Write a solution about today's sales for the following systems of the equations and then determine how much of each menu item you sold: e+f=48 and e=3f

Answer:

Step-by-step explanation:

Mia is 2 1/2 years older than Chloe.

Mia is 12 years old.

Chloe's age is:

Allen is 6 1/2 years younger than Chloe.

Allen’s age is:

The algebraic expression for the area is:

A = (2H - 8)*H/2

Here we want to write the expression:

"the area of a triangle that has a base 8 inches less than 2 times wider than the height."

Remember that for a triangle of base B and height H, the area is:

A = B*H/2

So if the base is 8 inches less than 2 times the height, we can write:

B = 2*H - 8

Replacing that in the area equation we get:

A = (2H - 8)*H/2

That is the equation for the area.

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Answer:

Hello answer: 1 1/3

work: 1/3 × 4 = 1 1/3

equation: 1/3 × 4 = 1 1/3

Answer:

see explanation

Step-by-step explanation:

(a)

\(\frac{1}{3}\) can → 1 cake

Number of thirds in 1 can = 3, then

Number of thirds in 4 cans = 3 × 4 = 12

Thus 12 cakes can be frosted with 4 cans

(b)

number of cakes = 4 ÷ \(\frac{1}{3}\) = 4 × \(\frac{3}{1}\) = 12

Step-by-step explanation:

3:

h(x)=(-3x-15)/5

let y=(-3x-15)/5

interchanging role of x &y

x=(-3y-15)/5

5x+15=-3y

y=-(5x+15)/3

h-1(x)=-(5x+15)/3

not

equal to f(x)=(-3x-6)/4

Given function are not function of each other .

4:

g(x)=2/3x-2/3

let

y=2/3(x-1)

interchanging role of x &y

x=2/3(y-1)

3/2x+1=y

g-1(x)=3/2x+1

not equal to f(x)=½x+1

Given function are not function of each other .

Problem 1

--------------------

Explanation:

One way to see if we have an inverse pair or not is to compute these two composite functions

If both result in x, and just that, then we have shown that they are inverses of one another.

f(x) = (2x)/3

f(x) = (2/3)x

f(g(x)) = (2/3)*g(x)

f(g(x)) = (2/3)*(3/2)x

f(g(x)) = x

The steps to show that g(f(x)) = x are very similar

g(x) = (3/2)x

g(f(x)) = (3/2)*f(x)

g(f(x)) = (3/2)*(2/3)*x

g(f(x)) = x

So this verifies that you have the correct answer.

======================================================

Problem 2

--------------------

Explanation:

We'll use the same idea as problem 1

f(x) = 2 - (3/4)*x

f(g(x)) = 2 - (3/4)*( g(x) )

f(g(x)) = 2 - (3/4)*( (-4/3)x + 8/3 )

f(g(x)) = 2 - (3/4)*(-4/3)x  - (3/4)*(8/3)

f(g(x)) = 2 + x - 2

f(g(x)) = x

So far so good, but we need to check the other way around as well

g(x) = (-4/3)x + 8/3

g(f(x)) = (-4/3)*( f(x) ) + 8/3

g(f(x)) = (-4/3)*( 2 - (3/4)*x ) + 8/3

g(f(x)) = (-4/3)*(2) + (-4/3)*(-3/4)*x + 8/3

g(f(x)) = -8/3 + x + 8/3

g(f(x)) = x

This verifies that f(x) and g(x) are inverses of each other.

Problems 3 and 4 will have similar steps.

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

The computed mean expenses of the XYZ Corporation based on the given information are 9,911.22.

The mean refers to the average value.

The mean is computed as the quotient that results from dividing the total value of the data set by the number of items in the set.

Name                      Total Sales      Total Expenses

Quezon City            14,950.00             4,933.50

Caloocan City         18,290.00             6,035.70

Marikina City          37,200.00           12,276.00

Cebu City                18,900.00            6,237.00

Davao City             45,000.00          14,850.00

Mandaluyong City 23,000.00           7,590.00

Cavite                     22,000.00          7,260.00

Laguna                    21,000.00          6,930.00

Manila                    66,000.00         21,780.00

Iloilo                       34,000.00          11,220.00

Total                                                  99,112.20

Mean Expenses = 9,911.22 (99,112.20 ÷ 10)

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(i) \(\lim_{x \to \pi/3}\) f(x) = 1 + √3.

(ii) \(\lim_{x \to \frac{\pi}{4}} f(x)\) does not exist.

For λ = 2.5, the function f(x) will be continuous at x = 0.

Given the function is,

f(x) = 1.5, when x = 0

    = 1 -2 sin x, when x < π/4

    = 1 + 2 sin x, when x > π/4

    = 1 + (sin λx/sin 5x)

Now,

\(\lim_{x \to \pi/3}\) f(x) = \(\lim_{x \to \pi/3}\) (1 + 2 sin x) [Since, π/3 > π/4]

                    = 1 + 2 sin (π/3)

                    = 1 + 2√3/2 = 1 + √3

Hence, \(\lim_{x \to \pi/3}\) f(x) = 1 + √3.

Now left hand limit is,

\(\lim_{x \to \frac{\pi^+}{4}}\) f(x) = \(\lim_{x \to \frac{\pi^+}{4}}\) (1 + 2sin x) = 1 +2 sin(π/4) = 1 + 2*(1/√2) = 1 + √2

and right hand limit is,

\(\lim_{x \to \frac{\pi^-}{4}}\) f(x) = \(\lim_{x \to \frac{\pi^-}{4}}\) (1 - 2 sin x) = 1 - 2*(1/√2) = 1 - √2

Since left hand limit and right hand limit are not equal so value of \(\lim_{x \to \frac{\pi}{4}} f(x)\) does not exist.

\(\lim_{x \to 0}\) f(x) = \(\lim_{x \to 0}\) (1 + (sin λx/sin 5x)) = 1 + \(\lim_{x \to 0}\) ((sin λx/λx)/(sin 5x/5x))*(λ/5) = 1 + λ/5

Since f(x) is continuous at x = 0.

So, \(\lim_{x \to 0}\) f(x) = f(0)

1 + λ/5 = 1.5

λ/5 = 1.5 - 1 = 0.5

λ = 2.5

Hence the value of λ will be 2.5.

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Step-by-step explanation:

• Question 1 :-

\(\tt\to \dfrac{1}{3}+? = 1 \\\\\tt\to ? = 1-\dfrac{1}{3}\\\\\tt\to ?=\dfrac{3-1}{3} \\\\\tt\to \boxed{\orange{ ? = \dfrac{2}{3}}}\)

_________________________________

• Question 2 :-

\(\tt\to \dfrac{3}{5}+? = 1 \\\\\tt\to ? = 1-\dfrac{3}{5}\\\\\tt\to ?=\dfrac{5-3}{5} \\\\\tt\to \boxed{\orange{ ? = \dfrac{2}{5}}}\)

The equation of the perpendicular line passing through (0, -1) is y = -9x - 1.

To find the equation of a line that is perpendicular to the given line y = (1/9)x + 2 and passes through the point (0, -1), we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other.

The given line has a slope of 1/9. To find the slope of the perpendicular line, we take the negative reciprocal of 1/9, which is -9.

Using the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept, we can substitute the slope and the coordinates of the given point (0, -1) into the equation.

y = -9x + b

Since the line passes through the point (0, -1), we can substitute the x-coordinate as 0 and the y-coordinate as -1 into the equation:

-1 = -9(0) + b

-1 = b

Therefore, the y-intercept (b) of the perpendicular line is -1.

Putting it all together, the equation of the line that passes through (0, -1) and is perpendicular to y = (1/9)x + 2 is:

y = -9x - 1

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Answer:

if it is 46-2004 then the answer is  -1958

Step-by-step explanation:

you can start by dividing the total length of the road by the distance that can be repaired per week:

13 km ÷ 3 1/2 km/week = 3.71 weeks

Rounding up, it will take 4 weeks to repair the entire 13 km stretch of road.

Answer: the visitor would save $8 with the coupon.

Step-by-step explanation: 10% of $80 = 0.1 x $80 = $8

The value is x≤1 or x>2

Equations don't always need to have a "equal to" symbol on both sides to be balanced. Sometimes it can be about a "not equal to" relationship, meaning that something is superior to or inferior to another. In mathematics, an inequality is a relationship between two numbers or other mathematical expressions that results in an unequal comparison. Inequalities are the name given to certain algebraic mathematical expressions.

2x +6≤8 or 2x + 8 > 12

2x +6≤8

2x ≤2

x≤1

2x +8>12

2x>4

x>2

The value is x≤1 or x>2

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The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm.

Step 1: State the hypotheses.

- Null Hypothesis (H₀): The mean length of the bolts is 4.00 cm (μ = 4.00).

- Alternative Hypothesis (H₁): The mean length of the bolts is not equal to 4.00 cm (μ ≠ 4.00).

Step 2: Compute the value of the test statistic.

To compute the test statistic, we will use the z-test since the population standard deviation (σ) is known, and the sample size (n) is large (n = 121).

The formula for the z-test statistic is:

z = (X- μ) / (σ / √n)

Where:

X is the sample mean (4.21 cm),

μ is the population mean (4.00 cm),

σ is the population standard deviation (0.83 cm), and

n is the sample size (121).

Plugging in the values, we get:

z = (4.21 - 4.00) / (0.83 / √121)

z = 0.21 / (0.83 / 11)

z = 0.21 / 0.0753

z ≈ 2.79 (rounded to two decimal places)

Step 3: Determine the critical value and make a decision.

With a level of significance of 0.02, we perform a two-tailed test. Since we want to determine if the mean length of the bolts is different from 4.00 cm, we will reject the null hypothesis if the test statistic falls in either tail beyond the critical values.

For a significance level of 0.02, the critical value is approximately ±2.58 (obtained from the z-table).

Since the calculated test statistic (2.79) is greater than the critical value (2.58), we reject the null hypothesis.

Conclusion:

Based on the computed test statistic, there is sufficient evidence to show that the manufacturer needs to recalibrate the machines. The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm, indicating that the machine's output is not meeting the desired length. The manufacturer should take action to recalibrate the machines to ensure the bolts meet the required length of 4.00 cm.

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From the description, we have an example of paired data.

Paired data refers to a set of two data values that are linked in some way, such as being obtained from the same individual or being measured under similar conditions. In statistical analysis, paired data is often used to compare two sets of data to see if there is a significant difference between them.

Paired data can be analyzed using a variety of statistical methods, such as the paired t-test, which is used to test whether there is a significant difference between the means of two paired samples.

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Answer:

The inverse of the function is \(f^{-1}(x) = \sqrt[3]{\frac{x-16}{8}}\)

Step-by-step explanation:

Inverse of a function:

Suppose we have a function y = g(x). To find the inverse, we exchange the values of x and y, and then isolate y.

In this question:

\(y = \frac{x^3}{8} + 16\)

Exchanging x and y:

\(x = \frac{y^3}{8} + 16\)

\(\frac{y^3}{8} = x - 16\)

\(y^3 = \frac{x-16}{8}\)

\(y = \sqrt[3]{\frac{x-16}{8}}\)

The inverse of the function is \(f^{-1}(x) = \sqrt[3]{\frac{x-16}{8}}\)

Answer:

It has letters

Step-by-step explanation:

Step-by-step explanation:

D is the right answer.

remember, the domain is the interval or set of all valid values of x (the input variable). that means the values from left to right. there is no limitation visible. especially not around x = -3.

the range is the interval or set of valid values of y (the result variable). that means the values from bottom to top. and here we see, that the function never goes below y=-3.

these 2 facts make D the right answer.

Answer:

third option

Step-by-step explanation:

under a counterclockwise rotation of 90° about the origin

a point (x, y ) → (y, - x )

Then

A (- 1, - 2 ) → (- 2, - (- 1) ) → (- 2, 1 )

B (2, - 2 ) → (- 2, - 2 )

C (1, - 4 ) → (- 4, - 1 )

The new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

From the question, we have the following parameters that can be used in our computation:

The figure,

Where, we have

A = (-1, -2)

B = (2, -2)

C = (1, -4)

The rule of 90 degrees counterclockwise is

(x, y) = (-y, x)

Using the above as a guide, we have the following:

A = (2, -1)

B = (2, 2)

C = (4, 1)

Hence, the new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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Answer:

the discount is 12.00$

Step-by-step explanation:

39.99 × 30% = 11.997

which equal 12

Answer:

25/4

Step-by-step explanation:

perimeter is total length of all side

height =2(x+2) (×2 bcause has 2 side)

length =2(3x-1) (×2 bcause has 2 side)

2x+4+6x-2=52

8x-2=52

8x=50 (8x is 8 times x, so move to the other side become divide)

x=50/8

simplify

x= 25/4

Answer:

C and E

Step-by-step explanation:

Answer:

<B, <C, <A

Step-by-step explanation:

The order from smallest to largest angle is the same as the order from shortest to longest opposite side.

Sides from shortest to longest:

120, 130, 180

Angles from smallest to largest:

<B, <C, <A

We don't know the number of pets that received checkups or vacinations, we need to find it, so we will assign variables to these numbers. The variable x will be the number of pets that received checkups and y will be the number of pets that were vaccinated. Therefore we can write an equation as shown below:

This means that each checkup costs $45, while each vaccination costs $90 so sum of the product of the pets that did either of those things must be equal to the revenue of the veterinary.

We were also informed that the number of check-ups was 6 greater than the number of vaccinations, therefore:

If we replace the second equation on the first one, we can solve for y as shown below:

We can solve for x by using this value on the second equation:

The solution to this is that 10 pets got checkups, while 4 got vacinations. So the answer is B.

Answer:

A) 2^12

Step-by-step explanation:

3x - y = 12

3(5) - 3 = 12

15 - 3 = 12

12 = 12

\(\frac{8^x}{2^y}\)

\(\frac{8^5}{2^3}\)

\(\frac{32768}{8}\)

4096

2^12

Hello!

surface area

= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)

= 160cm²