Answer:
18 miles
Step-by-step explanation:
To determine how many miles Brent can travel, we need to first determine the cost of the base fare and then subtract that from the total amount of money Brent has. The base fare is $1.23, so we can subtract that from the total amount of money Brent has to find out how much money he has left for the per-mile charge:
14.91 - 1.23 = 13.68
Now that we know how much money Brent has left for the per-mile charge, we can divide that amount by the per-mile charge to find out how many miles Brent can travel:
13.68 / 0.76 = 18 miles
Therefore, Brent can travel a maximum of 18 miles given the amount of money he has available to spend on the ride.
Question
the value of 2 cos x - cos 3x - cos 5x is
not spam
Required Answer -:
16cos³ x sin² x
Let's Begin2cos x - ( cos 3x + cos 5x )
= 2cos x - 2 cos 4x cos x
= 2cos x 2sin² 2x
= 4 cos x ( 2sin x cos x)²
= 16cos³ x sin² x
Thus,, the value of 2 cos x - cos 3x - cos 5x is = 16cos³ x sin² x
The temperature in Austin is 33.5◦F and rising at a rate of 2.5◦F per hour. The temperature in San Antonio is 37.5◦F and rising at a rate of 1.5◦F per hour. Write an inequality that shows how long the temperature in Austin will remain colder than that in San Antonio.
The inequality that shows how long the temperature in Austin will remain colder than that in San Antonio is 33.5 + 2.5t < 37.5 + 1.5t and the time is less than 4 hours
How to determine the inequality and the intervalsFrom the question, we have the following parameters that can be used in our computation:
Austin
Initial temperature = 33.5 degrees Fahrenheit
Rate of increment = 2.5 degrees Fahrenheit
San Antonio
Initial temperature = 37.5 degrees Fahrenheit
Rate of increment = 1.5 degrees Fahrenheit
The above parameters mean that
Current temperature = Initial temperature + Rate of increment x Number of hours
So, we have
Austin: A(t) = 33.5 + 2.5t
San Antonio: B(t) = 37.5 + 1.5t
When Austin is colder than San Antonio, we have
A(t) < B(t)
Substitute the known values in the above equation, so, we have the following representation
33.5 + 2.5t < 37.5 + 1.5t
Evaluate the like terms
t < 4
Divide both sides by 1
t < 4
Hence, the interval is less than 4 hours
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help meeeeeeeeeee pleaseee
(a) After 25 years 47.37g of the initial sample left in the sample. (b) 12.83 years takes the initial sample to decay half of its original amount.
Given:
[tex]A(t) = 200 e^{-0.054t}[/tex]
Substituting 25 for t in the expression, we get:
A(25) = 200e⁰.⁰⁵⁴ × 25
= 47.37 g
Thus, after 25 years, there will be 47.37g of the initial sample left in the sample.
(b.) 12.83 years takes the initial sample to decay half of its original amount.
We want to find t such that
[tex]A(t) = 200e^{0.054} \times t[/tex]
where, t = 100.
Solving for t, we get:
[tex]200e^{0.054} \times t = 100[/tex]
Dividing both sides by 200 and applying the natural logarithm to both sides, we get:
0.054 × t = ln(0.5)
Therefore,
[tex]t = \frac{\ln(0.5)}{0.054}[/tex]
= 12.83 years.
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i need help with math please okay help with math pelase
The function [tex]y = (\frac{1}{2})^x[/tex] is a decreasing function.
The function [tex]y = (\frac{1}{2})^x[/tex] is shallower from left to right.
The value of the function [tex]y = (\frac{1}{2})^x[/tex] is unity at the y-intercept.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
The given function is [tex]y = (\frac{1}{2})^x[/tex] which is an exponential function cause the exponent is the variable.
Now, At x = - 2 y = 4 ⇒ (- 2, 4),
x = - 1, y = 2 ⇒ (- 1, 2).
x = 0, y = 1 ⇒ (0, 1).
x = 1, y = 1/2 ⇒ (1, 1/2).
x = 2, y = 1/4 ⇒ (2, 1/4).
x = 3, y = 1/8 ⇒ (3, 1/8).
The function is a decreasing function as the value of x increases the value of the function is decreasing.
The function is shallower from left to right.
The value of the function is unity at y-intercept as anything raised to the zero power is 1.
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Consider the piecewise function shown on the graph, which is composed of three different function types.
-10 -8 -6 -4 -2
10-
8
6
4
2
-2
-4
6
-8-
02
-10-
4 6
Match each piece of the function with its domain.
8 10
The quadratic is the left-most piece. This exists on the interval (-infty, -2).
The linear piece is the center piece and exists on the interval (-2,6).
The square root piece is the right-most piece and exists on (6, infty).
These intervals are describing how each piece lines up with the x-axis, as illustrated in the picture.
The required description of the given piecewise function are as follows:
quadratic → (-∞, -2); linear → (-2, 6) and square root → (6, ∞).
What is a piecewise function?A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).
The graph is given in the question, as shown
1. quadratic function:
This the sub-function define between the interval (-∞, -2).
2. linear function:
This the sub-function define between the interval (-2, 6).
3. square root function:
This the sub-function define between the interval (6, ∞).
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Multiply and simplify: (12−y)2
The simplification of the given expression on the basis of identity is given as 144 - 24y + y².
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given expression is (12 - y)².
It can be expanded on the basis of the algebraic identity (a - b)² = a² - 2ab + b² as follows,
(12 - y)²
= 12²- 2×12y + y²
= 144 - 24y + y²
Hence, the given expression can be simplified as 144 - 24y + y².
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For 3 and 4, find the slope of the line that passes through the given points.
3. (0, 10) and (24, 6)
4. (0, 6) and (20, 14).
5. The graph shows the number of centimeters a particular plant grows over time.
a. What is the slope of the line?
b. Apply Math Models What does the slope mean?
Answer: 4. -1/6, 5. 2/5
Step-by-step explanation:
1. The formula for slope is rise/run. To find the slope, you subtract the y coordinates (it doesnt matter the order, and you divide it by the difference of the x coordinates.
2. The y coordinates for 3 are 10 and 6, and the x coordinates are 0 and 24.
10-6/0-24 is 4/-24 which is -1/6.
3. you do the same thing for #4. The y coordinates are 6 and 14, and the x coordinates are 0 and 20. 14-6/20-0=slope. 8/20 is the slope, and that is equal to 2/5.
4. the slope for 3 is -1/6 and the slope for 4 is 2/5.
Pls help I forgot how to do this.
HELP ASAAAPPPO! Dawn is making an abstract painting with two triangles. The dimensions of the painting are shown below:
Two triangles share the same height of 8 inches. One triangle has a base of 6 inches and the other is 10 inches.
The total area of the two triangles is
???
square inches.
the total area of the two triangles as shwon in the image is 70 in²
What is area?Area can be defined as the total portion occuppied by a plane fiqure.
To calculate the total area of the two triangles, we use the formula below.
Formula:
Total area of the triangle = Area of the pink triangle+Area of the purple triangleArea of the purple triangle = bh/2.................. Equation 1Where:
b = Base of the purple triangle = 8 inh = Height of the purple triangle = 10 inSubstitute these values into equation 1
Area of the purple triangle = 8×10/2Area of the purple triangle = 40 in²Similarly,
Area of the pink triangle = BH/2........ Equation 1Where:
B = 6 inH = 10 inSubstitute these values into equation 2
Area of the pink triangle = 6×10/2Area of the pink triangle = 30 in²Therefore, the total area of the two triangles is 40+30 = 70 in².
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Kim has $45 to spend for a day at the zoo. She pays $17 for admission, $8 for lunch, and $4 for a snack. Use integers to write an expression that represents the amount of money Kim has left and determine how much she has.
A new ramp is being built at the school. It will be two meters long and one meter high. What will the slope of the ramp be?
Answer:
1/2
Step-by-step explanation:
Slope is rise (height)/run(length)
Slope is 1 meter/2 meters
Can anyone solve this? 30 points (no bots, please)
see attached image giving brainliyest if correct
The slope of the line given in the graph will be [m] is - 0.78.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is the graph of a straight line.
The line passes through the coordinates as follows -
(- 1.8, 0) [lying on x-axis]
(0, - 1.4) [lying on y-axis]
The slope of the line can be calculated using the formula -
m = (y₂ - y₁)/(x₂ - x₁)
m = (- 1.4 - 0)/(0 + 1.8)
m = - 1.4/1.8
m = - 0.78
Slope of the line will be -0.78.
Therefore, the slope of the line given in the graph will be [m] = - 0.78.
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An amount of $250 is contributed at the end of each month, and the balance earns interest at an APR of 6.2%. What is the total amount accrued after 7 years?
The required amount at the end of the 7 years is given as $32,340
Given that,
An amount of $250 is contributed at the end of each month, and the balance earns interest at an APR of 6.2%.
Investment is defined as when an individual spends money on something that returns him or her higher money than the money they or invest.
here,
According to the question,
The total amount accrued after 7 years is given as,
[tex]y\:=\:250\cdot12\cdot 7\left[1\:+\:\frac{0.062}{12}\right]^{12\cdot 7}\\y = $32,340[/tex]
Thus, The required amount at the end of the 7 years is given as $32,340.
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5. Charlie deposits $1000 into his investment account. The account grows at a rate
of 8% per year. How much money total is in the account on the first day on
the 11th year.
Answer:
1100
Step-by-step explanation:
First, we start off by finding 10% which is $100. We divide that by 10 to get $10 which is 10%. Now we need to multiply 10% (which is $10) by 10 which is $100. That gives you this answer
The total amount in the account on the first day of the 11th year is if Charlie deposits $1000 into his investment account. The account grows at a rate of 8% per year is $1880.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given data:
Charlie deposits, P = $1000 into his investment account.
The account grows at a rate, r = 8% per year.
The time, t = 11 year
Calculate the simple interest as shown below,
[tex]SI = (P\times r\times t) / 100[/tex]
SI = (1000 × 8 × 11) / 100
SI = $880
Calculate the total amount by the formula given below,
Amount = A
[tex]A = P + SI[/tex]
A = 1000 + 880
A = $1880
Therefore, the total amount in the account on the first day of the 11th year is if Charlie deposits $1000 into his investment account. The account grows at a rate of 8% per year is $1880.
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please help!
The measure of angle J is 120⁰ and is supplementary to the measure of angle K. If the measure of angle K is 12 x , what is the value of x ?
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.
Using the fact that the angles are supplementary, we can write and solve a linear equation to find that x = 5°.
How to find the value of x?
Remember that two angles are supplementary if the addition of their measures is equal to 180°.
Here we know that angles J and K are supplementary, then we know that:
J + K = 180°
Here we also know that:
J = 120°
K = 12x
So we can write a linear equation of the form:
120° + 12x = 180°
12x = 180° - 120°
12x = 60°
x = 60°/12 = 5°
x = 5°
We conclude that the value of x is 5°.
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(2-3)^-1 in indices please answer
Answer:
1
Step-by-step explanation:
First, simplify the parentheses.
2 - 3 = -1
Then, put this simplified value into the original expression.
(2 - 3)^(-1)
= (-1)^(-1)
Finally, execute the exponent function.
(-1)^(-1) = 1/1 = 1
Find 8 * 3 1/2 using the distributive property
The value of the expression upon evaluation by using the distributive property as required is; 28.
What is the value of the given expression using the Distributive property?It follows from the task content that the distributive property is to be used to determine the value of the expression given.
Since the given expression is; 8 • 3 ½.
It follows that the expression can be written as follows;
8 ( 3 + ½ )
Hence, by the distributive property, it follows that we have;
( 8 × 3 ) + ( 8 × ½ )
= 24 + 4
= 28.
On this note, the value of the expression is; 28.
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Give the quotient and remainder.
355÷8
Answer:
355 ÷ 8 = 44 with remainder 3
Step-by-step explanation:
44
-------------------------
8 | 355
- 32
--------
35
- 32
------
3
Caleb went to the grocery store and purchased cans of soup and frozen
dinners. Each can of soup has 200 mg of sodium and each frozen dinner has
500 mg of sodium. Caleb purchased a total of 15 cans of soup and frozen
dinners which collectively contain 4500 mg of sodium. Determine the
number of cans of soup purchased and the number of frozen dinners
purchased.
Answer:
Cans of soup = 10
Frozen dinners = 5
Step-by-step explanation:
To determine the number of cans of soup and frozen dinners Caleb purchased, set up and solve a system of equations based on the given information.
Let x be the number of cans of soup Caleb purchased.
Let y be the number of frozen dinners Caleb purchased.
Each can of soup has 200 mg of sodium and each frozen dinner has 500 mg of sodium. The total amount of sodium in the purchased cans and frozen dinners is 4500 mg. Therefore:
[tex]200x + 500y = 4500[/tex]
Caleb purchased a total of 15 cans of soup and frozen dinners. Therefore:
[tex]x + y = 15[/tex]
To solve the system of equations, rearrange the second equation to isolate x:
[tex]\begin{aligned}x + y &= 15\\x + y -y&= 15-y\\x&=15-y\end{aligned}[/tex]
Substitute this into the first equation to eliminate the term in x, and solve for y:
[tex]\begin{aligned}200(15-y) + 500y &= 4500\\3000-200y + 500y &= 4500\\3000+300y &= 4500\\3000+300y-3000 &= 4500-3000\\300y&=1500\\300y \div 300&=1500 \div 300\\y&=5\end{aligned}[/tex]
Therefore, Caleb purchased 5 frozen dinners.
Substitute the found value of y into the rearranged second equation and solve for x:
[tex]\begin{aligned}x&=15-y\\x&=15-5\\x&=10\end{aligned}[/tex]
Therefore, Caleb purchased 10 cans of soup.
Answer:
Caleb purchased 10 cans of soup and 5 frozen dinners.
Step-by-step explanation:
Caleb purchased 10 cans of soup and 5 frozen dinners.
Let no. of can of soup be x and no. of frozen dinner be y.
To solve this, we can set up the following system of equations:
[tex]\tt x + y = 15[/tex]......[i]
[tex]\tt 200x + 500y = 4500[/tex]......[2]
Let's find the value by elimination method:
Multiplying equation one by 200.
we get,
[tex]\tt 200 x+ 200 y = 15*200[/tex]
[tex]\tt 200x +200 y =3000[/tex]
Subtracting equation 2 with equation 1.
[tex]\tt (200x+500y)-(200x +200 y) =4500-3000[/tex]
[tex]\tt \tt 300y = 1500[/tex]
[tex]\tt y =\dfrac{1500}{300}[/tex]
[tex]\tt y = 5[/tex]
Substitute the value of y into the first equation to find x.**
[tex]\tt x + 5 = 15[/tex]
[tex]\tt x = 15 - 5[/tex]
[tex]\tt x = 10[/tex]
Therefore, Caleb purchased 10 cans of soup and 5 frozen dinners.
help meeeeeeeeeee pleaseee
(a) The population of the state was 18.5 million in 2000. (b)The population of the state will reach 26.6 million in the year 2002
What is Population ?A population is a distinct collection of people, whether that group consists of a nation or a population that shares a specific trait. A population is the group of people from which a statistical sample is taken in statistics. As a result, a population can be defined as any group of people who have something in common.
Since t = 0 ,
Then A = 18.5
(b) The population of the state will reach 26.6 million in the year 2002
2002, by using the formula is 18.5e^0.173*t
Given,
A= 26.6
Then,
[tex]A = 18.5 x e^{(0.1708t)} 26.6[/tex]
[tex]= 18.5 x e^{(0.1708t)} \frac{26.6}{18.5}[/tex]
= [tex]e^{(0.1708t)} 1.437838[/tex]
= [tex]e^{(0.1708t)} \ln (\frac{1.437838}{0.1708})[/tex]
t = 2.126116
t =2
Therefore, 2 is the round down to the nearest years. So 2002 is the approximate year the population reached 26.6 million.
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help meeeeeeeeeee pleaseee
Step-by-step explanation:
your teacher could have explained this better by telling us that A(t) is the remaining amount of the original isotope.
(a)
we start with 200 g and let it do its thing for 25 years.
all we need to do is enter the number of years into the function formula (as this is a college question you are able to work with functions, right ?) and calculate :
A(25) = 200e^(-0.054 × 25) = 200e^-1.35 =
= 51.84805213... g ≈ 51.85 g
after 25 years, about 51.85 g of the sample will be left.
assuming you have a calculator (at least on your computer) that was really "difficult", don't you think ?
(b)
half of the original amount is 200/2 = 100 g.
so, we need to find the value for t so that A(t) = 100.
100 = 200e^(-0.054 × t)
100/200 = 1/2 = 0.5 = e^(-0.054 × t)
ln(0.5) = -0.054 × t
t = ln(0.5) / -0.054 = 12.8360589... years
I assume you need to round to the nearest hundredth here as well :
after about 12.84 years the sample will decay to half of the original amount.
Ethan is buying a pair of water skis that are on sale for 2/3 of the original price. The total cost is $115. What was the original price of the skis? Use x as the variable.
Answer:
$345 (PLEASE GIVE BRAINLYEST )
Step-by-step explanation:
1/3x=115
x=345
Helpppppp pleasee due soon
Answer:
[tex]y = \sqrt{34} \\\\x = \sqrt{106}[/tex]
Step-by-step explanation:
please help this is a final
By using arithmetic progression, it can be calculated that
The common difference is 12
Third option is correct
What is arithmetic progression?A series of numbers is called an arithmetic progression if the difference between each term in the sequence is the same.
If there is always the same difference between any two consecutive terms in a series of integers, then progression is known as an arithmetic progression. Simply put, it means that the previous number in the series is added to determine the next number in the series. A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms. One arithmetic progression with a common difference of 2 is the sequence 5, 7, 9, 11, 13, 15,...
This is a problem on arithmetic progression
[tex]a _1 = 5[/tex]
[tex]a_n = a_{n-1} + 12[/tex]
[tex]a_2 = a_1 + 12[/tex]
[tex]a_2 = 5 + 12 = 17[/tex]
[tex]a_3 = a_2 + 12 = 17 + 12 = 29[/tex]
[tex]a_4 = a_3 + 12 = 29 + 12 = 41[/tex]
[tex]a_2 -a_1 = 17 - 5 = 12\\a_3 - a_2 = 29 - 17 =12\\a_4 - a_3 = 41 - 29 =12[/tex]
So the common difference is 12
Third option is correct
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By using arithmetic progression, it can be calculated that, the common difference is 12.
Third option is correct
What is arithmetic progression?If the common difference between each term in the sequence is the same, a group of numbers is referred to as an arithmetic progression.
A progression is referred to as an arithmetic progression if there is consistently the common difference between any two successive terms in a series of integers. To put it simply, it indicates that the series' next number is produced by adding the previous one.
An arithmetic progression or arithmetic sequence, also known as AP, is a set of numbers where the terms are always different from one another. The numbers 5, 7, 9, 11, 13, and 15 make up one mathematical progression with a common difference of 2.
We know that the arithmetic progression, this is based on the same
[tex]\begin{aligned}& a_1=5 \\& a_n=a_{n-1}+12 \\& a_2=a_1+12 \\& a_2=5+12=17 \\& a_3=a_2+12=17+12=29 \\& a_4=a_3+12=29+12=41 \\& a_2-a_1=17-5=12 \\& a_3-a_2=29-17=12 \\& a_4-a_3=41-29=12\end{aligned}[/tex]
So the common difference is 12
Third option is correct
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Trapezoid ABCD where AB║CD is shown below
diagonals AC and DB intersect MN at E
and AD ≅ AE
If m∠ DAE =35° and m∠ DCE=25°
m∠ NEC=30° determine and state m∠ ABD
By using various properties of triangles, we get the value of [tex]\angle[/tex]ABD is 47.5°.
What are the properties of a triangle?
A triangle's sides and angles serve as the foundation for all of its characteristics. Triangular closed polygons with three sides and three vertices are what the word "triangle" means. The three internal angles of a triangle add up to 180°.
Let us first name a few angles that we will be using throughout the solution.
Let, [tex]\angle[/tex]DEN=a
[tex]\angle[/tex]ENC=c
[tex]\angle[/tex]MEB=b
[tex]\angle[/tex]EMB=d
Now, since it is given that AD ≅ AE, let us assume that triangle ADE is an isosceles triangle, with AD=AE.
Hence we get
[tex]\angle[/tex]DAE+[tex]\angle[/tex]ADE+[tex]\angle[/tex]AED=180° (angle sum property)
35°+2[tex]\angle[/tex]ADE=180°
[tex]\angle[/tex]ADE=[tex]\angle[/tex]AED=72.5°
Next, we know that
[tex]\angle[/tex]AED+a+[tex]\angle[/tex]NEC=180° (linear pair property of angles on a straight line)
72.5°+a+30°=180°
a=77.5°
Since a=b (opposite angles)
we get, a=b=77.5°
Now in triangle ENC, if we take the sum of angles, we get
[tex]\angle[/tex]NEC+[tex]\angle[/tex]NCE+c=180° (angle sum property)
30°+25°+c=180°
c=125°
We also know that the sum of interior angles made by an intersecting line between 2 parallel lines (given shape is a trapezoid) is 180, hence we get
c+d=180°
d=55°
In triangle MBN, we have
d+b+[tex]\angle[/tex]MBD=180° (angle sum property)
55°+77.5°+[tex]\angle[/tex]MBD=180°
[tex]\angle[/tex]MBD=47.5°
Therefore, we get the value of [tex]\angle[/tex]ABD=47.5°
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PLEASE HELP AWARDING 50 POINTS!
What is the volume of a cylinder with a base radius of 2 and height of 5?
Either enter an exact answer in terms of π or use 3.143.143, point, 14 for π, and enter your answer as a decimal.
Answer:
20π cubic units
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cylinder}\\\\$V=\pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
Given:
r = 2h = 5Substitute the given values into the formula for the volume of a cylinder and solve for V:
[tex]\implies V=\pi \cdot 2^2 \cdot 5[/tex]
[tex]\implies V=\pi \cdot 4 \cdot 5[/tex]
[tex]\implies V=\pi \cdot 20[/tex]
[tex]\implies V=20\pi\;\; \sf cubic \;units[/tex]
A student argues that y= x/9 does not represent a proportional relationship between x and y because we need to multiply one variable by the same constant to get the other one and not divide it by a constamt. Do you agree or disagree with this student
I disagree with the student because y = x/9 represents a proportional relationship
What is proportional relationship?
Proportional relationships are relationships between two variables where their ratios are equivalent
A proportional relationship can we written as follows:-
y = mx
Where 'y' is dependent variable, 'x' is independent variable, and 'm' is the slope or we can say 'm' is constant of proportionality.
'm' can take any value whether negative or positive, decimal or whole number. 'm' is a real number.
The given problem is y = x/9 and student says we can only multiply constant, and not divide. We disagree with this comment because m= 1/9 is correct.
So y = 1/9 x makes sense.
Hence, y = x/9 represents a proportional relationship.
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Evaluate 3×sup(2,4)+1.
Answer:
49
hope this helps!!
q and p of both prime numbers with p < q
they are each less than 15
give an example where p + q is odd but not prime
Answer:
17 and 18 because they are equal