Answer:
\(x = 120 \times \cos(45) - 0 = 120 \times 0.7 = 84 \\ y = 120 \times \sin(45) - 150 = 84 - 150 = 64\)
What is the end behavior asx --> infinity?
As the coefficient of the cubic polynomial is positive its behavior as
x ⇒ ∞ is (D) y ⇒ ∞.
What is the end behavior of a polynomial?A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.
The graph's final behavior is determined by a polynomial function's degree and leading coefficient.
We know a polynomial end behavior is determined by the degree of the polynomial.
Given a function is a cubic polynomial which is of degree 3 and the coefficient is positive.
As the coefficient is positive the function f(x) will reach infinity as x approaches infinity.
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Part A: Maci made $170 grooming dogs one day with her mobile dog grooming business. She charges $60 per appointment and earned $50 in tips. Write an equation to represent this situation and solve the equation to determine how many appointments Maci had.
Part B: Logan made a profit of $235 as a mobile groomer. He charged $75 per appointment and received $40 in tips, but also had to pay a rental fee for the truck of $10 per appointment. Write an equation to represent this situation and solve the equation to determine how many appointments Logan had.
Maci and 2 appointments and Logan had 3 appointments.
How many appointments did Maci and Logan have?The linear equation that represents the total amount earned by Maci is:
Total amount earned = (amount per appointment x number of appointments) + tips
$170 = ($60 x a) + $50
$170 = $60a + $50
$170 - $50 = $60a
$120 = $60a
a = $120 / $60
a = 2
The linear equation that represents the total amount earned by Logan is:
Profit = total revenue - total cost
Profit = (fee per appointment x number of appointments) + amount received in tips - (rental fee x number of appointments)
$235 = ($75 x a) + $40 - ($10 x a)
$235 = $75a + $40 - $10a
$235 = $65a + $40
$235 - $40 = $65a
$195 = $65a
a = $195 / 65
a = 3
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Consider the two triangles shown below. Which of the triangle congruence theorems could be used to prove the triangles congruent without establishing any additional information?
A: SAS
B: SSA
C: SSS
D: HL
By HL congruence, triangle ABC congruent to triangle DEF. Therefore, option D is the correct answer.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Consider the given triangles as ABC and DEF.
From the given triangles,
AC=DF=14 in.
BC=EF=20 in.
∠A=∠D=90°
The Hypotenuse-Leg (HL) Triangle Congruence Theorem is a special case that allows you to show that two right triangles are congruent. If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
By HL congruence, ΔABC ≅ ΔDEF
Therefore, option D is the correct answer.
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25 rays to4 ÷ 5 rays to3
Answer:
\( \frac{ {25}^{4} }{ {5}^{3} } \\ = \frac{ { {5}^{2} }^{4} }{ {5}^{3} } \\ = \frac{ {5}^{8} }{ {5}^{3} } = {5}^{5} \\ thank \: you\)
Harper's car used 9 gallons to travel 171 miles. How many miles can the car go for each gallon of gas?
Answer:
Step-by-step explanation:
7
An investor wants to save money to purchase real estate. She buys an annuity with yearly payments that earn 5.3% interest compounded annually payments will be made at the end of each year find the total value of the annuity in 16 years if each yearly payment is 693.
The total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.
To calculate the total value of the annuity in 16 years, we can use the formula for the future value of an annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV is the future value of the annuity,
P is the yearly payment,
r is the interest rate per compounding period, and
n is the number of compounding periods.
In this case, the yearly payment (P) is $693, the interest rate (r) is 5.3% or 0.053, and the number of compounding periods (n) is 16.
Let's substitute these values into the formula and calculate the total value of the annuity:
FV = 693 * ((1 + 0.053)^16 - 1) / 0.053
FV = 693 * (1.053^16 - 1) / 0.053
Using a calculator, we can evaluate the expression inside the parentheses:
1.053^16 ≈ 1.9738
Substituting this value back into the formula:
FV = 693 * (1.9738 - 1) / 0.053
FV = 693 * 0.9738 / 0.053
FV ≈ 12739.62
Therefore, the total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.
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PASAGUTAN PO NEEDED NA PO
MATH CHALLENGE: Read and solve. Given the following scenarios, tell which of the
four basic operations is involved.
A frog is at the bottom of a 15
m hole. During the day, it climbed
up 5 m but slid down 2 m at night.
How many days will it take for the
frog to climb up the hole?
Answer:
5 days I think
Step-by-step explanation:
1 day =5-2
=3
2 day =3+5
=8-2
=6
3 day =6+5
=11-2
=9
4 day =9+5
=14-2
=12
5 day =12+5
=17
The frog is now out on day five the hole is 15m tall
The expression x−y equals 0.7 if x and y have certain values. Evaluate the following expressions with the same values of x and y. What is y−x
Answer:
-0.7
Step-by-step explanation:
\(x-y=0.7\)
You can choose any digits you wish for \(x\) and \(y\) but the difference must be 0.7. I chose 1.0 and 0.3.
\(x=1\\y=0.3\\x-y=0.7\\\\y-x=\\0.3-1=\\-0.7\)
Which function has the same range as f (x) = negative 2 StartRoot x minus 3 EndRoot + 8?
g(x) = -2√x + 8 is the function that has the same range as f(x) = -2√(x - 3) + 8. Both functions have the range of y ≤ 8
The function that has the same range as f(x) = -2√(x - 3) + 8 is g(x) = -2√x + 8. Both functions have the range of y ≤ 8.There are a few steps involved in determining which function has the same range as f(x) = -2√(x - 3) + 8. The range of a function refers to all the possible output values that the function can produce.Let's begin by examining the original function:f(x) = -2√(x - 3) + 8The square root symbol (√) implies that x-3 must be greater than or equal to 0. If x-3 is negative, then the function would produce an imaginary result.
Let's solve for x when f(x) = 0:0 = -2√(x - 3) + 8-8 = -2√(x - 3)4 = √(x - 3)16 = x - 3x = 19This tells us that the x-value that produces an output of 0 is x = 19. To determine the range, we need to find the maximum and minimum output values. We can use a graphing calculator or sketch a graph to determine the shape of the function and the range.The shape of the function suggests that the range is y ≤ 8, which means that the maximum value of the function is 8. This tells us that any function with the same maximum output value of 8 will have the same range as f(x).
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help me please
Indicate the method you would use to prove the two triangles. If no method applies, enter "none".
AAS
SSS
NONE
SAS
ASA
Based on the information given, we know that the two triangles have two pairs of congruent angles. This is sufficient to prove that the two triangles are congruent using the AAS (Angle-Angle-Side) postulate. Therefore, the method I would use to prove the two triangles congruent is **AAS**.
I need help with
7\4+8\3=
Answer:
4\(\frac{5}{12}\) or \(\frac{53}{12}\)
Step-by-step explanation:
I hope this helps!
8.73E16 in standard form
Answer:
87,300,000,000,000,000
Step-by-step explanation:
The E16 is a way to write ×10¹⁶ that is used by some computers, spreadsheets, and calculators. As with any decimal number, the exponent of 10 tells you the number of decimal places between the place with that value and the decimal point.
8.73E16 = 8.73×10¹⁶ = 87.3×10¹⁵ = 87.3 × 1,000,000,000,000,000
= 87,300,000,000,000,000
_____
Some places, the "standard form" is 8.73×10¹⁶.
2. What is equivalent to the value of the complex number
(1 Point)
5i2
The equivalent value of the complex number 5i² will be -5.
What is a complex number?The number can be written in the form of a+bi and is called a complex number. The complex number consists of two parts first is the real part and the second is the imaginary part.
Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.
Given complex number is 5i². The equivalent expression can be written as:-
E = 5i²
E = 5 x ( -1 )²
E = 5 x -1
E = -5
Therefore, the complex number 5i² has an equivalent value of -5.
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Mark on the number line with a cross
What is the length of a radius of the circle represented by the equation below?
x2 + y2 - 4x – 4y + 4 = 0?
Answer:
2
Step-by-step explanation:
Given the circle: \(x^2 + y^2 - 4x - 4y + 4 = 0\)
To determine the length of the radius, we complete the square.
Step 1: Subtract 4 from both sides
\(x^2 + y^2 - 4x - 4y + 4 -4= 0-4\\x^2 + y^2 - 4x - 4y = -4\)
Step 2: Divide the coefficient of x and y by 2, square it and add it to both sides
\(x^2 - 4x+(-2)^2+ y^2 - 4y+(-2)^2 = -4+(-2)^2+(-2)^2\)
Step 3: Factorize the Left Hand side and simplify the Right Hand side.
\((x-2)^2+ (y-2)^2 = 2^2\)
Comparing with the standard form of the equation of a circle
\((x-h)^2+ (y-k)^2 = r^2\)
r=2
Therefore, the radius of the circle is 2.
helppp it's urgent and I don't understand dhow to do this please.
Answer:
i) Consecutive interior angles
ii) Supplementary angles
iii) The two oars are parallel by consecutive interior angles theorem
Step-by-step explanation:
i) m∠1 and m∠2 lie between two line and on the same side of the line passing through the two lines. Therefore, they are consecutive interior angles
ii)x = 10
m∠1 = 6x + 18
= 6(10) + 18
= 60 + 18
= 78
m∠2 = 9x + 12
= 9(10) + 12
= 90 + 12
= 102
m∠1 + m∠2 = 72 + 108 = 180
Since m∠1 and m∠2 add to 180, they are supplementary angles.
iii) The two oars are parallel
consecutive interior angle theorem:
If a transversal cuts through two line and the consecutive interior angles are supplimentary, then the two lines are parallel
Write an equation of the line that passes through (−1,4) and is perpendicular to the line shown. (will give brainliest)
Answer:
it is X-.3333 or X -1/3
Step-by-step explanation:
A supermarket is having a sale on canned foods. The sale includes 10 cans of beans for $12.50. What is the unit price per can of beans? A $0.80 C $1.75 B $1.25 D $2.25
(please show steps if you can)
thanks
Answer:
B. $1.25
Step-by-step explanation:
Sorry I didn't show the steps, but I hope this helps!
Answer:
10 cans of beans=12.50
Price per can of beans=12.50÷10
=1.25
Answer is B. 1.25
The radius of a circle is 3 feet. What is the length of a 75° arc?
Therefore , the solution of the given problem of circle comes out to be arc length 3.93 feet.
How do circles work?Every area of the plane that is separated by a specific amount from this additional point makes a circle (center). As a result, it is a curve made up of spots that are separated from one another on the surface. Additionally, it rotates similarly about the centre at every angle. Every collection of endpoints in the confined, two-dimensional sphere of a circle is uniformly spaced apart from the "centre."
Here,
A circle with a radius of 3 feet is equal to its diameter as follows:
=> C = 2πr = 2π(3) = 6π feet
Since there are 360° of angles in a circle's centre, the angle for a 75° curve is:
5/24 of a complete circle is 75/360.
Therefore, the 75° arc's extent is
5/24 × 6π = 5π/4 ≈ 3.93 feet
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HELP PLEASE!
The following inequalities form a system.
y is greater than or equal to two-thirds times x plus 2
y is less than negative one-third times x plus 1
Which ordered pair is included in the solution to this system?
(−6, −3)
(−6, −2)
(−6, 3)
(−6, 4)
The ordered pair which s included in the solution to this system of inequality y ≥ 2/3x + 2, y < - 1/3x + 1 is (-6, -2) and (-6, 3).
The correct answer option is option B and C
How to solve the system of inequality?y ≥ 2/3x + 2
y < - 1/3x + 1
Check all that applies:
(x, y) = (−6, −3)
(x, y) = (−6, −2)
(x, y) = (−6, 3)
(x, y) = (−6, 4)
It can be seen that x = -6Use this to find the value of yy ≥ 2/3x + 2
substitute x = -6 into the inequality
y ≥ 2/3(-6) + 2
y ≥ -12/3 + 2
y ≥ - 4 + 2
y ≥ - 2
(x, y) = (-6, -2)
y < - 1/3x + 1
substitute x = -6 into the inequality
y < -1/3(-6) + 1
y < 6/3 + 1
y < 2 + 1
y < 3
(x, y) = (-6, 3)
So therefore, the solution to the system of inequality is (-6, -2) and (-6, 3).
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Using the chart above, which of the following statements is true when comparing the account balances?
Did u get your answer I really need this fast
An employee worked 36 hours last week. This week, she worked 48 hours. Find the percent increase. Round to the nearest percent. O 25% increase 0 33% increase O 12% increase O 75% increase
Answer:
See below:
Step-by-step explanation:
Hello! My name is Galaxy and I will be helping you today!
We can solve this problem in two steps, one is Comprehending and another is Solving. I'll start off with Comprehending.
Comprehending
We can start off by looking at the problem, it wants us to find the percentage increase from 36 to 48. We can then find difference between 48 and 36; that would be 12.
Now that we know the increase from 36 to 48 is 12. We need to find how much percent 12 is of 36.
Now that we know what we have to do, we can start solving.
Solving
We can solve the problem by setting up and equation, but we can also just use our logic in finding it out.
Since we know that we need to find how much 12 is of 36, we can just solve for that and we will get our answer.
We can do that with one step.
\(\frac{12}{36}=0.33\)
Since it is a percent, we can multiply 0.33 by 100 and we get our answer of 33%
Write an inequality to describe the relationship between -1 2/3 and -1/4
If a video is getting 5,000 views every 10 minutes, how long will it take to reach 60,000 views?
Answer:
60,000÷5000=12
12×10=120 minutes.
Sanjay, Ajay and Anushka are employees of a company that has branches in Chennai, Bangalore and Mumbai. The company sends each of them to one of these cities at random. Let X X be a random variable that denotes the number of employees assigned to their favourite cities. If Chennai, Bangalore and Mumbai are the favourite cities of Sanjay, Ajay and Anushka, respectively, then find the possible values of X.
a. X= {0,1,2}
b. X= {0,1,2,3}
c. X= {0,1,3}
d. X= {0,[infinity]}
Answer:
c. X= {0,1,3}
Step-by-step explanation:
We have these possible outcomes:
None assigned to their favorite cities.
One assigned to their favorite city(The other two are assigned to the other's favorite city).
All are assigned to their favorite city.
Why is two not possible?
If two peooke are assigned to their favorite city, the third person necessary has to be assigned to their favorite city, as it will be the only option remaining.
So the correct answer is given by option c.
Find the unit price
9 colored pencils for $2.88
$
per colored pencil
Answer:
32 cents per color pencil
Step-by-step explanation:
well well if you divide $2.88 into 9 you'll get 32 cents
Meira is writing a children's book. On the first day, she writes
2 pages. The next day she writes 2' pages and the day after that she
writes 2¹ pages. If she keeps increasing the exponent by 1 each day,
how many more days of writing will it take her to finish 30 pages?
Show your work.
If she increases the exponent by 1 each day, she will need 3 more days.
How many more days of writing will it take her to finish 30 pages?So we know that the first day she writes 2 pages, then 2^1 pages and then 2^1 pages:
2 + 2 + 2 = 6
At this moment she has 6
And from now on, she increases the exponent by 1 each day, then the next day she writes:
2^2 = 4
Now she has 6 + 4 = 10
The next day she writes:
2^3 = 8
So now she has 10 + 8 = 18
The next day she writes:
2^3 = 16
So now she has:
18 + 16 = 34
So she will need 3 more days to finish the book.
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A person drove 30 miles per hour on a trip. If he had driven 40 miles per hour, he would have arrived 4 hours earlier. What was the distance the person drove?
Lacey filled a measuring cup with 1/2 of a cup of vegetable oil. Then she poured 1/3 of a cup of the oil into a frying pan. How much oil is left in the measuring cup?
Answer:
1/6 of a cup
Step-by-step explanation:
You're trying to figure out what 1/3 subtract 1/2 is, right?
Well first, convert both of them so they both have the same denominator.
Common Denominator = 6
So, 1/3 is 2/6 and 1/2 is 3/6 and 2/6 plus 3/6 is 5/6. Well, what's left in the cup? 6/6 subtract 5/6 is 1/6
Hope that helps!
9.2 puzzle time What is always in its house, no matter where it goes? 
only need 4,5,6, and 7
The missing value in the right triangle are
4. x = 12√2
5. x = 3√3
6. x = 11√3
7. x = 9
How to determine the missing valuesThe missing is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
4.
sin 45 = 12 / x
x = 12 / sin 45
x = 12√2
5.
sin 45 = x / 3√6
x = 3√6 sin 45
x = 3√3
6.
tan 30 = 11 / x
x = 11 / tan 30
x = 11√3
7.
cos 60 = x / 18
x = 18 cos 60
x = 9
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