4a + 6b=10
2a - 4b =12
What is 12a?

Answers

Answer 1

Hi!

4a + 6b = 10
2a - 4b = 12

First make both a terms equal
2a · 2 - 4b · 2 = 12 · 2
4a - 8b = 24

Subtract both expressions to cancel out the a term.
4a + 6b = 10
-4a - 8b = 24
14b = -14
b = -1

Now put the value in one of the equations and solve
2a - 4 · -1 = 12
2a + 4 = 12
2a = 8
a = 4

Since a = 4, 12a = 48.

The answer is 48

Hope this helps! :)

Related Questions

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]

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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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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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".

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.

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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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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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.

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]

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

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

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

The table below shows the number of marbles of different colors in a bag: Color of Marbles Number of Marbles Pink 5 Blue 2 Green 3 Ursula draws a marble from the bag randomly without looking. She then draws another marble from the bag without replacing the first one. Which expression shows the probability of drawing green marbles in both the trials? plz help!!!!

Answers

[tex] \frac{3}{10} [/tex] x [tex] \frac{2}{9} [/tex] = [tex] \frac{1}{15} [/tex]

[tex]|\Omega|=10\cdot9=90\\ |A|=3\cdot2=6\\\\ P(A)=\dfrac{6}{90}=\dfrac{1}{15}\approx6,7\%[/tex]

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

please help me!!!
The scale for the map of Missouri is 1 in = 30 mi. On the map, the distance from Springfield to Columbus is about 5.6 in. How far apart are the two cities? Round your answer to the nearest mile.

Answers

if 1 inch = 30 miles

thn multiply 30 x 5.6

30 x 5.6 = 168 miles apart

The actual distance between Springfield and Columbia is 168 miles.

Therefore, the correct answer is:

b. 168 mi

To find the actual distance between Springfield and Columbia, we can use the scale provided in the map.

Given that 1 inch on the map represents 30 miles in real life, and the distance on the map from Springfield to Columbia is 5.6 inches, we can use the following calculation to find the actual distance:

[tex]\[ \text{Actual distance} = \text{Map distance} \times \text{Scale factor} \][/tex]

[tex]\[ \text{Actual distance} = 5.6 \, \text{inches} \times 30 \, \text{miles/inch} \][/tex]

[tex]\[ \text{Actual distance} = 168 \, \text{miles} \][/tex]

So, the actual distance between Springfield and Columbia is 168 miles.

Therefore, the correct answer is:

b. 168 mi

The sum of two consecutive even integers is 138. Write an equation and solve

Answers

x+(x+2)=138
2x+2=138
2x=136
x=68
Final answers: 68,70

Final answer:

The two consecutive even integers that sum to 138 are 68 and 70. The equation n + (n + 2) = 138 was used to determine these integers.

Explanation:

The problem is asking for two consecutive even integers whose sum is 138. Let's denote the first integer as n (where n is an even number). As the problem says the numbers are consecutive even integers, we know the next number must be n + 2.

We can form an equation based on the information given. The sum of these two integers is equal to 138, so:

n + (n + 2) = 138

If we simplify the equation, it becomes:

2n + 2 = 138By subtracting 2 from both sides, 2n = 136We then divide both sides by 2 to get n = 68

Therefore, the two consecutive numbers are 68 and 70 as they add up to 138.

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How do you change a ratio into a fraction baseballs to basketballs

Answers

[tex]\bf baseballs:basketballs\implies \cfrac{baseballs}{basketballs} \\\\\\ anything:whatever\implies\cfrac{anything}{whatever}[/tex]

if that's what you mean.

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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Divide the decimal numbers 12.012÷6

Answers

12.012/6=2.002

Hope this helps!

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!

14. Simplify (4x^– 4)^– 3.

Answers

[tex](4x^{-4})^{-3}=4^{-3}\cdot x^{12}=\dfrac{x^{12}}{64}[/tex]

Which expression is equivalent to the given expression? 100pts giveaway 3x(1.05) 3x + 3x + 3x 1.05x + 1.05x + 1.05x x + 3.15 1.05x + 3

Answers

17.2x+6.15
i am not sure but they may be right

I got, 17.35x+6.15

Btw you know it shows how many points your giving for the question

can someone explain to me multi step algebra equations? 15 points Thaaaanks~

Answers

so take 4x-2x=4 first combine like terms so now u have 2x=4. now you will isolate the x to find what it equals. divide 2 from both sides so u have x=2. did this help any?

Final answer:

Multi-step algebra equations involve operations like addition, subtraction, multiplication, or division to solve for an unknown. These equations require simplifying terms, solving for unknowns, and checking the answers. Money examples and practice statements are useful for understanding these concepts.

Explanation:

Multi-step algebra equations are problems that require more than one operation, such as addition, subtraction, multiplication, or division, to solve for the unknown variable. The following steps are typically involved in solving these equations:

Eliminate terms wherever possible to simplify the algebra. This might involve combining like terms or canceling out terms on both sides of the equation.Solve the simultaneous equations for the unknowns. This can be done through methods such as substitution or elimination when dealing with more than one equation.Check the answer to ensure it fits the original equation. Substituting the solution back into the original equation can verify its correctness.

An example of this process could be the following scenario: You are given two equations in a word problem involving motion, one equation for velocity and another for time. To find the distance traveled, you would identify the known variables and the unknown variable (in this case, distance), simplify both equations as much as possible, and then combine them to solve for distance.

Money examples are often used for educational purposes because they provide a familiar context for understanding mathematical principles, making them easier to grasp. Additionally, practicing with state-ments, such as covering up a number to solve for it with the remaining information, can help build problem-solving skills.

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

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.

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

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)

What are the orders of 3,7,9,11,13,17 and 19(mod20)?does 20 have primitive roots?

Answers

[tex]3\equiv3\mod{20}[/tex]
[tex]3^2\equiv9\mod{20}[/tex]
[tex]3^3\equiv27\equiv7\mod{20}[/tex]
[tex]3^4\equiv3\cdot3^3\equiv3\cdot7\equiv21\equiv1\mod{20}[/tex]

[tex]7\equiv7\mod{20}[/tex]
[tex]7^2\equiv49\equiv9\mod{20}[/tex]
[tex]7^3\equiv7\cdot7^2\equiv63\equiv3\mod{20}[/tex]
[tex]7^4\equiv7\cdot7^3\equiv21\equiv1\mod{20}[/tex]

[tex]9\equiv9\mod{20}[/tex]
[tex]9^2\equiv3^4\equiv1\mod{20}[/tex]

[tex]11\equiv11\mod{20}[/tex]
[tex]11^2\equiv121\equiv1\mod{20}[/tex]

[tex]13\equiv-7\equiv13\mod{20}[/tex]
[tex]13^2\equiv169\equiv9\mod{20}[/tex]
[tex]13^3\equiv13\cdot13^2\equiv(-7)9\equiv-63\equiv-3\mod{20}[/tex]
[tex]13^4\equiv13\cdot13^3\equiv(-7)(-3)\equiv21\equiv1\mod{20}[/tex]

[tex]17\equiv-3\equiv17\mod{20}[/tex]
[tex]17^2\equiv(-3)^2\equiv9\mod{20}[/tex]
[tex]17^3\equiv(-3)^3\equiv-27\equiv3\mod{20}[/tex]
[tex]17^4\equiv(-3)^4\equiv81\equiv1\mod{20}[/tex]

[tex]19\equiv-1\equiv19\mod{20}[/tex]
[tex]19^2\equiv19(-1)\equiv-19\equiv1\mod{20}[/tex]

Generally speaking, a number [tex]x[/tex] coprime to [tex]n[/tex] will be a primitive root of [tex]n[/tex] if we have [tex]x^n\equiv x\mod{n}[/tex], or [tex]x^{n-1}\equiv1\mod{n}[/tex]. In other words, if [tex]x[/tex] is of order [tex]n-1[/tex] modulo [tex]n[/tex], then [tex]x[/tex] is a primitive root of [tex]n[/tex].

Since none of these numbers has order 19, it follows that 20 does not have any primitive roots.

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

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4a + 6b=10 2a - 4b =12 What is 12a?

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4a + 6b=10
2a - 4b =12
What is 12a?