Answer:
Your salary will be $62,500.
Step-by-step explanation:
This is an arithmetic sequence with first term $45,000 and common difference $2,500.
The appropriate formula is a(n) = a(1) + (n-1)d, where a(1) is the first term, n is a counter and d is the common difference.
In this particular case, a(8) = $45,000 + (8-1)($2,500) = $62,500
Your salary will be $62,500.
A function assigns the values. Your salary after completing the 8th year within the company will be $62,500.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that the starting salary will be $45,000 while the salary will increase every year by $2,500. Therefore, the function that can represent the salary after (n-1) years can be written as,
y = $45,000 + $2,500(n-1)
Now, the salary after 8th year will be,
y = $45,000 + $2,500(n-1)
y = $45,000 + $2,500(8-1)
y = $62,500
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Help with this trig math question
Answer:
8
Step-by-step explanation:
We want to evaluate the function f(x) = 3(log to the base 2 of x) + (log to the base 2 of 1/x) at x = 16.
Note that 2^4 = 16, so (log to the base 2 of 16) is 4.
Also note that 1/16 = 1/(2^4), so (log to the base 2 of 1/(2^4 is -4.
In summary, f(x) = 3(log to the base 2 of x) + (log to the base 2 of 1/x) at x = 16 is equal to 3(4) -4, or 8.
Edgar has birdbath that holds 2 gallons of water How many 1 pint containers does it take to fill birdbath? EXPLAIN
Answer:
16
Step-by-step explanation:
1 gallon is equal to 8 pints.
2 gallons is equal to 16 pints.
What is the best next step in the construction of an equilateral triangle?
Answer:
option B
Step-by-step explanation:
Use a compass to draw a circle centered at B with a radius that is length of AB.
then draw a circle centered at A with a radius that is length of AB
join the point of intersection of two circles through straight lines to point A and point B.
!
Answer with explanation:
Given a circle having center A, and radius equal to AB.
One side of equilateral Triangle = AB
We have to draw two sides which have length equal to AB.
Draw a circle having center B and radius equal to AB.The Circle will pass through center A and cuts the Original circle at P.Join AP and BP.This is the equilateral triangle that we are interested in.
The Next in the construction of an equilateral triangle is:
Option B:→ Use a Compass to draw a circle centered at B with a radius that is equal to AB.
Which of the following is a trigonometric identity?
A. cot theta + tan theta = 1
B. sec^2theta + csc^2theta = 1
C. tan^2theta = sin^2theta × sec^2theta
D. cos^2theta = sec^2theta × tan^2theta
option B is right answer
Solving Trigonometric Equations Using Inverses Quiz part 1
1. -2
2. -0.36
3. C
4. tan^2theta = sin^2theta × sec^2theta (This Question)
5. 60 degrees
6. 0.71
7. 0.09
8. 2pi/3 , 4pi/3
9. pi/4 , 5pi/4
Step-by-step explanation: I just took it...
These are the correct answers you're welcome
what is the value of x?
A: -39
B: -34
C: 26
D: - 26
E: 34
Answer:
B: -34
Step-by-step explanation:
The given angles are supplementary, so you have ...
(2x+146) + (4x+238) = 180
6x +384 = 180 . . . . . simplify
6x = -204 . . . . . . . . . subtract 384
x = -34 . . . . . . . . . . . .divide by 6
_____
Check
angle F is (2·(-34)+146)° = 78°
angle C is (4·(-34)+238)° = 102°
These angles indeed are supplementary, so the answer checks OK.
X=-34; add both expressions together and solve for x
Will someone please help me solve this !!
Answer:
∠H= 109º
∠F = 71º
∠G = 109º
Step-by-step explanation:
∠I = 71º
Interior opposite angles of parallel lines sums up to 180º.
∠H = 180 - 71 = 109º
Line IH is equal to Line FG.
∠F = ∠I
∠F = 71º
∠G = ∠H
∠G = 109º
Which descriptions from the list below accurately describe the relationship
between QRS and TUV? Check all that apply.
Answer:
There similar
Answer: Similar and Same shape
Step-by-step explanation:
I got it wrong and these were the correct answers ON G
Please help I need this answer.
Answer:
see below
Step-by-step explanation:
The images are mirrored right/left, so the reflection must be across the y-axis. That only leaves two answer choices.
If you translate ABC to the left, you will put it entirely in quadrant II, so reflection across the y-axis will put it in quadrant I. Obviously, that is not the correct sequence of transformations.
If you translate ABC 3 units to the right, it will put line AB on x=2. Then reflection across the y-axis will put that vertical segment on x = -2, exactly where corresponding segment DE is located.
The appropriate choice is the one shown below:
The variable z is directly proportional to x, and inversely proportional to y. When x is 7 and y is 7, z has the value 2. What is the value of z when x= 10, and y= 12
Answer:
z = [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
Given z is directly proportional to x and inversely proportional to y then the equation relating them is
z = [tex]\frac{kx}{y}[/tex] ← k is the constant of proportionality
To find k use the condition x = 7, y = 7 and z = 2
k = [tex]\frac{zy}{x}[/tex] = [tex]\frac{2(7)}{7}[/tex] = 2
z = [tex]\frac{2x}{y}[/tex] ← equation of proportionality
When x = 10 and y = 12, then
z = [tex]\frac{2(10)}{12}[/tex] = [tex]\frac{20}{12}[/tex] = [tex]\frac{5}{3}[/tex]
i need help asapppppppp
Answer:
Question 1 - f(x) = | x | - 2
First, let's find the 5 values requested:
x = -2 ==> | x | - 2 = | - 2 | - 2 = 2 - 2 = 0
x = -1 ==> | x | - 2 = | - 1 | - 2 = 1 - 2 = -1
x = -0 ==> | x | - 2 = | 0 | - 2 = 0 - 2 = -2
x = 1 ==> | x | - 2 = | 1 | - 2 = 1 - 2 = -1
x = 2 ==> | x | - 2 = | 2 | - 2 = 0 - 2 = -2
You can see the plotted graph attached.
Question 1 - f(x) = | x - 1 | - 1
First, let's find the 5 values requested:
x = -2 ==> | x - 1 | - 1 = | - 2 - 1 | - 1 = | - 3 | - 1 = 3 - 1 = 2
x = -1 ==> | x - 1 | - 1 = | - 1 - 1 | - 1 = | - 2 | - 1 = 2 - 1 = 1
x = 0 ==> | x - 1 | - 1 = | 0 - 1 | - 1 = | - 1 | - 1 = 1 - 1 = 0
x = 1 ==> | x - 1 | - 1 = | 1 - 1 | - 1 = | 0 | - 1 = 0 - 1 = -1
x = 2 ==> | x - 1 | - 1 = | 2 - 1 | - 1 = | 1 | - 1 = 1 - 1 = 0
You can see the plotted graph attached.
Question 14 Math Help please
ANSWER
(1,0) is a solution
EXPLANATION
The given inequality is
[tex]y \leqslant |x + 2|- 3[/tex]
We substitute the point to see which ones satisfy the inequality.
For (1,0)
[tex]0\leqslant|1+ 2|- 3[/tex]
[tex]0\leqslant 0[/tex]
This is true.
(1,0) is a solution.
For (-1-1)
[tex]- 1\leqslant | - 1 + 2|-3[/tex]
[tex]- 1\leqslant-2[/tex]
False
(-1,-1) is not a solution.
For (0,0)
[tex]0\leqslant|0+2|-3[/tex]
[tex]0\leqslant- 1[/tex]
False.
For (0,1)
[tex]1\leqslant|0+ 2|-3[/tex]
[tex]1\leqslant-1[/tex]
This is also false
Randomly selecting a seventh grader from a school that has 256 sixth graders, 225 seventh graders ,and 275 eighth graders
Answer:
225/756
Step-by-step explanation:
275+256+225
=756
We want to know what are the odds of selecting a seventh grader which is:
225/756
Someone mind helping me out? :)
Answer:
Step-by-step explanation:
Area of a circle is A = πr², and diameter of a circle is d = 2r.
d = 2r
72 = 2r
r = 36
A = πr²
A = π(36)²
A = 1296π
A ≈ 4069
Math is right about the answer
Plot 5-5i and write the number in trig form
Answer:5√2(cos(−π/4)+ isin(−π/4)) is in trig form
Step-by-step explanation:
Write the phrase "the product of 2 and a number" as a mathematical expression.
A. 2 + x
B. 2x
C. 2 – x
D. 2⁄x
Thanks! Will be marked for Brainlest if answered correctly.
answer for this question is (b)2X
The phrase "the product of 2 and a number" written as a mathematical expression is 2x
How to write algebraic expressionGiven:
The product of 2 and a number
Product means multiplication written as ×Let
The unknown number = x
So,
The product of 2 and a number
= 2 × x
= 2x
Therefore, the product of 2 and a number is written as 2x
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What is the surface area of a cube with a side length of 4 inches?
12 in2
48 in2
64 in2
96 in2
Answer:
96in^2
Step-by-step explanation:
because first find the area of two sides (Length*Height)*2 sides.
Find the area of adjacent sides (Width*Height)*2 sides.
Find the area of ends (Length*Width)*2 ends.
Add the three areas together to find the surface area.
Example: The surface area of a rectangular prism 5 cm long, 3 cm.
Answer:
96
Step-by-step explanation:
Did quiz
find the next two terms of the following sequence: 14,38,74,122,182,254
ANSWER
The next two terms are
338, 434
EXPLANATION
The given sequence is 14,38,74,122,182,254
Let us observe some pattern and use it to find the next two terms.
14+24=38
38+36=74
74+48=122
122+60=182
182+72=254
To get the next term we add 84 to 254
254+84=338
To get the next term,we add 96 to 338
338+96=434
In an election, 54% of the voters voted for a new school tax. What is the probability that a randomly selected voter did not vote for the tax? Express your answer as a percentage.
a. 46%
b. 17%
c. 15%
d. 54%
The correct answer is A. 46%
A textbook has a length of 6 inches wide inches and a width of X inches if the length of diagonal of the front covers 8 inches the length of the diagonal of the width of 7 inches find the values of XY
Answer: x=7 y=8
Step-by-step explanation:width is x and the width is 7inches
height is y and the diagonal length 8inches
Given the force field F, find the work required to move an object on the given orientated curve. F=<y,x> on the parabola y=7x^2 from (0,0) to (4,112)
[tex]y = 7 {x}^{2}[/tex]
The work done by the force field on the object moving on the parabola y=7x^2 from (0,0) to (4,112) is calculated by integrating the force along the path. The total work done is found to be 224 units of work.
To find the work done by a variable force on an object moving along a given curve, we utilize the concept of a line integral in vector calculus. Given the force field F = and the parabolic path described by y = 7x2, from point (0,0) to (4,112), we want to integrate the force field along the curve. To calculate this line integral, we parameterize the curve using x as the parameter, since y is already expressed as a function of x. We then express the force field in terms of x, evaluate the dot product of the force field and the differential of the position vector, and integrate from the start to the end of the curve.
The work, W, is found by integrating the dot product of F and dx from the initial to the final position:
W = \\int (F . dx).
In our case, the force field becomes F(x, y(x)) = F<7x2, x> = <7x2, x>. The differential displacement along the parabola, expressed in vector form, is dx = <1, 14x>dx because dy/dx = d(7x2)/dx = 14x. Thus, the infinitesimal work is dW = F .dx = 7x2 * 1dx + x * 14xdx = 21x2dx. Finally, we integrate from x = 0 to x = 4 to find the total work:
W = \\int_{0}^{4} 21x2dx = 7x3\\right]_{0}^{4 = 7 * 43 = 224.
Therefore, the work done by the force field along the parabolic path from (0,0) to (4,112) is 224 units of work.
The work required to move an object along the parabola y = 7x^2 from (0,0) to (4,112) under the force field F = <y, x> is approximately 149.33 units.
To find the work required to move an object along a curve under the influence of a force field, we can use the line integral of the force field along the curve. The line integral is given by the formula:
∫ F · dr = ∫ (F1 dx + F2 dy)
Given the force field F = <y, x> and the parabola y = 7x^2, we need to parameterize the curve to express it in terms of a single variable.
Let's parameterize the curve using x as the parameter:
x(t) = t
y(t) = 7t^2
Now, we can calculate the differential elements dx and dy:
dx = x'(t) dt = dt
dy = y'(t) dt = 14t dt
Substitute the expressions for F, dx, and dy into the line integral formula:
∫ F · dr = ∫ (y dx + x dy)
= ∫ (7t^2 dt + t * 14t dt)
= ∫ (7t^2 + 14t^2) dt
= ∫ 21t^2 dt
= 7t^3 / 3 + C
Evaluate the integral from t = 0 to t = 4:
Work = [7(4)^3 / 3] - [7(0)^3 / 3]
= (7 * 64 / 3) - 0
= 448 / 3
≈ 149.33
Therefore, the work required to move an object along the parabola y = 7x^2 from (0,0) to (4,112) under the force field F = <y, x> is approximately 149.33 units.
Helena is purchasing a house for $210000 with a 15-year fixed -rate mortgage at 4.5% interest. She has made 5% down payment . The house is valued at $200,000 and the local tax rate is 3.5% . Her homeowners insurance is $720 per year . What are her total monthly payments
Answer:
$2169.49
Step-by-step explanation:
The mortgage payment is ...
A = (210,000·0.95)(0.045/12)/(1 -(1 +0.045/12)^(-12·15)) ≈ 1526.16
The monthly set-aside for taxes is ...
3.5%·200,000/12 = 583.33
The monthly set-aside for insurance is ...
720/12 = 60
So the total of P&I + taxes + insurance will be ...
$1526.16 +583.33 +60.00 = $2169.49
Answer:
2202.72
Step-by-step explanation:
just got the answer right on the quiz
What is the domain of the function y= radical x?
Answer: [tex]x\geq0[/tex] or [tex][0,\infty)[/tex]
Step-by-step explanation:
You have the function:
[tex]y=\sqrt{x}[/tex]
The domain of the function is the set of all the possible input values that the function can has.
We know that the square root of a negative number is not defined in the Real numbers. Therefore, "x" cannot be a negative number.
Then the domain of f(x) will be:
[tex]x\geq0[/tex] or [tex][0,\infty)[/tex]
Answer:
Step-by-step explanation:
Can you write this as y = √x?
The domain of the function y = √x is [0, ∞ ). In elementary algebra, before you encounter imaginary numbers, y = √x is not defined for negative x.
The circle graph shows the distribution of age groups of people living in a city. Identify the measure of arc PR. HELP ASAP!!
Answer:
100.8°
Step-by-step explanation:
∠POR = ∠POQ + ∠QOR
∠POQ is 20% of 360° ( measure of the angles in a circle )
= 0.2 × 360° = 72°
∠QOR is 8% of 360° = 0.08 × 360° = 28.8°
Hence
arc PR = ∠POR = 72° + 28.8° = 100.8°
Simplify.
(7y)^2
Write your answer without parentheses.
Answer:
Step-by-step explanation:
(7y)² = 7²×y² = 49y²
In order to simplify the expression (7y)^2, we need to apply the exponent to both the numerical coefficient and the variable inside the parentheses. Here's how to do it step-by-step:
1. The expression (7y)^2 denotes that everything inside the parentheses is to be squared. That means we multiply 7y by itself.
2. When squaring a product, we square each factor separately. So we have to square both the 7 and the y.
3. Squaring 7 gives us 7^2, which equals 49.
4. Squaring the variable y gives us y^2.
5. Now, we multiply 49 by y^2 to combine our results.
Putting these steps together, we see that (7y)^2 simplifies to 49y^2.
The final simplified expression without parentheses is 49y^2.
A circle has a circumference of approximately 113.04 inches. What is the diameter and the radius of the circle.
Answer:
The diameter of the circle is [tex]D=36\ in[/tex] and the radius is [tex]r=18\ in[/tex]
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=\pi D[/tex]
where
D is the diameter of the circle
we have
[tex]C=113.04\ in[/tex]
substitute and solve for D
[tex]113.04=(3.14)D[/tex]
[tex]D=113.04/(3.14)[/tex]
[tex]D=36\ in[/tex]
Find the radius r
[tex]r=36/2=18\ in[/tex] -----> the radius is half the diameter
What is the equation of the line written in general form?
a.) -x + y - 2 = 0
b.) x + y - 2 = 0
c.) 2x + y - 2 = 0
this question isn't fully complete. comment a full question below and I'll try for ya ;) - Josie Annette
A car salesperson sells a used car for $8,800 and earns 5% of the sale price as commission. How many dollars does the salesperson earn in commission?
Final answer:
To calculate the commission, multiply the sale price of $8,800 by the commission rate of 5% to get a commission of $440.
Explanation:
The question is asking to calculate the commission a salesperson earns from selling a used car. The salesperson earns a 5% commission on the sale price of the car, which is $8,800. To find the commission, we multiply the sale price by the commission rate:
Sale Price = $8,800
Commission Rate = 5% (or 0.05 in decimal form)
Commission = Sale Price × Commission Rate
Commission = $8,800 × 0.05
Commission = $440
Therefore, the salesperson earns a commission of $440.
BRAINLIEST - ALGEBRA HELP! See image.
Answer:
Option a
[tex]f(x) = e^{x-1} -2[/tex]
Step-by-step explanation:
If the graph of the function [tex]y=f(x+h) +b[/tex] represents the transformations made to the graph of [tex]y= f(x)[/tex] then, by definition:
If [tex]b> 0[/tex] the graph moves vertically upwards b units.
If [tex]b <0[/tex] the graph moves vertically down b units
If [tex]h<0[/tex] The graph moves horizontally h units to the right
If [tex]h>0[/tex] The graph moves horizontally h units to the left
In this problem we have the parent function [tex]y=e^x[/tex]
We know that the parent function is translated 1 unit rigth and 2 units down.
This is:
[tex]h<0 = -1\\\\b < 0 = -2[/tex]
Finally the transformation is:
[tex]y=f(x-1) -2[/tex]
[tex]f(x) = e^{x-1} -2[/tex]
Help, with this multiple choice question?
Phillip is looking at two different jobs. One has a higher hourly pay rate, while the other
offers benefits. The first job pays $25 an hour, while the second job pays $20 an hour.
Benefits from the second job are equivalent to $100 per pay period. How many hours per
pay period will Phillip have to work in the first job to make the same as the second job,
including benefits?
a. 10
b. 14
c. 20
d. 16
he would hove to work 20 hours to meet the second job I think
To make the same total earnings at the first job as the second job (including benefits), Phillip would have to work an additional 4 hours (to account for the $100 benefits). If the workdays are 8 hours each, then for every two days (which is 16 hours) worked at job 2, Phillip would need to work an additional 4 hours at job 1, summing up to 20 hours.
Explanation:This problem is about comparing the earnings from the two jobs. For the second job, Phillip earns $20 per hour and also gets benefits equivalent to $100 per pay period.
If Phillip wants to earn the same amount in the first job (which does not offer any benefits), we calculate how many hours he would need to work to earn an additional $100 (the value of the benefits).
To do this, we divide $100 (benefits of the second job) by the first job's hourly pay rate ($25) which results in 4 hours.
So, Phillip must work an additional 4 hours to make up for the benefits. Meaning, for any given number of hours he would work at the second job, he would need to work an extra 4 hours at the first job to get the same total earnings.
Therefore, the right answer is not among the choices given because we have an extra step to add to each option. If we consider a standard 8-hour workday, working at the second job for two days gives 16 hours with an additional $100 for benefits. To make the same in the first job, Phillip would need to work, 16 hours (from the second job) + 4 hours (to compensate for the $100 benefits) = 20 hours.
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Please help!!!!!!!!!!!
Answer:
y = 51.3°
Step-by-step explanation:
tan(y) = Opp./Adj
tan(y) = 10/8
tan(y) = 1.25
y = 51.3°