what is e/4 + 2f-3 when e =12 andf =1/2

Answers

Answer 1

Hey!

When putting in a number for a variable, we want to put it on parenthesis. So, let's write the problem with the variables substituted.
[tex](12)/4+2(1/2)-3[/tex]
We could also write it like this:
[tex]\frac{\left(12\right)}{4}+2\left(\frac{1}{2}\right)-3=1[/tex]
To start, we have to remove the parenthesis.
[tex]=\frac{12}{4}+2\cdot \frac{1}{2}-3[/tex]
Let's simplify the first fraction.
[tex]\frac{12}{4}=3[/tex]
Let's simplify the second part:
[tex]2\cdot \frac{1}{2}[/tex]
[tex]=\frac{1\cdot \:2}{2}[/tex]
[tex]=\frac{2}{2}[/tex]
[tex]=1[/tex]

We would be left with,
[tex]=3+1-3[/tex]
Simplify.
[tex]=1[/tex]

Thanks!
-TetraFish

Answer 2

Hello there! Thank you for asking your question here at Brainly. I will be assisting you with this problem and will teach you how to handle it on your own in the future.

Let's take a look at our question.
"What is e/4 + 2f -3 when e = 12 and f = 1/2?"

To solve for this, we need to plug in our values to their proper values.

Let's replace "e" with "12" and "f" with "0.5" (0.5 is equal to 1/2).

Our expression should look like this now:
12/4 + 2(0.5) -3

Well, we can simplify two parts of our expression: 12/4 and 2(0.5).

We can simplify 12/4 into 3, as 12 divided by 4 is 3.
We can also simplify 2(0.5) into 1, as multiplying by 0.5 is the same as dividing by 2.

We now have:
3 + 1 - 3
We can cancel out 3 and -3 to make 0.
We are now left with 1.

Your answer remains as "1".

I hope this helps! :)

Related Questions

The price of a calculator dropped from $32.88 to $25.95. What was the percent decrease in price

Answers

%change=100(final-initial)/initial

%change=100(25.95-32.88)/32.88

%change≈ -21.08%

So the percent decrease in price was about 21%

32.88 - 25.95 is 6.93

well, if we take the 32.88 to be the 100%, how much is 6.93 off of it in percentage?

[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 32.88&100\\ 6.93&x \end{array}\implies \cfrac{32.88}{6.93}=\cfrac{100}{x}[/tex]

solve for "x".

Jane noticed as she was doing her morning run that a 12 m flagpole cast a 18 m shadow. A tree was casting a 36 m shadow. The tree was __? ___ m tall.

Answers

The tree was 30 meters long

Using the formula in model 1, choose the correct answers for the new balance and amount of interest earned in the following compound interest problem. $1,050 at 6%, for 25 years, compounded annually. Total Amount = $ Interest Amount =$

Answers

To find the total amount
The formula is
A=p (1+r)^t
A total amount?
P present value 1050
R interest rate 0.06
T time 25 years
A=1,050×(1+0.06)^(25)=4,506.46

Interest amount
I=A-p
I=4,506.46−1,050
I=3,456.46

what's 6 3/4 divided by 1 7/8

Answers

6 3/4 divided by 1 7/8
= 27/4 divided by 15/8
= 27/4 x 8/15
= 18/5
= 3 3/5

The value of 6 (3/4) divided by 1 (7/8) is 3 (3/5).

What is a fraction?

A fraction is a part of the whole represented by a/b, where a and b are any integers

The given numbers are 6 (3/4) and 1 (7/8).

Simplify the mixed fractions:

6(3/4) = 27/4 and 1 (7/8) = 15/8

Now, divide 27/4 by 15/8:

27/4 ÷ 15/8

= 27/4 × 8/15

= 18/5

= 3 (3/5)

Hence, The value of 6 (3/4) divided by 1 (7/8) is 3 (3/5).

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(05.02 MC)

Trevor solved the system of equations below. What mistake did he make in his work?

2x + y = 5
x − 2y = 10

y = 5 − 2x
x − 2(5 − 2x) = 10
x − 10 + 4x = 10
5x − 10 = 10
5x = 0
x = 0

2(0) + y = 5
y = 5

Answers

His work should have looked like this.

2x + y = 5
x − 2y = 10

y = 5 − 2x
x − 2(5 − 2x) = 10
x − 10 + 4x = 10
5x − 10 = 10 When he added in both sides, he subtracted 10 from 10,
5x = 20 instead of adding 10 from 10 to make 20.
x = 4
2(4) + y = 5
8 + y = 5

y = -3

"4. Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x= 12. y = -10 when x = 2 "

Answers

If y varies directly with x:
y = k * x
When x = 2, y = - 10.
- 10 = k * 2
k = - 10 : 2
k = - 5
Therefore: y = - 5 x
And when x = 12 ;
y = - 5 * 12
Answer:
y = - 60

Answer:

5/ 2 x

Step-by-step explanation:

Aurora earns a salary of $25,000 per year. Her benefits are equal in value to 30 percent of her salary. What is the value of Aurora's benefits?

Answers

$25,000 * 0.7 + $17,500 thus $25,000-$17,000=$7,5000

Value of Aurora's benefits as 30percent of her salary is equals to $7500.

What is percentage?

" Percentage is defined as the hundredth part of the given whole number."

According to the question,

Salary amount of Aurora = $25,000

Benefit value = 30 percent of ( $25,000)

Therefore,

30 percent of ( $25,000) = 30% of 25,000

= [tex]\frac{(30) * (25,000)}{100}[/tex]

= $7,500

Hence, value of Aurora's benefits as 30percent of her salary is equals to $7500.

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Simplify the expression by using a double-angle formula. 2 cos^2 4 theta -1

Answers

You are given 2cos² (4θ - 1). You are asked to simplify the expression by using a double-angle formula.

Apply the double angle of the cosine function
cos2θ = 2cos² θ - 1

Rearranging the expression and then substituting them
2cos² θ = cos2θ + 1
2cos² (4θ - 1) = cos 2(4θ - 1) + 1
cos2(4θ - 1) + 1

is 70 thousand written in standard form or word form

Answers

70 thousand is written in word flrm

Standard form is using numbers for example 1,000 word form use words for example one thousand so since you already said the standard form the word form is seventy thousand and its a word form hope that helps.

EASY 5 POINTS!!!!! You have a 1-gallon paint can in the shape of a cylinder. One gallon is 231 cubic inches. The radius of the can is 3 inches. What is the approximate height of the paint can? Use 3.14 for pi.

A.) 5 inches
B.) 25 inches
C.) 8 inches
D.) 26 inches

Answers

We know that the volume is: V = 1 gallon = 231 in³
Also : r = 3 in.
The volume of a cylinder: V = r² π h
231 = 3³ · 3.14 · h
231 = 9 · 3.14 · h
231 = 28.26 h
h = 231 : 28.26
h = 8.17 ≈ 8 in
Answer: C) 8 in.

Answer:

The height of the cylinder shaped can = 8.17 inches

Step-by-step explanation:

Volume of the cylinder shaped can = 1 gallon

1 gallon = 231 cubic inches

So, Volume of the cylinder shaped can = 231 cubic inches

Radius of the can = 3 inches

[tex]\text{Now, Volume of the cylinder = }\pi\times radius^2\times height\\\\\implies 231=3.14\times 3^2\times height\\\\\implies height=\frac{231}{3.14\times 9}\\\\\implies height\approx 8.17\text{ inchjes}[/tex]

Hence, The height of the cylinder shaped can = 8.17 inches

Under what circumstance are two non right triangles congruent

Answers

Only if three sides are equal.

Josh estimates the height of his desk. Which is the best estimate?

Answers

A usual desk is 28-30 inches for a person who is 5 foot 8-10 inches

Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.

Answers

[tex]\bf \begin{array}{rlclll} (8&,&-15)\\ \uparrow &&\uparrow \\ a&&b \end{array} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{8^2+(-15)^2}\implies c=\sqrt{289}\implies \boxed{c=17}\\\\ -------------------------------\\\\[/tex]

[tex]\bf sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad cos(\theta)=\cfrac{adjacent}{hypotenuse} \quad % tangent tan(\theta)=\cfrac{opposite}{adjacent} \\\\\\ % cotangent cot(\theta)=\cfrac{adjacent}{opposite} \qquad % cosecant csc(\theta)=\cfrac{hypotenuse}{opposite} \quad % secant sec(\theta)=\cfrac{hypotenuse}{adjacent}[/tex]

you've got all three values, plug them in.

Answer with explanation:

It is given that, Angle θ is in standard position.

A line from origin O to point , P(8,-15) is joined and then perpendicular to x and y axis, is drawn cutting X axis at Point M and Y axis at point N.

OM= 8 units

ON=P M=15 units

By Pythagorean Theorem

[tex]OM^2 + PM^2=OP^2\\\\ 8^2 +15^2=OP^2\\\\ OP^2=64 +225\\\\OP^2=289\\\\OP^2=17^2\\\\OP=17\\\\ Sin (\theta)=\frac{\text{Perpendicular}}{\text{Hypotenuse}}=\frac{-15}{17}\\\\Cos(\theta)=\frac{\text{Base}}{Hypotenuse}=\frac{8}{17}\\\\Tan(\theta)=\frac{\text{Perpendicular}}{Base}=\frac{-15}{8}\\\\ Cosec(\theta)=\frac{1}{Sin(\theta)}=\frac{-17}{15}\\\\ Sec(\theta)=\frac{1}{Cos(\theta)}=\frac{17}{8}\\\\ Cot (\theta)=\frac{1}{Tan(\theta)}=\frac{-8}{15}[/tex]

Point(8,-15), lies in Quadrant four. In Quadrant four Cosine and Secant Function are positive and all other trigonometric functions, Sine,Cosecant, Tangent,and Cotangent are Negative.

(08.03 MC)
A system of equations is shown below:

y = 3x – 7
y = 2x + 1

What is the solution to the system of equations? (1 point)

A. (8, 17)

B. (–8, 17)

C. (–8, –17)

D. (8, –17)

Answers

Answer:

(8, 17)

Step-by-step explanation:

Here you have two functions equalling y.

To find x, we set these two functions equal to one another, which eliminates y:

3x - 7 = 2x + 1.

Find x. To do this, subtract 2x from both sides, obtaining x - 7 = 1.

Next, add 7 to both sides: x = 8.

Finally, find y. Do this by subbing 8 for x in either of the two given equations.

Working with the 2nd equation: y = 2(8) + 1 = 17

Thus, the solution is (8, 17).

I believe the answer is (8 , 17)

The Panthers, a high school basketball team, charges $6 for adult tickets and $3 for children’s tickets. If 120 people went to the most recent game, and the total earnings for ticket sales was $612, how many children went to the game?
There were 36 children at the game.
There were 50 children at the game.
There were 84 children at the game.
There were 108 children at the game.

Answers

Answer:

The answer is 36 children

Step-by-step explanation:

There were 36 children at the game

The number of children who went to the game was 36

What is Linear Equation in 2 variables?

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c = 0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Given data ,

Let the number of children be = x

Let the number of adults be = y

Cost of ticket for 1 child = $ 3

Cost of ticket for 1 adult = $ 6

Total number of people who went to the game = 120

So , x + y = 120

Total earnings for the ticket sales = $ 612

Total earnings =
( Cost of one child x Number of children ) + ( Cost of one adult x Number of adult)

Total earnings = 3x + 6y

Now , we have 2 equations to solve

x + y = 120 be equation (1)

3x + 6y = 612 be equation (2)

Multiply equation (1) by 3 , we get

3x + 3y = 360 be equation (3)

Subtract equation (3) from equation (2)

3x + 6y - ( 3x + 3y ) = 612 - 360

3y = 252

Divide by 3 on both sides , we get

y = 84

So , the number of children who went to the game will be

x + y = 120

x + 84 = 120

Subtract 84 on both sides , we get

x = 36

Hence , the number of children who were at the game was 36

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Can anyone please solve the attached file?

Answers

The given matrix is
[tex] A= \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] [/tex]

A given vector is of the form [a b c]'.
If a given vector {x} is an eigenvector of A, then
[tex]det \left[\begin{array}{ccc}1-a&2&3\\4&5-b&6\\7&8&9-c\end{array}\right] =0[/tex]

Test the vector x₁ = [1 -2 1]'
[tex]det \left[\begin{array}{ccc}0&2&3\\4&7&6\\7&8&8\end{array}\right] =-2(32-42)+3(32-49)=-31[/tex]
This is not an eigenvector because the determinant is not zero.

Test x₂ = [-1 0 1]'
[tex] det \left[\begin{array}{ccc}2&2&3\\4&5&6\\7&8&8\end{array}\right] =2(40-48)-2(32-42)+3(32-35)=-5[/tex]
This is not an eigenvector because the determinant is not ero.

Test x₃ = [0 0 0]'
[tex]det \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] =(45-48)-2(36-42)+3(32-35)=0[/tex]
This vector is an eigevector because the determinant is zero.

Answer:
The eigenvector is x₃

Name the properties that were used to derive the properties of logarithms.

Answers

The properties that were used to derive the properties of logarithms are the properties of exponent because logarithms are exponents. The properties of exponents are: product of powers, power to a power, quotient of powers, power f a product and power of a quotient.

As an example, the log property log(a^k) = k log (a) can be derived from the exponential property (b^a)^k = b^(ak).

Likewise,

log (ab) = log (a) + log (b) comes from c^(a+b) = c^a*c^b

Proof:

Let x = c^a and y=c^b

Then,

log (x) = a and log (y) = b (base c)

log (xy) = log (c^a * c^b) = log (c^(a+b)) = a+b = log(x) + log (y)

The value of a car decreases by 20% per year Mr. Singh for purchase is a $22,000 automobile what is the value of the car the end of the second year

Answers

[tex]\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=I(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &22000\\ r=rate\to 20\%\to \frac{20}{100}\to &0.20\\ t=\textit{elapsed time}\to &2\\ \end{cases} \\\\\\ A=22000(1-0.2)^2[/tex]

Answer: the answer is $26,400

Step-by-step explanation:

Answers

The distribution of the number of occurrences of the letter t on the pages of a book is found to be a normal distribution with a mean of 44 and a standard deviation of 18. If there are 500 pages in the book, which sentence most closely summarizes the data?

A. The letter t occurs less than 26 times on approximately 170 of these pages.

B. The letter t occurs less than 26 times on approximately 15 of these pages.

C. The letter t occurs more than 26 times on approximately 420 of these pages.

D. The letter t occurs more than 26 times on approximately 80 of these pages.

.Answer:
mean = 44
sd = 18
that means that "26" is 1 s.d. down, or at the 16th %ile

so, there is a .16 chance that "t" will occur less than 26 times on any single page.
consequently, there is a .84 chance that it will occur more than 26 times on any single page.

Using that information, and knowing that 16% of 500 is 80, and 84% of 500 is 420, can you see where "C" is correct?

Final answer:

The data represents a normal distribution where approximately 68 percent of the pages will have a number of occurrences of the letter t within one standard deviation of the mean, 95 percent within two standard deviations, and more than 99 percent within three standard deviations.

Explanation:

The sentence that most closely summarizes the data is: For data having a distribution that is bell-shaped and symmetric, the following are true:

Approximately 68 percent of the data is within one standard deviation of the mean.Approximately 95 percent of the data is within two standard deviations of the mean.More than 99 percent of the data is within three standard deviations of the mean. This is known as the Empirical Rule.

Using this information, we can conclude that approximately 68 percent of the pages in the book will have a number of occurrences of the letter t within one standard deviation of the mean, which is 44. Approximately 95 percent of the pages will have a number of occurrences within two standard deviations, and more than 99 percent will have a number of occurrences within three standard deviations.

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jack is mowing a lawn that has a shed. needs to know area of lawn to mow. dimensions of yard are 5x by 13 x-4 . she'd are 2x by 2x+4. " find polynomial that describes area of lawn needed to mow. Polynomial in answer should have two terms.
please help.

Answers

The diagram of the lawn and the shed is shown below.

The area of the lawn needed to be mowed equals to the area of the yard minus the area of the shed

The area of the yard = [tex](5x)(13x-4) = 65 x^{2} -20x[/tex]
The area of the shed = [tex](2x)(2x+4)=4 x^{2} +8x[/tex]

The area of the lawn = [tex]65 x^{2} -20x-(4 x^{2} +8x)[/tex]
The area of the lawn = [tex]65 x^{2} -20x-4 x^{2} -8x[/tex]
The area of the lawn = [tex]61 x^{2} -28x[/tex]

Simplifying expressions with exponents

Answers

When dividing two terms with the same base, subtract the exponent in the denominator from the exponent in the numerator: Power of a Power: To raise a power to a power, multiply theexponents.

[tex]\bf (2x^2y^3)^2(3y)\implies (2x^2y^3)^2(3y^1)\implies (2x^{2\cdot 2}y^{3\cdot 2})(3y^1) \\\\\\ 2x^4y^63y^1\implies 2\cdot 3x^4y^{6+1}\implies 6x^4y^7[/tex]

Mr. Pham wrote the equation below on the board. 18 - 7x = -20.5 What is the value of x?

Answers

Use the arithmetic operations to get the variable x on one side of the equation and everything else on the opposite side.

If something is being is being done to a variable, we undo that operation by using the inverse of that operation.

For example, if 10 is being added to x, we use the inverse of addition or subtraction.

18 - 7x = -20.5

We variable x is being multiplied by 7 and is subtracting 18. We need to undo all those operations.

18 - 7x = -20.5
-7x = -38.5

Now the variable is only being multiplied by -7. Reverse the operation.

-7x = -38.5
x = 5.5

So, x is equal to 5.5.

Answer: The answer should be D(x=5 1/2)

Step-by-step explanation:

Trust me I did the equation and work.

Divide the decimal numbers 12.012÷6

Answers

12.012/6=2.002

Hope this helps!

Ava wants to wash one load of laundry at a local laundromat. At laundromat A, it costs $6.35 to wash and $1.25 to dry one load of laundry. At laundromat B, it costs $5.95 to wash and $0.85 to dry one load of laundry. Which laundromat has the better price for doing one load of laundry, and by how much?

Answers

Laundromat A = 6.35 +1.25 = 7.60 for one load

Laundromat B = 5.95 +0.85 = 6.80 for one load

7.60-6.80 = 0.80

Laundromat B is has the better price by 0.80 cents

Rita attends school 180 days out of the 365 days in a year. For what fraction of the year is Rita in school? Write your answer in simplest form.

Answers

the fraction is 180/365

this can get reduced to 36/73

A square with an area of 169 cm^2 is rotated to form a cylinder. What is the height of the cylinder?

Answers

check the picture below.

Answer:

13 cm

Step-by-step explanation:

Area of the square is [tex]169 \:\:cm^{2}[/tex]

The square is rotated to form a cylinder. Now, we first need to find the side of the square, the cylinder is formed by rotating along its side.

Now area of square [tex]169 \:\:cm^{2}[/tex]

We know that area of square is [tex]\text{side}\times\text{side}[/tex]

So, [tex]\text{side}\times\text{side}=169[/tex]

[tex]\text{side}\times \text{side}=13\times13[/tex]

[tex]\text{side}=13 \:\text{cm}[/tex]

Now, as the cylinder is formed by rotating along its length, and we know that all the sides of a square is equal.

So, one side becomes the height of the cylinder and the other becomes the circumference.

Hence, the height of the cylinder is 13 cm.

Solve l=14j+3k for j.

Answers

l = 14j + 3k
l - 3k = 14j
(l - 3k) / 14 = j
j = (l - 3k) / 14 (Flipped sides for aesthetics. I like having the thing I solve for on left, but that is completely optional)

Final answer:

To solve the equation l = 14j + 3k for j, subtract 3k from both sides and then divide by 14, giving j = (l - 3k) / 14.

Explanation:

To solve the equation l=14j+3k for j, you need to isolate j on one side of the equation. Here's how it is done step by step:

Start with the original equation: l = 14j + 3k Subtract 3k from both sides of the equation to isolate the term with j in it: l - 3k = 14j Divide both sides of the equation by 14 to solve for j: j = (l - 3k) / 14

Therefore, the solution to the equation for j is: j = (l - 3k) / 14.

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Factor completely 2x3 + 14x2 + 4x + 28.

Answers

6 + 28 + 4x +28

34 +28 + 4x

62 + 4x?

Not quite sure if that was what you were looking for

Hi there!

2x³ + 14x² + 4x + 28

2(x+7)(x² +2)

I hope that helps!

What is the largest possible value of y, if y = - | 3 - x | + 5

Answers

Given any expression A, absolute value of A, that is |A|, is always positive or 0.

So |3-x| is always positive or 0, thus -|3-x| is always negative or 0.

Since we want the largest value of - | 3 - x | + 5, we must keep - | 3 - x | as large as possible, that is, we must keep | 3 - x | as small as possible.

The smallest possible value of | 3 - x | is 0. This happens for x=3.

The largest possible value of y = - | 3 - x | + 5 = 0+5 =5

Answer: 5

Find all values of c such that f is continuous on (-∞, ∞). $ f(x) = \left\{ \begin{array}{lcl} {\color{red}5} - x^{2}, & & x \le c \\ x, & & x > c \end{array}\right. $

Answers

[tex]f(x)=\begin{cases}5-x^2&\text{for }x\le c\\x&\text{for }x>c\end{cases}[/tex]

will be continuous as long as

[tex]\displaystyle\lim_{x\to c^-}f(x)=\lim_{x\to c^+}f(x)=f(c)[/tex]

We have

[tex]\displaystyle\lim_{x\to c^-}f(x)=\lim_{x\to c}(5-x^2)=5-c^2[/tex]

[tex]\displaystyle\lim_{x\to c^+}f(x)=\lim_{x\to c}x=c[/tex]

so we must satisfy

[tex]5-c^2=c\implies c^2+c-5=0\implies c=\dfrac{-1\pm\sqrt{21}}2[/tex]

The values of c such that the function f is continuous are: c = -2.79 and c = 1.79

The function is given as:

[tex]f(x) = \left\{ \begin{array}{lcl} {5} - x^{2}, & & x \le c \\ x, & & x > c \end{array}\right.[/tex]

For the function to be continuous, then the following must be true

[tex]5 - x^2 = x[/tex]

Substitute c for x

[tex]5 - c^2 = c[/tex]

Express as a quadratic function

[tex]c^2 + c - 5 = 0[/tex]

Using a graphing calculator, the values of c are:

c = -2.79 and c = 1.79

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