Please look at the picture and answer the question thank you

[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_{3}(y+5)+\log_3(6)~~ = ~~\log_3(66) \\\\[-0.35em] ~\dotfill\\\\ \log_3[(y+5)\cdot 6]=\log_3(66)\implies (y+5)6=66 \\\\\\ y+5=\cfrac{66}{6}\implies y+5=11\implies \boxed{y=6}[/tex]

Answer:

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Given system:

First simplify the second equation by dividing all terms by 2:

We got the same equation as the first one. It means the two lines overlap, so there are infinitely many solutions.

If we use elimination method, we will subtract the two equations then end up with equation 0 = 0.

Answer:

Let's call the amount his wife paid for her car "x". We know that:

Marc's car = $52,000

Marc's car = 2x - $7,600

We can substitute the first equation into the second equation

52,000= 2x-7600

52,000+7600=2x

59,600=2x

x=29,800

His wife paid $29,800 for her car.

Answer:

$29,800.00

Step-by-step explanation:

52000 = 2x - 7600  Add 7600 to both sides

52000 + 7600 = 2x

59600 = 2x  Divide both sides by 2

29800 = x

Answer: the estimated maintenance cost of cars when the age of cars is 12 years is 16.5 ( in 100 birr)

Step-by-step explanation:

To obtain the regression equation for costs related to age of cars, we can use the method of least squares. This method involves finding the line of best fit that minimizes the sum of the squared differences between the predicted values and the actual values.

The equation for a linear regression line is:

y = a + bx

where a is the y-intercept and b is the slope of the line.

To find the slope of the line (b), we can use the formula:

b = (n(∑xy) - (∑x)(∑y)) / (n(∑x^2) - (∑x)^2)

To find the y-intercept (a), we can use the formula:

a = (∑y - b(∑x)) / n

Given the data provided, we can calculate the following values:

∑x = 142

∑y = 150

∑xy = 2430

∑x^2 = 10304

n = 8

By substituting these values into the formulas for b and a, we can find the slope and y-intercept of the line:

b = (8(2430) - 142(150)) / (8(10304) - 142^2) = 0.5

a = (150 - 0.5(142)) / 8 = 13.5

Therefore, the regression equation for the costs related to age of cars is:

y = 13.5 + 0.5x

To estimate the maintenance cost of cars when the age of cars is 12 years, we can substitute x = 12 into the equation and solve for y:

y = 13.5 + 0.5(12) = 16.5

So the estimated maintenance cost of cars when the age of cars is 12 years is 16.5 ( in 100 birr)

An empty number line is a visual tool used to represent numbers and their relative positions. It can be used to compare, order, and perform operations on numbers.

A number with more digits is always greater than a number with fewer digits, according to Rule I.

Rule II states that when two numbers have the same number of digits, we compare the digits starting from the leftmost position until we find an unequal number of digits. Greater numbers are those with more digits.

As far as we are aware, a number with more digits is always greater than one with fewer digits.

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Answer:

Assuming the question is how many l of paint he needs the answer would be 5L

Step-by-step explanation:

1L- 4 chairs

?L- 20 chairs

Therefore 5L- 20 chairs

Answer:  Ryan should sell his CDs for $13 to maximize his revenue.

Step-by-step explanation:

To find the price at which Ryan should sell his CDs to maximize his revenue, we need to use the information provided about the relationship between price and sales, and the formula for revenue (price x quantity sold).

Step 1: Identify the relationship between price and sales. We know that a $1 increase in the price of a CD leads to a drop of 5 CDs per week in sales.

Step 2: Create an equation that relates price, quantity sold, and revenue. Let P be the price of a CD, Q be the quantity sold, and R be the revenue. Then, we have R = P x Q

Step 3: Create a table that shows the relationship between price, quantity sold, and revenue.

Price Quantity Sold         Revenue

10       80                            800

11       75                              825

12      70                                     840

13     65                                        845

14     60                                         840

15     55                                        825

16     50                                   800

17     45                                  785

18     40                                720

19     35                                      665

20     30                                              600

Step 4: Identify the price that maximizes revenue. From the table we can see that the revenue is maximum at $13 which is 845 and this is the price at which Ryan should sell his CDs to maximize his revenue.

Therefore, Ryan should sell his CDs for $13 to maximize his revenue.

From the coordinates we can see the rule for this transformation is:

It is a dilation by a scale factor of 2 and reflection in the y-axis.

It means this is a similarity transformation, since the figure has changed its size.

Answer:

Dilation of scale factor 2 centered at the origin, followed by a reflection in the y-axis.

Similarity transformation.

Step-by-step explanation:

Given vertices of ΔABC:

Given vertices of ΔA'B'C':

From observation, the series of transformations the transforms ΔABC to ΔA'B'C' are:

This is a similarity transformation as the two triangles have the same shape but different sizes.

The area of the triangle shown is 51.96 unit²

An equation is a expression that shows the relationship between numbers and variables.

The area of a triangle can be found given two adjacent sides and an angle between the two sides. It is given as:

Area = (1/2) * product of adjacent sides * sin(angle)

Hence:

Area of triangle shown = (1/2) * 10 * 12 * sin(60) = 51.96

The area is 51.96

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Answer: 9n-7

Step-by-step explanation:

9n-7 because there are no like terms

Answers:

(a)    $1092.03

(b)    $1093.08

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

Work shown for part (a)

A = P*(1+r/n)^(n*t)

A = 1000*(1+0.09/2)^(2*1)

A = 1000*(1+0.045)^(2)

A = 1000*(1.045)^(2)

A = 1000*1.092025

A = 1092.025

A = 1092.03

Don't forget to round to the nearest penny, aka nearest hundredth.

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

Work shown for part (b)

A = P*(1+r/n)^(n*t)

A = 1000*(1+0.09/4)^(4*1)

A = 1000*(1+0.0225)^(4)

A = 1000*(1.0225)^(4)

A = 1000*1.09308331878906

A = 1093.08331878906

A = 1093.08

Answer:

Step-by-step explanation:

S= 2πrh

<=> 3520= 2x3.142xrx40

=> r ≈ 14

The radius of the cylindrical lampshade is approximately 13.98 cm.

The formula for the curved surface area of a cylinder is 2πrL, where r is the radius, L is the height and π is pi. Given that the curved surface area of a cylindrical lampshade is 3520 cm² and the height is 40cm.

We know that:

2πrL = 3520cm²

So we can solve for the radius by dividing both sides by 2πL:

r = 3520cm² / (2π * 40cm)

Substituting the value of pi we have

r = 3520cm² / (6.284 * 40cm) = 3520cm² / 251.36cm = 13.98cm

The radius of the cylindrical lampshade is approximately 13.98 cm.

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Let x = the original price of the electric wok.

r(x) = x - $5 (the price after the rebate)

p(x) = x * (1 - 0.25) (the price after the discount)

Given that x = $38, we can substitute that value in to find the final cost of the wok in each composition:

r(p(x)) = r(p(38)) = r(38 * (1 - 0.25)) = r(28.5) = 28.5 - $5 = $23.50

p(r(x)) = p(r(38)) = p(38 - $5) = p(33) = 33 * (1 - 0.25) = $24.75

So, r(p(x)) = $23.50 and p(r(x)) = $24.75

r(p(x)) will save her the most money.

Answer:

  x = 18.3

Step-by-step explanation:

You want the length of the hypotenuse of a right triangle given the side opposite the 41° angle is 12 units.

The sine relation is ...

  Sin = Opposite/Hypotenuse

This can be rearranged to ...

  Hypotenuse = Opposite/Sin

  x = 12/sin(41°) ≈ 18.3 . . . . units

The value of x is about 18.3.

__

Additional comment

This is the SOH relation from the mnemonic SOH CAH TOA, which is intended to remind you of the relation between trig functions and sides of a right triangle. The others tell you ...

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

In the attached, note the calculator mode is set to DEG (degrees) so the argument of the Sin( ) function will be interpreted properly.

Answer:

$1850×4÷100×8=$592 as interest

Answer:

It means there is no solution.

Step-by-step explanation:

When you work on a system of equations and the variable falls out of the equation and you're left with a false statement...that means there is no solution.

Answer:

Step-by-step explanation:

Do you mean "isn't complete or not in final form?"

If it does, it is because the equation is not yet simplified. You can still change its structure by distributing the negative sign to the right parenthsis to make it a whole polynomial.

[tex](2x^{2} + 5) - (4x-1)\\2x^{2} + 5 - 4x + 1\\2x^{2} - 4x + 6\\[/tex]or

[tex]2 (x^{2} - 2x + 3)[/tex]

[tex]-10w=-9[/tex]

Divide both sides by -10(to isolate the variable):

[tex]\dfrac{-10w}{-10} =\dfrac{-9}{-10}[/tex]

[tex]=0.9[/tex]

The result of the expression 3(x + 2)² - 4 is equivalent to 44.

        [tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]

Given is the equation as -

(x + 2) = 4

We have to find the result of -

3(x + 2)² = 4

It is given that -

(x + 2) = 4

So, we can write -

3 x 4 x 4 = 4

48 - 4

44

Therefore, the result of the expression 3(x + 2)² - 4 is equivalent to 44.

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{Question in english -

If (x+2)=4 what is the result of 3(x+2)^2=4}

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$200\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (200)(0.10)(1) \implies I = 20~\hfill \underset{total~amount~in~savings}{\stackrel{200~~ + ~~20}{\text{\LARGE 220}}}[/tex]

Answer:

$ 220

Step-by-step explanation:

i = prt = 200 * .1 * 1  = 20  dollars interest

  add in her original deposit of 200 for a total of 220 dollars

Answer:

28.1 ft

Step-by-step explanation:

d  =  350 * ( tan 10.5 - tan 6)  = 28.1 ft

Using substitution method, the values of a and b in the system of linear equations are 6.3 and 3.65

A system of linear equations is a set of two or more linear equations that contain two or more variables. The goal of solving a system of linear equations is to find the values of the variables that satisfy all of the equations in the system simultaneously. Linear equations are equations that can be written in the form of ax + b = y, where a, b, and x are constants and x is the variable.

To solve this problem, we have to solve the equations simultaneously using either substitution or elimination method.

0.95a + 1.1b = 10 ...eq(i)

a + b = 9.95 ...eq(ii)

From equation (ii)

a + b = 9.95

a = 9.95 - b ...eq(iii)

Put eq(iii) into eq(i)

0.95(9.95 - b) + 1.1b = 10

b = 3.65

put b = 3.65 into eq(ii)

a + 3.65 = 9.95

a = 6.3

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Answer:

synthetic division method use it

An equation is represented by the table is y= -4x+3. Therefore, option B is the correct answer.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

From the given table, we have coordinates (0, 3) and (1, -1)

Here, m=(-1-3)/(1-0)

m=-4

Substitute m=-4 and (x, y)=(0,3) in y=mx+c, we get

3=-4(0)+c

c=3

Substitute m=-4 and c=3 in y=mx+c, we get

y= -4x+3

Therefore, option B is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

Which equation is represented by the table?

y=-3x+1

y=-4x+3

y=3x-4

y=-2x+1

Answer:

The total amount in your bank account per year is not a linear relationship, it's compound interest.

Step-by-step explanation:

The total amount in your bank account per year is not a linear relationship because it is not a straight line. Linear relationships are defined by an equation in the form of y = mx + b, where m is the slope of the line, x is the independent variable and y is the dependent variable, and b is the y-intercept.

In this case, the total amount in your bank account per year is not a straight line, it is a curve. The total amount in your bank account will increase as a function of time, but the rate of increase is not constant as it is with linear relationships.

The amount of money in your account will increase over time as the interest is compounded. The interest is calculated on the principal + accumulated interest, so the growth rate of the account is not constant, it increases as the balance grows.

For example, the first year you will earn $5000.03 = $15 in interest, and the second year you will earn $5150.03 = $15.45 in interest, the next year the interest will be $530.45*0.03 = $15.91 and so on.

Answer:

The derivative of f(x) = 3 ÷ x + 2 is f'(x) = -3 ÷ (x+2)².

Step-by-step explanation:

This is found by using the first principle method of differentiation, which states that the derivative of a function is the rate of change of the function with respect to the indepedent variable. In other words, the derivative of a function measures how much the output of the function changes with respect to a small change in the input.

To find the derivative of f(x) = 3 ÷ x + 2, we start by taking the limit as h approaches 0 of the difference quotient (f(x + h) - f(x)) ÷ h.

The difference quotient is (3 ÷ (x + h + 2) - 3 ÷ (x + 2)) ÷ h. Simplified, this becomes 3h ÷ (x + h + 2)(x + 2).

When h approaches 0, the difference quotient becomes 3 ÷ (x + 2)², which is the derivative of f(x).

Answer:

-4

Step-by-step explanation:

[tex] 6^5 \times 6^n = 6^1 [/tex]

When you multiply powers with the same bases, add the exponents.

[tex] 6^{5 + n} = 6^1 [/tex]

[tex] 5 + n = 1 [/tex]

[tex] n = -4 [/tex]

Answer: -4

The required values are ∠B ≈ 59° and ∠C ≈ 31° for the given triangle.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The triangle is given in the question, as shown

As per the tangent function,

tan ∠B = AC/AB

tan ∠B = 35/21

∠B = tan ⁻¹(35/21)

∠B = tan ⁻¹(1.667)

∠B ≈ 59°

tan ∠C = AB/AC

tan ∠C = 21/35

∠C = tan ⁻¹(21/35)

∠C = tan ⁻¹(0.6)

∠C ≈ 31°

Thus, the required values are ∠B ≈ 59° and ∠C ≈ 31°.

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Answer:

12

Let X be the unknown number we are supposed to find.

Given information from the question, we can form up an equation:

2X + 7 = 3X - 5

3X - 2X = 7 + 5

X = 12

Therefore the unknown number is 12