height}&\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+65t+6[/tex]
Check the picture below, the maximum occurs at the vertex of the parabolic path, so
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+65}t\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left(-\cfrac{ 65}{2(-16)}~~~~ ,~~~~ 6-\cfrac{ (65)^2}{4(-16)}\right)\implies \left(\cfrac{65}{32}~~,~~6+\cfrac{4225}{32} \right) \\\\\\ \left(\cfrac{65}{32}~~,~~\cfrac{4609}{32} \right) \implies \stackrel{maximum~height}{(2.03125~~,~~\stackrel{\downarrow }{72.015625})}[/tex]
8. Which two-dimensional figure is formed when a right rectangular pyramid
is sliced by a plane through the pyramid's vertex and perpendicular to the
pyramid's base?
A. a square
B. a triangle
C. a trapezoid
D. a parallelogram
Answer: B
Step-by-step explanation:
What is the surface area of this right prism?
48 in²
84 in²
96 in²
120 in²
Answer:
96 in²
Step-by-step explanation:
I took the test :)
Answer:
96 in² for K12
in the given figure, prove that triangle ABC = triangle ABD
Answer:
Step-by-step explanation:
HELP PLEASE!!!!!!!!!!!!!!!!!!!
Answer:
x=12
Step-by-step explanation:
ALready, we know that in a right angles, the total sum gives ninety degrees.
Hence,
6x-2+20=90
6x+18=90
Collect like terms
6x=90-18
6x=72
Divide both sides by the coefficient of x, 6
Therefore, x=12
When condensing a logarithm using the the product property, you combine the answers by dividing them.
Group of answer choices
True
False
When condensing a logarithm using the the power property, you move the front number to become the exponent on the log.
Group of answer choices
True
False
When condensing a logarithm using the the quotient property, you combine the answers by dividing them.
Group of answer choices
True
False
#1
log_a(bc)=log_a^b+log_a^cNot divide we multiply
False#2
logb^a=alogbYes
True#3
Yes it's reverse of first one
TrueAnswer:
False
True
True
Step-by-step explanation:
[tex]\textsf{Product Rule}:\quad \log_n(x)+\log_n(y)=\log_n(xy)[/tex]
When condensing a logarithm using the product rule, you combine the answers by multiplying them.
[tex]\textsf{Power Rule}:\quad a \log_n(x)=\log_n(x)^a[/tex]
When condensing a logarithm using the power rule, you move the front number to become the exponent on the log.
[tex]\textsf{Quotient Rule}:\quad \log_n(x)+\log_n(y)=\log_n\left(\dfrac{x}{y}\right)[/tex]
When condensing a logarithm using the the quotient rule, you combine the answers by dividing them.
somebody HELP ME PLS IM TRYING TO GET MY GRADES UP FROM AN F! IF ITS CORRECT AND HELPFUL U WILL BE BRAINLIEST
Find the area of the figure.
Answer:
144
Step-by-step explanation:
A=BH
your base is 9 and your height is 16. 16 times 9= 144. Hope this helps :)
According to the line plot what is the total weight of the dog toys that weighed 1/8 of a pound or 3/8 of a pound
Answer:
7/8
Step-by-step explanation:
I took the test
The total weight of the dog toys that weighed 1/8 of a pound or 3/8 of a pound is 7/8.
How to add two fractions?Let we have to add two fractions:
[tex]\dfrac{a_1}{b_1} + \dfrac{a_2}{b_2}[/tex]
Then we will find the Lowest Common Multiple (LCM) of b_1 and
b_2. That will help to make the denominate or same.
Once the denominators become the same, the numerators can add up directly, giving us the final result of the addition.
According to the line plot;
The total weight of the dog toys that weighed 1/8 of a pound or 3/8 of a pound
= 3/8 + 3/8 + 1/8
=7/8
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Combine the terms to simplify the expression below. 14x - (2x + y)
FAST
Answer:
12x - y
Step-by-step explanation:
14x - (2x + y) ← distribute parenthesis by - 1
= 14x - 2x - y ← collect like terms
= 12x - y
Answer:
12x - y
Step-by-step explanation:
14x -(2x +y)
14x -2x -y
12x -y
Kalina is choosing a sandwich and a drink for lunch. She can choose between turkey, ham, and vegetarian sandwiches. She chooses her drink from a selection of water, orange juice, milk, or lemonade.
How many possible ways can one sandwich and one drink be chosen?
If one more drink choice were added to the selection, the number of possible ways to choose one sandwich and one drink would increase by
.
Answer: possible wayways 3 × 4 = 12
If one more drink was added, possibilities will become 3× 5 = 15
Number of possi left ways will increase by 15 - 12 = 3
Step-by-step explanation:
__
What is the length of HI to the nearest hundredth?
1.32 km
16.33 km
38.02 km
Answer:
16.33 km
Step-by-step explanation:
The square length of hypotenuse is equal to the sum of two legs' square value:
|HI|^2 + |JI|^2 = |HJ|^2
|HI|^2 + (24.28)^2 = (29.26)^2
|HI|^2 + 589,5184 = 856,1476 (these are full values and will be easier to calculate with a calculator, if not we can use the approximate values: 589,5 and 856,1)
subtract 589,5184 from both sides
|HI|^2 = 266,5636 find the root of boths sides
HI = 16.33 approximately
The base HI of the right triangle is approximately 16.26 km.
Given is a right triangle with perpendicular JI = 24.28 km and hypotenuse HJ = 29.26 km we need to find the base HI.
To find the base HI of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's denote the base HI as x.
According to the Pythagorean theorem:
HJ² = JI² + HI²
Substituting the given values:
(29.26 km)² = (24.28 km)² + x²
Simplifying the equation:
855.4276 km² = 590.7584 km² + x²
264.6692 km² = x²
To find x, we take the square root of both sides:
x = √(264.6692 km²)
Calculating the value:
x ≈ 16.26 km
Therefore, the base HI of the right triangle is approximately 16.26 km.
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pleaseee i need some help on these 3 questions
Answer:
a) the product is equal to 953.
b) the product is greater than 443.
c) the product is greater than 181.
Step-by-step explanation:
a) 953 × 63/63 = 953
Therefore, the product is equal to 953.
b) 443 × 86/79 = 482.25
Therefore, the product is greater than 443.
c) 181 × 30/28 = 193.93
Therefore, the product is greater than 181.
Hope this helps =)
Show division using an area model. Can you show 24÷ 4 with one rectangle?
Answer:
Shown division using an area model above, Yes, shown 24 ÷ 4 with one rectangle above. Question 2. Answer: Shown division using an array as shown above, 25 ÷ 4 = Quotient = 6 and Remainder = 1, Shown division using an area model above, Yes, shown 25 ÷ 4 with one rectangle above and showed
HELP 2 FOR MY SIS no hurry
First Step:
Parentheses,
7 + 5 = 12
Divide,
12 / 3 = 4
Add,
4 + 3 = 7
Multiply,
10 x 7 = 70
Answer is 70!!
hope this helps
PLSS HELP WILL GIVE BRAINLIST:DDDDDD
Use the number line to help you decide which statement is true.
1
3
<
2
6
1
3
>
2
6
1
3
=
2
6
Answer:
It's 13<26
Step-by-step explanation: