Answer:
w = [tex]\frac{P-2i}{2}[/tex]
Step-by-step explanation:
P = 2w + 2i ( subtract 2i from both sides )
P - 2i = 2w ( isolate w by dividing both sides by 2 )
[tex]\frac{P-2i}{2}[/tex] = w
Given that y is inversely proportional to x y =0.25 when x =4, find the value of y when x =5
Answer: y=0.2
Step-by-step explanation:
y∝(1/x)
this implies that
y=k/x eq(*)
when y =0.25 when x =4
0.25=k/4
k=1
for y when x=5
y=k/x
y=1/5
y=0.2
The angle of elevation to a nearby tree from a point on the ground is measured to be 74^{\circ} ∘ . How tall is the tree if the point on the ground is 54 feet from the tree? Round your answer to the nearest tenth of a foot if necessary.
The height of the tree whose angle of elevation is [tex]74^{0}[/tex] and 54 feet tall is 188 foot.
Height of the tree= 188 foot (rounding off nearest tenth)
What is angle of elevation?The angle of elevation in math is "the angle formed between the horizontal line and the line of sight when an observer looks upwards is known as an angle of elevation".
We know by trigonometric ratios,
[tex]tan \; \theta = \frac{P}{B}[/tex]
[tex]tan \; 74^0 \;[/tex] = [tex]\frac{P}{54}[/tex]
3.48 = [tex]\frac{P}{54}[/tex]
P= 3.48 x 54
= 187.92 feet
≈ 188 foot (rounding off nearest tenth)
The height of the tree whose angle of elevation is and 54 feet tall is 188 foot.
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Answer: 188.3 feet tall*
Step-by-step explanation:
2 Latoya has 60 CDs in her collection.
• 40 are Pop
. 12 are Country
• 6 are Rock
• 2 are Jazz
.
If she randomly selects a CD from her collection, what is the probability that she will NOT select a Country CD?
60 cds - 12 country = 48 cds are not country.
probability of picking one that is not country = total of non country/ total cds
probability = 48/60 which reduces to 4/5
answer: 4/5
(sqrt3-sqrt3i)^4
(-1+sqrt3i)^12
(sqrt 3-i)^6
(sqrt2-sqrt2i)^8
(sqrt2-i)^6Simplify the complex numbers and arrange them in increasing order of their absolute value (modulus).
The increasing order of the complex numbers is (√2 - i)⁶ < (√2 - √2i)⁸ = (√3 - i)⁶ = (-1 + √3i)¹² < (√3 - √3i)⁴.
Absolute values of the complex numbersThe absolute values of the complex numbers are determined as follows;
(sqrt3-sqrt3i)^4 = (√3 - √3i)⁴
[tex]|z| = \sqrt{(\sqrt{3} )^2 + (\sqrt{3 }\times1 )^2} } \\\\|z| = \sqrt{6}[/tex]
(-1+sqrt3i)^12 = (-1 + √3i)¹²
[tex]|z| = \sqrt{(-1)^2 + (\sqrt{3)^2} } \\\\|z| = \sqrt{4} \\\\|z| = 2[/tex]
(sqrt 3-i)^6 = (√3 - i)⁶
[tex]|z| = \sqrt{(\sqrt{3})^2 + (-1)^2 } \\\\|z| = \sqrt{4} \\\\|z| = 2[/tex]
(sqrt2-sqrt2i)^8 = (√2 - √2i)⁸
[tex]|z| = \sqrt{(\sqrt{2} )^2 + (\sqrt{2})^2 } \\\\|z| = 2[/tex]
(sqrt2-i)^6 = (√2 - i)⁶
[tex]|z| = \sqrt{(\sqrt{2})^2 + (-1)^2} } \\\\|z| = \sqrt{3}[/tex]
Increasing order of the complex numbers;
(√2 - i)⁶ < (√2 - √2i)⁸ = (√3 - i)⁶ = (-1 + √3i)¹² < (√3 - √3i)⁴.
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Answer:
see screenshot below
Step-by-step explanation:
correct on edmentum
Prove all the relation of quadric polynomial.
Kindly need help!!!
[tex]{\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]
Let [tex]\alpha[/tex] and [tex]\beta[/tex] be the two zeroes of P(x) = [tex]\sf {a}^{2} + bx + c[/tex]
• A polynomial is always equal to it's factors, also the constant "k" is not equal to zero
[tex] \tt \sf {a}^{2} + bx + c = k(x - \alpha )(x - \beta )[/tex]
• Using distributive property
[tex]\tt \sf {a}^{2} + bx + c = k \bigg( {x}^{2} - \beta x - \alpha x + \alpha \beta \bigg)[/tex]
[tex]\tt \sf {a}^{2} + bx + c = k {x}^{2} -k (\beta x )- k(\alpha x )+k( \alpha \beta )[/tex]
• Taking common
[tex]\tt \sf {a}^{2} + bx + c = k {x}^{2} -kx (\beta + \alpha)+k( \alpha \beta ) - - (1)[/tex]
• Equating coefficients of like terms
[tex] \sf \: a = k - - (2)[/tex]
[tex] \sf b = - k( \alpha + \beta ) - - (3)[/tex]
[tex] \sf c = k \alpha \beta - - (4)[/tex]
★ From 3
[tex] \sf b = - k( \alpha + \beta ) - - (3)[/tex]
★ From 2 we have a = k so we have -
[tex] \sf b = - a( \alpha + \beta ) [/tex]
[tex]\sf - \dfrac{b}{a} = ( \alpha + \beta ) [/tex]
[tex]\sf \therefore \boxed {{ \red{( \alpha + \beta ) = - \dfrac{b}{a} } }}[/tex]
• Sum of zeros = [tex]- \dfrac{b}{a}[/tex]
★ From 4
[tex] \sf c = k \alpha \beta - - (4)[/tex]
★ From 2 we have a = k so we have -
[tex] \sf c = a \: \alpha \: \beta[/tex]
[tex]\sf \dfrac{c}{a} = \alpha \beta[/tex]
[tex]\sf \therefore \boxed {{ \red{( \alpha \beta ) = \dfrac{c}{a} } }}[/tex]
• Product of zeros = [tex] \dfrac{c}{a}[/tex]
Also,
★ From 1
[tex]\tt \sf {a}^{2} + bx + c = k {x}^{2} -kx (\beta + \alpha)+k( \alpha \beta ) - - (1)[/tex]
[tex]\tt \sf {a}^{2} + bx + c = k \bigg( {x}^{2} -x ( \alpha + \beta ) + ( \alpha \beta \bigg) [/tex]
• Now just put S instead of sum of zeroes and P instead of product of zeroes
[tex] \tt \sf {a}^{2} + bx + c = k \bigg( {x}^{2} -x ( S ) + ( P \bigg) [/tex]
[tex]\tt \sf{a}^{2} + bx + c = \boxed{ \red{ \sf \tt k \bigg( {x}^{2} - Sx + ( P \bigg ) }}[/tex]
[tex]\rule{280pt}{2pt}[/tex]
Cathleen Brooks obtained an 18 month loan of $3,200. The interest rate is 15% Her monthly payment is $199.68. The balance of the loan after 6 payments
is $2,341.45.
a. What is the interest for the first payment?
b. What is the interest for the seventh payment?
a. The interest for the first payment is $40.
b. The interest for the seventh payment is $29.27.
What is interest?In financial accounting and management, interest refers to the finance charge for obtaining or giving a loan or credit.
The interest payment or revenue is based on the interest rate applied to the principal or loan balance.
Data and Calculations:Loan = $3,200
Monthly payment = $199.68
Interest rate = 15%
Loan balance after 6 payments = $2,341.45
Interest for the first payment = $40 ($3,200 x 15% x 1/12)
Interest for the seventh payment = $29.27 ($2,341.45 x 15% x 1/12)
Thus, while the interest for the first payment is $40, the interest for the seventh payment is $29.27.
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Maths problem in simultaneous equations
Answer:
Question 6: The cost of a chocolate bar is $1.20 and the cost of a box of gum is $0.75
Question 7: There were 7 students
Step-by-step explanation:
Question 6:We will be using system of equations which a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations intersect.
Our Variables:
- chocolate bar which will be represent as b in the equation
- box of gum which will be represent as g in the equation
Forming the equations:
Sally -
bought 2 chocolate bars (b)
bought 1 box of gum (g)
to a total of $3.15
so 2b + 1g = $3.15
Evans -
bought 1 chocolate bars (b)
bought 2 box of gum (1)
to a total of $2.70
so 1b + 2g = $2.70
Solving using substation:
2b + 1g = $3.15 we want to isolate b to input into the other equation
1b + 2g = $2.70
2b + 1g = $3.15 subtract 1g from both sides, divided both sides by 2
2b / 2 + 1g - 1g = $3.15 - 1g / 2
b = $3.15 - 1g / 2
Now substation b into the second equation
1b + 2g = $2.70 becomes 1($3.15 - 1g / 2) + 2g = $2.70
simplify,
$3.15 + 3g / 2 = $2.70 isolate g
$3.15 + 3g / 2 x 2 = $2.70 x 2 multiply both sides by 2
$3.15 + 3g = $5.40 subtract $3.15, divided by 3 from both sides
$3.15 - $3.15 + 3g / 3 = $5.40 - $3.15 / 3
g = $5.40 - $3.15 / 3
g = $2.25 / 3
g = $0.75
Now plug in g to get b into any equation:
If Sally equation is used
2b + 1g = $3.15
2b + 1(0.75) = $3.15 → 2b + 0.75 = $3.15
2b + 0.75 - 0.75 = $3.15 - 0.75
2b = $2.40 → 2b / 2 = $2.40 / 2
b = $1.20
If Evans equation is used
1b + 2g = $2.70
1b + 2(0.75) = $2.70 → 1b + 1.50 = $2.70
1b + 1.50 - 1.50 = $2.70 - 1.50
1b / 1 = $1.20 / 1
b = $1.20
Question 7:
Our Variables:
- adult which will be represent as A in the equation
- student which will be represent as S in the equation
Forming the equations:
- sample size: group of 30
- Adult cost $5 (A)
- Student cost $2 (S)
- Five members are free
to a total cost is $104
so A + S = 30 - 5
this is how many of each variable from the total group and we subtract 5 as 5 members were free
so 5A + 2S = $104
Solving using substation:
A + S = 25 we want to isolate a to input into the other equation
5A + 2S = $104
a = 18
s =7
Area is measured in square units. This means that if we divide the shape into squares that are equal in size and count them up, the area is the total number of squares. Square units are always one unit of length long and one unit of length wide. In the song, the unit of length we use is feet. So each square unit is one foot long and one foot wide, or one square foot. Since there are 72 of these units in total, we say the area is 72 square feet. Square units can use other units of length, like inches or miles. Make sure you know what unit of length you’re using.
Jason is finding the area of a rectangle that is 7 inches long and 4 inches wide. Jason says the area of the rectangle is 28 inches. Is Jason correct or incorrect?
A: Jason is correct because 7 x 4 = 28.
B: Jason is incorrect because the area is 28 square inches.
C: Jason is incorrect because 7 + 4 = 11.
D: Jason is incorrect because the area is 28 square feet.
Answer:
B
Step-by-step explanation:
Area is always squared; area of a rectangle is length x width so 7*4= 24in^2
If this answer helped you I would greatly appreciate brainliest :D.
thats the questin i need halp with
Answer:
40% increase
Step-by-step explanation:
7-5=2
plug in:
2/5=x/100
x=40
40% increse
The sandwhich increased by 2 dollars. The amount of change must be divided by the original. 7-5 is 2, which means we must divide 2 by 5. 2/5 is .40. Which translates to 40% or 40/100. This means that the price of the sandwhich increased 40%.
Hope this helped you <3!
Lucas has 2 chocolate bars more than Caidon. Together they have 30 chocolate bars. How
many chocolate bars does Lucas have? (hint: use only one variable)
Help me
Answer:
Lucas has 16 chocolate bars
Step-by-step explanation:
Let x = number of chocolate bars Lucas has
⇒ x - 2 = number of chocolate bars Caidon has
If they have 30 chocolate bars altogether then:
⇒ x + x - 2 = 30
⇒ 2x - 2 = 30
⇒ 2x = 32
⇒ x = 16
Therefore, Lucas has 16 chocolate bars (and Caidon has 14 chocolate bars).
Just please help me!!!!!
Answer:
n= 5/3 or 1.67
Step-by-step explanation:
9n^2 -9 =16
9n^2 = 16 + 9
9n^2 = 25
n^2 =25/9
n^2 =25/9
[tex]\sqrt{n^2} = \sqrt{\frac{25}{9} }[/tex]
n= 5/3 or 1.67
[tex]~~~~~~9n^2 -9 = 16\\\\\implies 9(n^2 -1) = 16\\\\\implies n^2 -1 = \dfrac{16}9\\\\\implies n^2 = \dfrac{16}{9}+1\\\\\implies n^2 = \dfrac{25}{9}\\\\\implies n=\pm\sqrt{\dfrac{25}{9}}\\\\\implies n= \pm\dfrac 53\\\\\implies n = \pm1.67[/tex]
PLEASE 100 POINTS AND BRAINLIEST IF U DO IT ALL PLSSSSS I NEED HELP!!!PLSSSSSS HELP PLSSSSS
Applying the volume of a rectangular prism, the following are determined:
A & G has a solution of 120.
B & F: 714
C & E: 56
D & H: 9.5
What is the Volume of a Triangular Prism?Volume = base area × height of prism = 1/2(bh) × H
A. Volume = 1/2(bh) × H = 1/2(6)(8) × 5 = 120 units³
B. Volume = 1/2(bh) × H = 1/2(6)(14) × 17 = 714 units³
C. Volume = 1/2(bh) × H = 1/2(12)(8) × x = 2,688 units³
48x = 2,688
x = 2,688/48
x = 56 units (height of the prism)
D. Volume = base area × height of prism
Plug in the given values
27.36 = base area × 2.88
27.36/2.88 = area of triangular base
area of triangular base = 9.5 units².
E. Volume = 1/2(bh) × H = 1/2(8)(15) × x = 3,360 units³
60x = 3,360
x = 3,360/60
x = 56 units (height of the prism)
F. Volume = 1/2(bh) × H = 1/2(17)(4) × 21 = 714 units³
G. Volume = 1/2(bh) × H = 1/2(3)(5) × 16 = 120 units³
H. Volume = 1/2(bh) × H = 1/2(1.9)(2) × 5 = 9.5 units³
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Solve the following inequality.
3x+5<6x-1
Answer
x > 2
Step-by-step explanation:
Isolate the variable by dividing each side by factors that dont contain the variable
Peter brought chocolate and vanilla cupcakes to school for his birthday. 2 students picked a vanilla cupcake and 23 students picked a chocolate cupcake. What percentage of the students picked a vanilla cupcake?
Answer:
8%
Step-by-step explanation:
Add 2 and 23 together to get 25.
Divide 2 by 25 to get 0.08.
Covert 0.08 into percentage: 8%
( marking right as brainliest and 5.0 star! ) Seaira measures and records the lengths, in feet, of 9 lizards. The line plot below shows the information she records, based on the line plot what is the difference between the lengths in feet, of the longest lizards and the shortest lizards?
Answer:
5/8
Step-by-step explanation:
The longest lizard there is, is 3/4 feet. The shortest lizard is 1/8. The equation to solve this is 3/4 - 1/8. The answer to this is 5/8. I hope this helps :)
Suppose the McCall family wants to rent a truck for a day. They have a choice of two truck rental companies. After how many miles are the cost at the two companies equal?
if explanation is given with steps I will give brainliest
Company A: $20 per day plus $ .70 per mile
Company B: $45 per day plus $ .25 per mile
Answer:
the trip is 10 miles long
Step-by-step explanation:
im sorry i dont know the steps
can anyone help me find the area pls ty
Which graph shows a proportional relationship between x and y?
A)
B)
C)
D)
Answer:
C
Step-by-step explanation:
If the graph of a relationship is a line or a ray through the origin, then it is proportional.
The line in graph C goes through the origin (0,0)
Ricardo has a bag of mixed fruit snacks. In the bag, there are 12 cherry fruit snacks and 18 strawberry fruit snacks. What is the ratio of strawberry to cherry?
A.
3:2
B.
1:12
C.
2:3
Answer:
18:12 = A. 3:2
Step-by-step explanation:
Because they are equivalent ratios, they are the same, it also said ratio of strawberries to cherries so I put it in that order.
Can I please have branliest
okay thank you have a good day
Eight meters is equal to how many centimeters
Answer:
800 Cm
Step-by-step explanation:
bro typa question is that its common sense that 100 cm = 1 meter
Surface area and volume of cone
The surface area and the volume of the cone is 816.4 km² and 7536 km³ respectively.
What is volume?Volume is the capacity of an object.
To calculate the surface area and volume of the cone shown above, we use equation 1 and equation 2 respectively.
Formula:
S = πr√(r²+h²)............. Equation 1V = πr²h.................. Equation 2Where:
S = Surface area of the coneV = Volume of the coner = Radius of the base of thye coneh = Vertical height of the cone.From the diagram,
Given:
r = 10 kmh = 24 kmπ = 3.14Substitute these values into equation 1 and equation 2 respectively.
S = 3.14×10[√(24²+10²)S = 31.4(√676)S = 31.4×26S = 816.4 km²Also for the volume of tyhe cone
V = 3.14×10²×24V = 7536 km³Hence, The surface area and the volume of the cone is 816.4 km² and 7536 km³ respectively.
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Find the area of the semicircle. Round your answer to the nearest hundredth.
The number of Smart TVs owned by residents in Picayune increased by 25% this year. Assuming that the 824 Smart
TVs owned last year are still being viewed, what is the total number of Smart TVs in Picayune this year?
A)
206
B)
618
942
D)
1,030
Answer:
25% of 824
25/100 × 824
206
New prices of the TV is
824+206= 1030
if each polygon has 12 sides and each side length was 20 cm what is the area
Answer: approximately 4478.46096908264 square cm.
==========================================================
Explanation:
I'm assuming this is a regular 12-sided polygon
The area formula for regular polygons is
[tex]A = 0.25n*s^2*\cot(180/n)[/tex]
where in this case we have n = 12 sides and each side is of length s = 20
So,
[tex]A = 0.25n*s^2*\cot(180/n)\\\\A = 0.25*12*(20)^2*\cot(180/12)\\\\A = 0.25*12*(20)^2*\cot(15)\\\\A = 0.25*12*(20)^2*\frac{1}{\tan(15)}\\\\A \approx 4478.46096908264\\\\[/tex]
The area of this regular polygon is approximately 4478.46096908264 square cm.
Make sure your calculator is in degree mode when computing that value of cot(15) or 1/tan(15).
Carol's last credit card statement said that she had an account balance of -$118. Which of the following account balances represents a debt greater than Carol's?
A: -157
B: $157
C: $79
D: -$79
Answer: A. -$157
Step-by-step explanation:
This is would be much more in debt for his credit card statement, it would take him longer to pay off.
Find the probability of the event.
A class has seven students. What is the probability that exactly four of the students were
born on a weekday (Monday through Friday)? (round to the nearest thousandths when
needed)
Which of the following is the sum of 1/2 and -2/3
-1/6
hope it helps...!!!
Divide. 8,375 ÷ 45 number and remainder
Answer: 186 with a remainder of 5.
Method One:
See attached for my work, I used long divison.
Method Two:
We will use a calculator to find the value, then multiply the value (without the decimals) by the divisor. Lastly, we will subtract. This makes more sense with the work:
8,375 ÷ 45 = 186.11111111
186 * 45 = 8,370
8,375 - 8,370 = 5
Carlos wrote the number 52,700,000 in scientific notation. Which number did he write?
Answer:
5.27 × 10⁷ is the scientific notation for 52,700,000.
How many two-digit, positive integers can be formed from the digits 1, 3, 5, and 9, if no digit is repeated?
24
16
12
Answer:
12
Step-by-step explanation:
Using Permutation Formula :
⁴P₂4! / 2!4 x 3 x 2! / 2!4 x 312