Optionally you can replace 0.25 with the fraction 1/4
===================================================
Explanation:
The variable y varies directly with x, which means we have the template of y = kx for some constant k.
Plug in x = 8 and y = 2. Then solve for k
y = kx
2 = k*8
8k = 2
k = 2/8
k = 1/4
k = 0.25
Therefore, we go from y = kx to y = 0.25x
-------------
Check:
Plugging in x = 8 should get us to y = 2
y = 0.25x
y = 0.25*8
y = 2
The answer is confirmed.
All whole numbers can also be classified as
integers and rational numbers.
True
False
Answer:
True
Step-by-step explanation:
We use definitions to help us in this problem. The definition of an integer is a whole number that is not a fraction or has any fractional value. This definition includes all whole numbers, so we know that all whole numbers can be classified as integers. That's one condition done. The definition of a rational number is a number that can be written as a fraction. All whole numbers can be written as a fraction (i.e. 12/1, -3/1, 10000/1). This means that all whole numbers are also rational numbers, giving us our final answer of True.
FINAL ANSWER: True
Give the equation of the resulting function.
The function f(x)= 3^x is reflected across the y-axis
The function which results from the reflection of the given function; f(x) = 3^x is; f(x) = 3^(-x).
What is the equation of the resulting function?It follows from the task content that the function given is; f(x) = 3^x.
The function in discuss is reflected across the y-axis, hence, it follows from transformation rules that the resulting function involves multiplying x by -1 as follows;
f(x) = 3^(-1×x)
f(x) = 3^(-x).
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there is a stack of old algebra books in the library. Each book is 1 1/4 inches thick. let b represent the number of books in a stack and s(b) represent the total height of the stack in inches. what is the equation?
The equation which represents the height of the books is [tex]s(b)=\frac{5}{4} b[/tex]
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. An equation between two sums of monomials of degree 0 or 1 is known as a linear equation.
The books are stacked one above the other and each book is [tex]1\frac{1}{4}[/tex] inches thick.
So to calculate the total height of the stack we have to multiply the number of books in the stack with the thickness of each book.
The total thickness is represented in the from of a function as
s(b) and the thickness of each book is [tex]1\frac{1}{4}=\frac{5}{4}[/tex] inches
total height=[tex]\frac{5}{4}\times b[/tex]
Therefore the required equation is [tex]s(b)=\frac{5}{4} b[/tex].
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A rectangular solar panel has a length that is 12 inches shorter than 3 times its width. If the perimeter of the panel is 132 inches what are the dimensions of the panel?
Answer: 46.5 by 19.5
Step-by-step explanation:
P=perimeter of panel. L=length. W=width
L=3W-12
P=2L+2W
132=2(3W-12)+2W
132=6W-24+2W
132=6W+2W-24
132=8W-24
156=8W
W=19.5
P=2L+2W
132=2L+2(19.5)
132=2L+39
2L=93
L=46.5
46.5 by 19.5
create and equivalent expression for 12^-7 x 12^5
The required equivalent expression to 12⁻⁷ x 12⁵ is 12⁻².
Given that,
To determine the equivalent expression for 12⁻⁷ x 12⁵.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
= 12⁻⁷ x 12⁵
Simplifying
= 12⁻⁷ x 12⁵
Since, when the same value has a difference in the exponent in the product then it retains the base value and the addition of the exponent takes place.
= 12⁻⁷⁺⁵
=12⁻²
Thus, the required equivalent expression to 12⁻⁷ x 12⁵ is 12⁻².
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28% of 80 is what number?
Answer:
22.4
Step-by-step explanation:
28% of 80 = [tex]\frac{28}{100}[/tex] of 80
=[tex]\frac{28}{100}[/tex] of 80 = [tex]\frac{28}{100}[/tex]*80
cut the zeros
=[tex]\frac{28}{10}[/tex]*8
=[tex]\frac{28}{5}[/tex]*4
=[tex]\frac{112}{5}[/tex]
=22.4
What is the measure of Lx?
30°
45
x
Answer:
75 =x
Step-by-step explanation:
We can use angle addition to find the measure of angle x
30 + 45 = x
75 =x
Answer:
x = 75°
Step-by-step explanation:
x = 30° + 45°
x = 75°
Tina spent $182 on 13 pamphlet sets for her beauty shop. How much does each pamphlet set cost?
Answer:
14 dollars
Step-by-step explanation:
182 divided by 13 is 14 dollars
may starclan light ur path
The winning times for the 200-meter dash can be approximated by f(x)=-0.05577x+146.2, where x is the year what is the slope of f
The slope of f is m= -0.05577.
Given : The winning times for the 200-meter dash can be approximated by f(x) = - 0.05577x+146.2 , where x is the year.
To find : The slope of f
Solution : Using slope intercept form a linear function is represented as
y = mx+b
where, m is the slope and b is the y-intercept.
We can write the function as f(x) = - 0.05577x+146.2
Comparing with slope intercept form,
m= -0.05577 and y-intercept = 146.2
Therefore, The slope of f is m= -0.05577
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the side of a square is 9in. what is the perimeter?
Answer:
36in
Step-by-step explanation:
A square has four sides. If the length of one is 9 inches, then we multiply it by four to get 9*4 = 36in as our perimeter.
FINAL ANSWER: 36in
|3k| >30 what is the compound inequality
Answer:
k < - 10 or k > 10
Step-by-step explanation:
inequalities of the type | x | > a have solutions of the form
x < - a or x > a , then
3k < - 30 or 3k > 30 ( divide each interval by 3 )
k < - 10 or k > 10
Luis is helping to make tacos for a school fundraiser. He needs to buy tortillas. Happy Grocery sells small packs of 20 tortillas for $4.40 and large packs of 45 tortillas for $8.55. Luis has been given $48 to spend on tortillas. Fill in the blanks to complete the statements. Tortillas The unit price for the small pack is $ A per tortilla. The unit price for the large pack is $ B per tortilla.
Answer:
A. $0.22 per tortilla
B. $0.19 per tortilla
Step-by-step explanation:
A. All you gotta do is divide the money by the amount of product.
4.40 ÷ 20 = 0.22
B. All you gotta do is divide the money by the product.
8.55 ÷ 45 = 0.19
Therefore, the best pack to spend your money on would be the larger pack B.
What is the domain of the function on the graph?
all real numbers
all real numbers greater than or equal to 0
O all real numbers greater than or equal to -2
O all real numbers greater than or equal to -3
The domain of the function given on the graph is basically all numbers which are real and greater than or equal to -3.
Given a graph of a function.
We are required to choose the correct domain of the function from the options.
Function is basically a relationship between two or more variables that are expressed in equal to form. The values that we enter in the function are known as part of domain of that function and the values that we get from the function are known as part of range of that function.
Because the lowest point on x axis on which the curve starts is -3 and it continuously increases, so the domain of the function given on the graph is basically all real numbers which are greater than or equal to -3.
Hence the domain of the function given on the graph is all real numbers which are greater than or equal to -3.
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Question is incomplete as it should include the attached figure.
Help!!
Find the after-tax return to a corporation that buys a share of preferred stock at $49, sells it at year-end at $49, and receives a $4 year-end dividend. The firm is in the 21% tax bracket.
This is what I got so far:
Before-tax:
(49-49)+4 = 4,
4/49 = 0.0816,
After-tax:
0.0816 (1-021) = 0.06448 or 6.45%
Based on the calculation below, the after-tax return to the corporation is $3.16 per share or 6.44% if expressed in percentage.
How do we calculate the after-tax return?The after-tax return can be calculated using the following formula:
After-tax return = Total return * ( 100% - tax rate) .............. (1)
Where:
Total return Received = Dividend received + Change in price = $4 + ($49 - $49 ) = $4 + $0 = $4
Tax rate = 21%
Substituting the values into equation (1), we have:
After tax return = $4 * ( 100% - 21%)
After-tax return = $3.16 per share
The after-tax return can also be expressed in percentages as follows:
After-tax return in percentage = After-tax return / Share price = $3.16 / $49 = 0.06444897 = 6.44%
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A dressmaker needs to cut 18-inch pieces of ribbon from rolls of ribbon that are 6 feet in length. How many 18-inch pieces can the dressmaker cut from 5 of these rolls of ribbon?
Before you try that problem, answer the question below.
How many inches of ribbon does the dressmaker have, in total?
(on delta math)
Answer: 20 pieces, 72 inches of ribbon
Step-by-step explanation: 6/1.5=4 4x5=20 6x12= 72 inches
when two items are thrown from the same height how does it affect the two in different ways if so
The height from which any two objects is thrown affects their time of motion, the greater the height, the more time the objects spend in air and vice versa.
What is time of motion?
The time of motion of an object is the time taken for an object to travel from point of projection to the projection plane or it can be said as the time a projected object spent in air.
The time taken for an object dropped from a certain height is calculated as follows;
h = vt + ¹/₂gt²
where;
h is the height from the which the object is droppedv is the initial vertical velocity of the objectt is the time of motion of the objectg is acceleration due to gravitywhen the object is dropped from rest, v = 0
h = ¹/₂gt²
t = √(2h/g)
Thus, the height from which any two objects is thrown affects their time of motion, the greater the height, the more time the objects spend in air and vice versa.
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Evaluate the expression:
2
3
+
6
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Assuming}[/tex]
[tex]\mathsf{\dfrac{2}{3} + 6}[/tex]
[tex]\huge\textbf{If so:}[/tex]
[tex]\mathsf{\dfrac{2}{3} + 6}[/tex]
[tex]\mathsf{= \dfrac{2}{3} + \dfrac{6}{1}}[/tex]
[tex]\mathsf{= \dfrac{2}{3} + \dfrac{6\times3}{3\times1}}[/tex]
[tex]\mathsf{= \dfrac{2}{3} + \dfrac{18}{3}}[/tex]
[tex]\mathsf{= \dfrac{2 + 18}{3 - 0}}[/tex]
[tex]\mathsf{= \dfrac{20}{3}}[/tex]
[tex]\mathsf{= 6 \dfrac{2}{3}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{20}{3}\ or\ 6 \dfrac{2}{3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Find the first five terms of the recursive sequence. Show all your work. an = 3a n-1 - 6 where a1 = 7
======================================================
Work Shown:
First replace every copy of n with 2
[tex]a_n = 3*(a_{n-1}) - 6\\\\a_2 = 3*(a_{2-1}) - 6\\\\a_2 = 3*(a_{1}) - 6\\\\a_2 = 3*(7) - 6\\\\a_2 = 21 - 6\\\\a_2 = 15\\\\[/tex]
Notice how the second term [tex]a_2[/tex] relies on the first term [tex]a_1[/tex]
Then repeat for n = 3
[tex]a_n = 3*(a_{n-1}) - 6\\\\a_3 = 3*(a_{3-1}) - 6\\\\a_3 = 3*(a_{2}) - 6\\\\a_3 = 3*(15) - 6\\\\a_3 = 45 - 6\\\\a_3 = 39\\\\[/tex]
Same goes with n = 4
[tex]a_n = 3*(a_{n-1}) - 6\\\\a_4 = 3*(a_{4-1}) - 6\\\\a_4 = 3*(a_{3}) - 6\\\\a_4 = 3*(39) - 6\\\\a_4 = 117 - 6\\\\a_4 = 111\\\\[/tex]
Finally plug in n = 5
[tex]a_n = 3*(a_{n-1}) - 6\\\\a_5 = 3*(a_{5-1}) - 6\\\\a_5 = 3*(a_{4}) - 6\\\\a_5 = 3*(111) - 6\\\\a_5 = 333 - 6\\\\a_5 = 327\\\\[/tex]
-----------------------------------
We have this summary:
[tex]a_1 = 7\\\\a_2 = 15\\\\a_3 = 39\\\\a_4 = 111\\\\a_5 = 327\\\\[/tex]
The first five terms are: 7, 15, 39, 111, 327
Find the midpoint of the segment with endpoints (9,3) and (6,-7)
Answer:
(7.5, -2)
Step-by-step explanation:
Label the coordinates(x₁,y₁) and (x₂,y₂)
Input the values into the formula (x₁ + x₂)/2, (y₁ + y₂)/2
Add the values in the parentheses and divide each result by 2
Can someone pls help me with this i only have a little bit of time left pls hurry
c. A parallelogram
has an area of 7 square units. If the height that corresponds to
a base is unit, what is the base?
If a parallelogram has an area of 7 square units, and the height corresponding to a base is [tex](\frac{1}{4})[/tex] units, then the base is 28 units.
As per the question statement, a parallelogram has an area of 7 square units, and the height corresponding to a base is [tex](\frac{1}{4})[/tex] units.
We are required to find out the base of the parallelogram.
To solve this question, we need to know the formula to calculate the area of a parallelogram, which goes as
Area of Parallelogram = (Base * Height)
Putting our data obtain from the question statement, in the above-mentioned formula, we can calculate the value of the base of our concerned parallelogram, i.e.,
[tex]7=(base*\frac{1}{4})\\or, base=(7*4)\\or, base = 28[/tex]
Therefore, base of our concerned parallelogram is 28 units.
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The average professional hockey player makes $2.78 million a year. They play an average of 82 games
much does the average hockey player make per game?
(a)A tram moved downward 21meters in 7 seconds at a constant rate. What was the change in the tram's elevation each second?
(b)In a lab, a substance was heated by 4 Celisse each hour for 40hours. What was the total change in temperature?
(a) The change in the tram's elevation (speed) each second is 3 meters/Sec
(b) The total change in temperature of the substance was 160 Celsius.
(a) The tram moves downward 21 meters in 7 second. So, the speed of the tram is 21/7 = 3 meters/Sec, which is the tram’s elevation each second.
We know that, speed = (total distance travel)/(Total travelling time)
(b) The substance was heated by 4 Celsius each hour for 40hours.
Therefore, the total change in temperature is = (4x40) = 160 celcius.
The degree Celsius is the unit of temperature on the Celsius scale, originally known as centigrade scale
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Answer:
(a) The change in the tram's elevation (speed) each second is 3 meters/Sec
(b) The total change in temperature of the substance was 160 Celsius.
Step-by-step explanation:
Perform the indicated operation.
4
0 -4 -8
0
1
0
0
0
1
-1
3
4R3+R1 R1
0
0
0
1
0
0
1
-1
3
Answer:
Can someone help me please
Answer: 4 0 4
Step-by-step explanation:
An Internet store charges a base fee plus $1.50 per pound to ship items. The table shows samples of their shipping rates.
Shipping Rates
Weight of Package
(pounds)
Shipping Cost
(dollars)
2
8.00
5
12.50
7
9
18.50
10
17
30.50
Derek wants to ship items that weigh a total of 7 pounds, and Keisha wants to ship items that weigh a total of 10 pounds. How much more does Keisha pay for shipping than Derek?
Answer:
Derek needs to pay 3 more pounds
Which ordered pair is a solution to every linear equation of the form y = mx, where m is a real
number?
The ordered pair which is a solution to every linear equation of the form given is; (0, 0).
Which ordered pair is a solution to the linear equation?It follows from the task content that the ordered pair which satisfies the equation of the form y =Mx be determined.
On this note, since the product of any real number, slope in this scenario and 0 is; 0.
Ultimately, it follows that the required ordered pair is; (0, 0) for any real number value of the slope, m.
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√38 I’m not sure how to solve these kinds of equations
Answer:
√38
Step-by-step explanation:
√38
step 1: Check which squared numbers can be multiplied by another number to get 38.
Start with these numbers: 4, 9, 16, and 25
Step 2: Testing out the numbers
√25 × __ = 25 can't be divided by 38
√16 × ___ = 16 can't be divided by 38
√9 × ____ = 9 can't be divided by 38
√4 × ____= 4 can't be divided by 38
Step 3: Answer
After trying the square root numbers that could possibly work with √38 none work; which means √38 can't be simplified. So the answer is √38
I hope this helps!
Simplify the expression by first substituting values from the table of exact values and then simplifying the resulting expression. Answer exactly.
(sin60∘+cos60∘)^2=
The harvest was cornucopian as it was 45 percent greater than last year. If the yield was 140795 bushels, how many bushels were harvested last year
After solving for x in the constructed equation, 97100 bushels were harvested last year.
What is an equation?
A mathematical statement known as an equation is consisting of two expressions joined together by an equal sign.A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.The point-slope form, standard form, and slope-intercept type are the three main types of linear equations.Constructing equation to determine no. of bushels.
Bales from the previous year = x + 0.45 x
= 140795 1.45 x
= 140795 X
= 97100 bales
After solving for x in the constructed equation, 97100 bushels were harvested last year.
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Answer:97100
Step-by-step explanation:
help please question is in picture
