Answer:
function defined on different intervals by different domain rules
hope it helps
The terms absolute value, continuous function, step function, and piecewise-defined function are matched with their respective definitions: the absolute value measures distance from zero, a continuous function has a graph without breaks, a step function has a graph with horizontal steps, and a piecewise-defined function has different rules for different intervals.
Matching Vocabulary to Definitions
Let's match each mathematical term to its correct definition:
Absolute value - This is the function whose output equals the input for non-negative numbers, and whose output is the opposite of a negative input. It can be thought of as the distance from zero on the number line, regardless of direction.
Continuous function - A function whose graph has no breaks is known as continuous. It means you can draw the function without lifting your pen off the paper, indicating it has no jumps or holes.
Step function - Such a function has a graph that consists of horizontal line segments. The value of the function changes in 'steps' rather than smoothly.
Piecewise-defined function - When a function is defined on different intervals by different domain rules, it is known as a piecewise-defined function. It's like having multiple functions strung together each applicable to different parts of the domain.
Tomas Gomez's gross weekly pay is $750. What amount is deducted weekly for Social Security taxes, if the tax rate is 6.2%?
$41.85
$962.55
$52.70
$46.50
Final answer:
The amount deducted weekly for Social Security taxes from Tomas Gomez's gross weekly pay of $750 at a tax rate of 6.2% is $46.50.
Explanation:
The question relates to calculating deductions for Social Security taxes from Tomas Gomez's weekly pay. To calculate the amount deducted weekly for Social Security taxes at a tax rate of 6.2%, you multiply the gross weekly pay by the tax rate.
Gross Weekly Pay: $750
Social Security Tax Rate: 6.2%
Calculation: $750 * 6.2% = $750 * 0.062 = $46.50
Thus, the amount deducted weekly for Social Security taxes from Tomas Gomez's gross pay is $46.50.
Find the value of x for which line a is parallel to line b
Answer:
20
Step-by-step explanation:
The question tells us that line a is parallel to line b (even if they don't seem to be in the image).
∠8 = ∠4 and ∠5 = ∠1 since line t crosses the parallel lines.
We are given ∠4 = 3x and ∠5 = 6x.
Since we know ∠8 = ∠4 , we can then say
∠8 = 3x and ∠5 = 6x
Since ∠8 and ∠5 are complementary and combined they form a flat angle of 180 degrees, we can say:
3x + 6x = 180
9x = 180
x = 20
Angle A is 5x-15. Angle B is 2x+21. Solve for x then find the measure for Angle B
To find the measure of Angle B, solve the equation 5x - 15 = 2x + 21, which gives x = 12. Then, substitute x back into the expression for Angle B to get 2(12) + 21 = 45°. Thus, Angle B measures 45°.
Solve for x and find the measure of Angle B
To solve for x and find the measure of Angle B, follow these steps:
Set the expressions for Angle A and Angle B equal to each other:Now, substitute x back into the expression for Angle B:
Angle B = 2x + 21
= 2(12) + 21
= 24 + 21
= 45°
Therefore, the measure of Angle B is 45°.
Which of the following best represents Pon the
2-10
NEXT QUESTION
Answer:
[tex]2*10^{-1}[/tex]
Step-by-step explanation:
From 0 to 1, there are 5 units, so each of the lines are 1/5.
Hence, it is 0, 1/5, 2/5, 3/5, 4/5, 1
The point P is the first line, so that is 1/5, or in decimal, 0.2
Now we check all the options:
First Choice: 2 ^ -1 = 1/2^1 = 1/2 NO
Second Choice: 2 ^ 0 = 1 (anything to the power 0 is 1) (NO)
Third Choice: 2 ^ 1 = 2 (NO)
Fourth Choice: 2 * 10 ^ -1 = 2 * 1/10 = 1/5 or 0.2 (RIGHT)
So, last choice is correct.
PLEASE HELP 12 POINTS
Answer:
153.86
Step-by-step explanation:
To find the area the equation is pi* radius squared
so it's 3.14*7 squared it's
3.14*49
The answer is 153.86
What is the value of x?
Answer:
x = 3Step-by-step explanation:
Look at the picture.
We have the triangles 45° - 45° - 90° and 30° - 60° - 90°.
The sides of those triangles are in ratio:
1 : 1 : √2 and 1 : √3 : 2
Therefore
If AC = 6√2 then AB = BC = 6
If BC = 6 then x = 6 : 2 = 3
Ashley runs a hardware store. She has decided to apply a markdown of 15% to one item in order to draw customers into the store, and she will apply a markup of 10% to three different items, which she hopes the customers will purchase after purchasing the marked-down item. She has chosen four candidates for this process: a power drill with an initial price of $51.49, a ceiling fan with an initial price of $64.79, a miniature circular saw with an initial price of $45.99, and a screwdriver set with an initial price of $37.39. After applying the changes, the total cost of purchasing one of each item is $3.77 more than it was before applying the changes. Which item was marked down?
a.
power drill
b.
ceiling fan
c.
circular saw
d.
screwdriver set
Answer:
correct answer is option b.
Step-by-step explanation:
so Ashley has markdown one item by 15%
and mark up other items by 10% to get $3.77
assuming she marked ceiling fan mark down by 15%
if each item is sold
= 0.85 × $64.79 +1.1 × $51.49 +1.1 × $45.99 + 1.1 × $37.39
= $203.4285
profit
= $203.4285 - $64.79 -$51.49 - $45.99 -$37.39
=$3.7685 ≅$3.77
hence ceiling fan price will be draw down by 15%
hence correct answer is option b.
The item that was marked down was the b. ceiling fan, from $64.79 to $55.07.
What are markdown and markup?A markdown reduces the cost or price of an item by the percentage markdown.
A markup, on the other hand, increases the cost of the item.
Data and Calculations:Markdown = 15%
Markup = 10%
Items Prices
Power drill $51.49
Ceiling fan 64.79
Circular saw 45.99
Screwdriver set 37.39
Total price $199.66
Increase in the price = $3.77
New price = $203.43 ($199.66 + $3.77)
Decision:Most likely, Ashley will mark down the Ceiling fan to attract customers to purchase other items.
Therefore, the new prices after applying the changes will be:
Items Prices Markup/down
Power drill $51.49 $56.64 ($51.49 x 1.1)
Ceiling fan 64.79 55.07 ($64.79 x 0.85)
Circular saw 45.99 50.59 ($45.99 x 1.1)
Screwdriver set 37.39 41.13 ($37.39 x 1.1)
Total price $199.66 $203.43
Comparison of new total price with old total price:New total price = $203.43
Old total price = $199.66
Increase in cost = $3.77 ($203.43 - $199.66)
Thus, the item that was marked down was the b. ceiling fan.
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find the vertex and the y-intercept of the graph of y = -x^2 + 14x - 47
Answer:
(7,2)
y= -47 or (0,-47)
Step-by-step explanation:
You can use a graphing calculator to find the vertex and y intercept
The coordinates of the vertex are - V(7, 2) and the y - intercept will have coordinates - Y(0, - 47).
What is Parabola?A parabola is a curve which forms by joining all the points which are at an equal distance from a fixed point (the focus) and a fixed straight line (the directrix).The previous section shows that any parabola with the origin as vertex and the y axis as axis of symmetry can be considered as the graph of a function - f(x) = ax² with a ≠ 0.Given is the following equation -
- x² + 14x - 47
We can write the vertex as -
[tex]{\displaystyle V=\left(-{\frac {b}{2a}},{\frac {4ac-b^{2}}{4a}}\right)}[/tex]
So, we can write -
V = (-14/-2, {4 x -1 x -47 - 196}/{-4})
V = (7, 2)
and the point of the parabola intersecting the y - axis has coordinates -
(0, c)
(0, - 47)
Therefore, the coordinates of the vertex are - V(7, 2) and the y - intercept will have coordinates - Y(0, - 47).
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The volume of a rectangular prism has 5376 cubic inches the prism is 14 in long and 16 in wide how tall is the prism
Answer:
The height of the prism is [tex]24\ in[/tex]
Step-by-step explanation:
we know that
The volume of the rectangular prism is equal to
[tex]V=LWH[/tex]
In this problem we have
[tex]V=5,376\ in^{3}[/tex]
[tex]L=14\ in[/tex]
[tex]W=16\ in[/tex]
substitute in the formula and solve for H
[tex]5,376=(14)(16)H[/tex]
[tex]H=5,376/[(14)(16)][/tex]
[tex]H=24\ in[/tex]
Please help. I don't understand this...
Answer:
Y=-2.9x+120
Step-by-step explanation:
The most simple way to solve is plug any x value into each equation and see if it works
Answer:
2nd option choice or third
a Square prism with base length 7 m and height 15 m
the answer is:
Area =518
Volume =735
hope this helps you good luck!!
PLEASE HELP ASAP! I NEED HELP!
3. Remy is participating in a bowl-a-thon to benefit the local hospital. Each sponsor will pay Remy $2 plus $0.10 per pin, x, that he knocks down. Write an equation to show how much Remy will raise per sponsor, B, for knocking down x pins.
Answer:
[tex]y=B(2+0.1x)[/tex]
Step-by-step explanation:
B = number of sponsors
x = number of pins
Equation :
[tex]y=B(2+0.1x)[/tex]
log3 (x+1)+log3 2x= log3 (3x+1)
Answer:
hello : x=1
Step-by-step explanation:
look this solution :
???add up the sides?????
Answer:
PR = 20
Step-by-step explanation:
The perimeter is the sum of the 3 sides, thus
4z + z + 3 + 3z + 2 = 45 ← simplify left side
8z + 5 = 45 ( subtract 5 from both sides )
8z = 40 ( divide both sides by 8 )
z = 5
PR = 4z = 4 × 5 = 20
Answer:
40
Step-by-step explanation:
Using the triangle perimeter formula [P=2(l) + 2(w) / 2]:
45 = 2 (z + 3) + 2 (3z + 2) / 2
45 = 2z + 6 + 6z + 4 / 2
45 = 8z + 10 / 2
45 = 4z + 5
40 = 4z
z = 10
PR
4z
4 (10)
40
Please help! I need to know the surface area of this! I will mark brainliest!
the assumption here, being that it's a square pyramid, thus its base is a square, namely a 6x6, Check the picture below.
notice, the pyramid has four triangular faces with a height of 9 and a base of 6, and the squarish base, so we can simply get the area of each of those figures and sum them up.
[tex]\bf \stackrel{\textit{area of four triangles}}{4\left[\cfrac{1}{2}(6)(9) \right]}+\stackrel{\textit{area of base}}{(6\cdot 6)}\implies 108+36\implies 144[/tex]
Write the algebraic expression that matches each graph (pictures are not drawn to scale!!):
WILL GIVE 20 POINTS AND BRAINLIEST!!!!!
Answer:
y = -|x| +3
Step-by-step explanation:
Answer:
-/x/-3
Step-by-step explanation:
Use the coordinates of the plotted points to complete the calculation below. Pay attention to negative signs
answer:
-1/2
explanation
1-2 / 4-2 = -1/2
Slope between two points
[tex](x_{1},y_{1}) \text{and},(x_{2},y_{2}) \text{is equal to}\\\\\text{and}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{1-2}{4-2}\\\\=\frac{-1}{2}[/tex]
Option D
[tex]\frac{-1}{2}[/tex]
Marco took out an unsubsidized student loan for $20,000 which he will start paying in four years after he graduates if the interest rate is 4.2% what is the amount he will or once he graduates
Answer:
I'm going to assume that this is compound interest, as simple interest in this case would not make sense.
Let A be the final amount ( in this case, after 4 years). A = 20,000(1+0.042/12)^12*4. In this formula, I am assuming that the interest compounds 12 times a year, or every month. I am also assuming that he pays it off once he hits the 4-year mark.
If the assumptions are correct, he would be paying $23651.79 at the 4-year mark.
Step-by-step explanation:
Final answer:
Marco will owe approximately $23,521.93 on his unsubsidized student loan after graduation, calculated using the future value formula for a loan with compounded interest.
Explanation:
To calculate the amount Marco will owe after he graduates, we need to apply the formula for the future value of a loan when interest is compounded annually and no payments are made until after a certain period. Since Marco's unsubsidized student loan does not require payments while he is in school, the interest will be capitalized and added to the principal amount of the loan.
The formula for future value FV of a present value PV after n periods at an interest rate r is:
FV = PV * (1 + r)ⁿ
Where:
PV is the initial loan amount ($20,000)
r is the annual interest rate (4.2% or 0.042 as a decimal)
n is the number of periods (years in this case) before he starts repaying the loan (4 years)
Using the formula, we get:
FV = $20,000 * (1 + 0.042)⁴
FV = $20,000 * (1.042)⁴
F = $20,000 * 1.1760965435
FV = $23,521.93
Thus, Marco will owe approximately $23,521.93 once he graduates, before he starts making any payments on the loan.
For each given pair of functions, multiply or divide as instructed. Be sure to show all the steps
required to write your answer in simplest form. Review the rubric to see how your work will be
graded.
1) f(x)=2x
g(x)=3x^3
f(x)/g(x)=?
[tex]\frac{f(x)}{g(x)} =?[/tex]
Since you know f(x) = 2x and g(x) = 3x^3, you can substitute that into the function
[tex]\frac{f(x)}{g(x)} =?[/tex]
[tex]\frac{2x}{3x^3} =?[/tex]
When a variable(x or y) with an exponent is divided by another variable with an exponent, you subtract the exponents, only if the variables are the same.
For example:
[tex]\frac{x}{y}[/tex] Since the variables on the top and bottom are not the same, you can't simplify it (or its already simplified)
[tex]\frac{x^3}{x^2} =x^{3-2} =x^1[/tex]
[tex]\frac{y^5}{y^7}=y^{5-7}=y^{-2} = \frac{1}{y^2}[/tex] (when an exponent is negative, you move it to the other side of the fraction to make the exponent positive)
[tex]\frac{2x}{3x^3} =?[/tex]
[tex]\frac{2x}{3x^3}= (\frac{2}{3})x^{1-3}= (\frac{2}{3})x^{-2} = (\frac{2}{3})\frac{1}{x^2}[/tex] Since you can't simplify 2/3, you get:
(not sure if this is how it should look ---> (2/3)x^(1-3) but i'm assuming it is)
[tex]\frac{2}{3x^2}[/tex]
Zara is serving a fresh pie.she starts by cutting the pie in half and then cuts each half into 4 equal pieces what fraction of the whole pie is each piece
Answer:
[tex]\boxed{\frac{1}{8}}[/tex]
Step-by-step explanation:
You are starting with ½ pie. Then you cut it into four pieces.
You want to evaluate ½ ÷ 4
Step 1. Treat the integer as a fraction
[tex]\frac{1}{2}\div{\frac{4}{1}}[/tex]
Step 2. Invert the divisor and change divide to multiply
[tex]\frac{1}{2}\times{\frac{1}{4}}[/tex]
Step 3. Multiply numerators and denominators
[tex]\frac{1}{2}\times{\frac{1}{4}} = \mathbf{\frac{1}{8}}\\\\\text{Each piece is } \boxed{\mathbf{\frac{1}{8}}} \text{ of a whole pie.}[/tex]
Answer:
1/8
Step-by-step explanation:
(13 points) asap!! please help!!!!
Answer:
(-1,4)(1,4)
2
Step-by-step explanation:
One kilogram of cheese costs £4.90How much would 400g cost?
Answer:
£ 1.96
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
1 kg = £ 4.90
( ÷ 10 )
100 g = £ 0.49
( × 4 )
400 g = £ 1.96
Answer:
£1.96
Step-by-step explanation:
1kg = 1000g
1 kg = £4.90
1000g = £4.90
1000g = £4.90
100 g = 4.90 ÷ 10 = £0.49
100g = £0.49
400g = 0.49 x 4 = £1.96
u(m+2)+w(m-3)=z(m-1) solve for m
Answer:
[tex]\large\boxed{m=\dfrac{3w-2u-z}{u+w-z}}[/tex]
Step-by-step explanation:
Use the distributive property: a(b + c) = ab + ac
[tex]u(m+2)+w(m-3)=z(m-1)\\\\um+2u+wm-3w=zm-z\qquad\text{subtract}\ 2u\ \text{from both sides}\\\\um+wm-3w=zm-z-2u\qquad\text{add}\ 3w\ \text{to both sides}\\\\um+wm=zm+3w-2u-z\qquad\text{subtract}\ zm\ \text{from both sides}\\\\um+wm-zm=3w-2u-z\qquad\text{distributive}\\\\(u+w-z)m=3w-2u-z\qquad\text{divide both sides by}\ (u+w-z)\neq0\\\\m=\dfrac{3w-2u-z}{u+w-z}[/tex]
Pls help me with this
Answer:
[tex]x=630[/tex]
Step-by-step explanation:
The Exponential Product rule tells us that...
[tex]x^m*x^n=x^{m+n}[/tex]
Therefore, [tex]x=1+2+3...+35[/tex].
Therefore, [tex]x=630[/tex]
Jeff made $243.75 last week. If he worked 25 hours, how much is he paid for one hour of work? Jeff made $243.75 last week. If he worked 25 hours, how much is he paid for one hour of work?
Answer:
$9.75 per hour
Step-by-step explanation:
243.75/25= 9.75
Hope this helps you out!
Answer:
Jeff is paid $9.75 for one hour of work.
Step-by-step explanation:
Jeff made last week = $243.75
He worked 25 hours for a week.
We have to calculate his pay per hour, so we divide his total pay by the time he worked.
total pay ÷ time he worked ( in hours)
pay per hour = 243.75 ÷ 25 = $9.75/hour
Jeff is paid $9.75 for one hour of work.
Hall is baking cookies. The diameter of each cookie is 6 centimeters.
What is the area of each cookie (use 3.14 for pi and round to nearest
tenth)?
Area of each cookie is approximately 28.3 cm2.
The area of a circle can be calculated using the formula A = πr2. Given that the diameter of each cookie is 6 centimeters, the radius would be half of the diameter, which is 3 centimeters. Plugging in the values, we get: A = 3.14 x (3 cm)2 = 3.14 x 9 = 28.26 cm2. Rounded to the nearest tenth, the area of each cookie is approximately 28.3 cm2.
David borrowed $2500 from his local bank. The yearly interest rate is 8%. If David pays the full principle and interest in the first year of the loan, how much money will he pay to the bank?
Answer:$2700
Step-by-step explanation: Really depends on the kind of interest, but you would take the initial amount, and multiply it by the APR for the amount of interest, then add the interest to the initial amount.
To repay the full principle and interest in the first year of the loan with an interest rate of 8%, David borrowed $2500 from his local bank, would need to pay a total of $2700 to the bank.
Explanation:To answer your question, we first need to calculate the interest David needs to pay. The formula used to calculate the interest on a loan is: Principal sum x Annual interest rate. David's principal sum is $2500 and the annual interest rate is 8%.
Here's the calculation step-by-step:
Convert the interest rate from a percentage to a decimal by dividing it by 100. So, 8% becomes 0.08.Multiply the principal sum by the interest rate: $2500 * 0.08 = $200.The total amount of money he will pay in the first year is the principal sum plus the interest, which is: $2500 + $200 = $2700.So, if David pays the full principle and interest in the first year of the loan, he will pay a total of $2700 to the bank.
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If you miss your ex and he doesn't know should you start talking to him again or stay friends for a while to see how things go?
Answer:
Stay friends. Make him think you are over him.
Step-by-step explanation:
This will make him question if maybe you have found someone else. An opportunity to get back together might pop up out of it.
Answer:
Honestly as a boy I think that you should start talking to him again.
Step-by-step explanation:
Like we cant read minds. If you miss him then maybe if he sees that u have feelings for him then maybe yall can work things out. Also it depends on the boy. What type is he. and it depends on you. what type of girl are you. If you like can I please get brainliest
If a=i-2j and b= 2i - xj are parallel, then x is.....
a) 4 3 2 ) 2 d 4.
Answer:
x = 4
Step-by-step explanation:
a = i-2j
b = 2i-xj
1 = k•2
-2 = k•(-x)
=> 1/2 = k
=> (-2)/(-x) = k
=> 1/2 = (-2)/(-x) => 1/2 = 2/x => x = 4
Solve and graph
1. 3x-7>5
2. -1y<3
Answer:
1. x>4
2.y>-3