2/3x+y=7/3
2/3x-y=1

Solve the equation without graphing

After solving the given inequality the answer is 3logx+log₁₀(x+2)>1.

So,

Given: 3log x + log(x+2) > 1

3log x + log(x+2) > 1 ⇒ 3logx+log₁₀(x+2)>1

Therefore, after solving the given inequality the answer is 3logx+log₁₀(x+2)>1.

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In mathematics, an inverse function is one that "reverses" another function. The inverse of y = 2x + 8 is f⁻¹(x) = x/2 − 4.

The inverse function of a function f in mathematics exists a function that reverses the operation of f. If the inverse of f exists, it is shown by the f⁻¹. The inverse of f exists if and only if f exists bijective.

An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f ⁻¹.

Let the function be y = 2x + 8

Interchange the variables.

x = 2y + 8

Solving for y

y = x/2 − 4

Replace y with f⁻¹(x), we get

f⁻¹(x) = x/2−4

Verify if f⁻¹(x) = x/2−4 is the inverse of f(x) = 2x+8.

The inverse of y = 2x+8 is f⁻¹(x) = x/2−4.

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Answer:

No

Step-by-step explanation:

Its not a function because there wouldn't be a reasonable answer if you try solving the equation.

Answer:

yes, it is a function

Step-by-step explanation:

y = -x + 4 is a line. In order to be a function every input can have only one output. Any x you put into that equation will spit out only one y. It passes the vertical line test (ALL lines except a vertical line pass the vertical line test.) So it is a function.

The total Cost of a bench is 1.008x.

According to the statement,

We have to find that the cost of the bench.

So, For this purpose, we know that the

The cost function may be accustomed find the typical cost, which is that the average amount of cash it costs to provide a unit.

From the given information:

The owner of the outdoor furniture center decides to use the 120% markup. at the tip of the season, he wants to sell all the benches that are available. he sells the benches for 20% off.

Then

Since we've provided that

Let the price price be 'x'.Mark up % = 120%

So, price value would be 120x/100

Then

Discount % = 20%

Amount of discount is given by

20* 1.2x/1000.

24x

So, it becomes,

Amount after discount is given by

1.2x - 0.24x = 0.96x

Amount of sales tax would be

100+5/100*0.96x

105/100*0.96x

1.008x.

So, The total Cost of a bench is 1.008x.

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Answer:

answer is 9

Step-by-step explanation:

a*a+b.

-2*-2+5.

4+5=9

Answer: 9.1 - 12.9 = -3.8

Step-by-step explanation:

9.1

12.9

———-

-3.8

the smaller number is getting subtracted by the bigger number which makes it a negative unless u made a error and placed the numbers in wrong order. The order of numbers won’t matter if it’s multiplication or addition. But if it’s division or subtraction it will change the final answer

Answer:

Step-by-step explanation:

1. 170, 13 7/8, 13.5, 64/5

2. Plant D = 5.2 in Plant B =5.3 in Plant C = 5.5in Plant A =5.92

3. Chelsea, Finn, Erin, Mitchell

Answer:

[tex]x = 14[/tex]

Step-by-step explanation:

[tex](6-x)-(x-5)-(4-x)=-\frac x2 \text{ // Distribute}\\\to 6 - x - x + 5 - 4 + x = -\frac x2 \text{ // Simplify}\\\to 7 - x = -\frac x2 \text{ // Multiply by 2}\\\to 2(7 - x) = 2(-\frac x2) \text{ // Distribute}\\\to 14 - 2x = -x \text{ // Add 2x}\\\to 14 = x[/tex]

The circle below has a sector 120° shaded. 120° 22. Then area of sector is 200.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Area of sector=theta/360*πr^2

Given π = 7,

theta=120 degrees

d=22, so r=11.

Area of sector=210/360*7*7^2

=0.583*7*7*7

=200.08

Therefore area of sector is 200.

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The rate r with the given distance is 65 miles/hour.

Given that, the formula d=2r can be used to find the distance d travelled after 2 hours at rate r.

Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, the distance may refer to a physical length or an estimation based on other criteria.

Now, the given formula is d=2r.

So, the formula for r is r=d/2

Distance = 130 miles

Then, the rate r = 130/2 = 65 miles/hour

Therefore, the rate r with the given distance is 65 miles/hour.

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Answer:

[tex](-8)^7[/tex]

Step-by-step explanation:

You are multiplying (-8) 7 times. Therefore, it can be simplified down to [tex](-8)^7[/tex].

[tex]23^8\cdot 23^n=(23^5)^3\implies \underset{same~base}{\stackrel{same~exponent}{23^{8+n}=23^{(5)(3)}}}\implies 8+n=(5)(3) \\\\\\ 8+n=15\implies n=7[/tex]

The order of transformation which best describes how to sketch the graph of h(x) = ∛1 - x is: A. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the left one​ unit, and then reflect the graph about the​ y-axis.

Generally, there are different types of transformation and these include the following:

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In this context, we can reasonably infer and logically deduce that the order of transformation which best describes how to sketch the graph of h(x) = ∛1 - x is to start by plotting the graph of the basic function y = ∛x, and then horizontally shift the graph of function y = ∛x to the left one​ unit, and then reflect the graph about the​ y-axis.

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Complete Question:

Which of the following order of transformations best describes how to sketch the graph of h(x) = ∛1 - x?

A. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the left one​ unit, and then reflect the graph about the​ y-axis.

B. Starting with the graph of the basic function y = ∛x, vertically shift the graph up one​ unit, and then reflect the graph about the​ y-axis.

C. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the left one​ unit, and then reflect the graph about the​ x-axis.

D. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the right one​ unit, and then reflect the graph about the​ y-axis.

The area of the running track to the nearest tenth of a yard is 1456 yards

The length of the field is 100 yards with a width of 40 yards.

Notice that the two semicircles on both ends form a circle with diameter 40 yards. Since it's diameter is 40, then it's radius is 20. We can get the length of the rectangle by subtracting two 20 from 100 or subtracting it's diameter to the entire length 100:

= 100-20-20

=100-40

=60

Since we formed a rectangle with two semicircles on both ends, we have the length of the rectangle 60 yards and the width 40 yards.

We first get the circumference of the circle.

C=πd

=(3.14)(40)=125.6

Then we get the measure of the two lengths of the rectangle which is 60

60+60=120

We multiply 145.6 by 10 and we get 1456

Therefore, the area of the running track to the nearest tenth of a yard is 1456 yards.

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Answer:

3570 square yards.

Step-by-step explanation:

A=  ℓh-ℓh+πr square-πr square

A=60 * 100 - 40 * 100 + π(30) square - π(20) square

A= 6000-4000+900π-400π

A=2000+500π

A=2000+500*3.14

A=3570 square yards.

694 divided by 41 is  16 remainder 38.

A division is a process of splitting a specific amount into equal parts.

given:

694÷41 is equal to 10+3+2+1

Now, performing the division

41  | 694  | 1 6

     - 41

__________

        284

         246

-___________

         38

So, when 694 is divided by 41 gives remainder 38.

Hence,  694 divided by 41 is  16 remainder 38.

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The volume of the square pyramid that has a side length of 7 and a height of 21 is calculated as: 343 units³.

A square pyramid is a type of pyramid that has a square base and four triangular faces.

The volume of a square pyramid can be calculated using the formula expressed as:

Volume (V) = 1/3(a²)(h), where a is the length of a side and h is the height of the square pyramid.

Given:

Side length (a) = 7 units

Height of the square pyramid = 21 units

Substitute

Volume (V) = 1/3(7²)(21)

Volume (V) = 1/3(49)(21)

Volume (V) = 1(49)(7)

Volume = 343 units³

Therefore, the volume of the square pyramid that has a side length of 7 and a height of 21 is calculated as: 343 units³.

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The equation to describe the linear relationship between x, the number of weeks from now, and y, the amount Jaycee has in her vacation savings is y = 75 + 15x

The equation to describe the linear relationship:

The amount Jaycee has in her vacation savings = Amount Jaycee has saved + Additional amount jaycee saved per week(Number of weeks Jaycee saved)

y = 75 + 15(x)

y = 75 + 15x

For instance, if jaycee has saved for 5 weeks, the

amount Jaycee has in her vacation savings is

y = 75 + 15x

y = 75 + 15(5)

= 75 + 75

y = $150

Therefore, the equation to describe the linear relationship between x, the number of weeks from now, and y, the amount Jaycee has in her vacation savings is y = 75 + 15x

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of 98000}}{\left( \cfrac{7}{100} \right)98000}\implies 6860[/tex]

Answer: P = 4x + 2, A = x² + x - 6

Step-by-step explanation:

       Perimeter is the distance around a shape, or all the sides added together. We will create an equation, plug in the known values, and then solve. The first step is to distribute, then we combine like terms.

   P = 2l + 2w

   P = 2(x + 3) + 2(x - 2)

   P = 2x + 6 + 2x - 4

   P = 4x + 2

       The area of a rectangle is found by multiplying the width by the length. We will use the FOIL method.

A = (x + 3)(x - 2)

A = x² + x - 6

First ➜ x * x = x²

Outside ➜ x * -2 = -2x

Inside ➜ 3 * x = 3x

Last ➜ 3 * -2 = -6

Add together ➜ x² + 3x - 2x - 6 = x² + x - 6

Answer:

Step-by-step explanation:

Let two consecutive odd integers be x and x+2

Given, their sum is 20.

x+x+2=20

2x=20−2

2x = 18

x=9

Therefore, other number is

x+2=9

9+2=11.

Thus, the numbers are 9,11.

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

check

9 + 9 + 2 = 20

20 = 20

the answer is good

The value of the greater integer is 7.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

The sum of an integer and 2 times the next consecutive integer is 20.

let, the number = x

so, the next consecutive integer = x+1

ATQ, x+2(x+1)=20

    ⇒3x+2=20

    ⇒3x=18

    ⇒x=6

i.e. the greater integer = x+1 = 7

Hence, the value of the greater integer is 7.

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2 log(x) = -1 => x = 0.3162, by properties of logarithm.

Now,

2 log(x) = -1

=> log (x) = [tex]\frac{-1}{2}[/tex]

Since, generally the base of log is 10, raising them to 10.

=> [tex]10^{log_{10}(x)}=10^{\frac{-1}{2}}[/tex]

=> x = 0.3162 ( as [tex]a^{log_a(x)} = x[/tex])

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Answer:

C I think would be the answer.

If we expand the expression [tex]log_{10}[/tex] m⁴ n⁻², then we will get

4m-2n.

Given that the expression is [tex]log_{10}[/tex] m⁴ n⁻²

We are required to find the expansion value of the expression.

The change of base formula is basically the formula which will give us the answer of a log with a different base by using only log calculations with a base of 10.

The expression or function is [tex]log_{10}[/tex] m⁴ n⁻².

(We know that log mn=log m +log n)

So,

[tex]log_{10}[/tex] m⁴ n⁻² =4m-2n  (log [tex]a^{b}[/tex]=b log a)

Hence if we expand the expression [tex]log_{10}[/tex] m⁴ n⁻², then we will get

4m-2n.

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Answer:

-12

Step-by-step explanation:

putting value of n in the equation will give you the answer

the temperature will be 2.5 degrees per second.

We are given the data:

Seconds       Temperature (°F)

0                            75

10                          100

20                         125

30                         150

We need to find the temperature in degrees per second.

So, we get that:

Seconds       Temperature (°F)                    degrees / sec

0                            75                                            Nil

10                          100                           (100 - 75) / (10 - 0) = 2.5

20                         125                         (125 - 100) / (20 - 10) = 2.5      

30                         150                         (150 - 125) / (30 - 20) = 2.5            

Therefore, the temperature will be 2.5 degrees per second.

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Answer:

x - y - 1 = 0

Step-by-step explanation:

Using y-intercept

b = y - m × x

b = 7 - (1) × (8) = -1

y = mx + b/Flip expression, subtracting from all sides

assuming x ≠ 0 for x = 1

assuming y = 0

y = x - 1

x - y - 1 = 0

We need to know about translation, reflection and rotation to solve the problem. (1) We translate a triangle with respect to a horizontal and vertical direction. (2) We rotate a traingle about a given angle. (3) We refelct a triangle about a line of reflection which can be axis or vector.

(1) Translation of a triangle means changing it's position without changing the shape or size of the triangle. We translate a triangle with respect to a horizontal and vertical direction. We get the new triangle by adding the horizontal translation value to the x-coordinate and the vertical translation value to the y-coordinate.

(2) Rotation of a triangle is turning the triangle by an angle around a center point. When a triangle is rotated by 90° clockwise then (x,y) becomes (y,-x), when rotated by 90° anticlockwise (x,y) becomes (-y,x), when rotated by 180° clockwise or anticlockwise (x,y) becomes (-x,-y).

(3)Reflection of a triangle is finding a mirror like image of the triangle about  a line of reflection. The line of reflection may be either of the axes, a vector. To find the image we have to find the coordinates of the triangle that are of same distance from the line of reflection on the opposite side like they are from the original triangle.

Therefore we learnt about translation, reflection and rotation and saw that (1) Translation needs a horizontal and vertical direction for translating, (2) Rotation needs an angle of rotation and a center point and (3) Reflection needs a line of reflection.

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The quotient that best represents the rate of change in the mountain goat’s elevation is 2.27 feet/minute.

Quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number.

The rate of change can be defined as a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.

Mathematically, the rate of change can be calculated by using this formula;

Rate of change = Δy/Δx = Change in height/Change in time

Substituting the given parameters into the formula, we have;

Rate of change = Quotient = 50 feet/22 minutes

Rate of change = Quotient = 2.27 feet/minute.

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Using the calorie count C for a serving of food C=4h+7f+5​p, the formula for f is derived to be f =( C - 4h - 5p ) / 7

Given data

C = 4h + 7f + 5​p

C is the calorie count

h is the number of grams of carbohydrate

f is the number of grams of fat

p is the number of grams of protein

solving for f in the given equation

C = 4h + 7f + 5​p

make f the subject of formula

C - 4h - 5p = 7f

7f = C - 4h - 5p

dividing through by 7

f =( C - 4h - 5p ) / 7

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Answer:

D

Step-by-step explanation:

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