. Solve for x in the equation log (7x+5) -log(x - 1) = 1(with full working​

Answer: The slope is the cost per hour (in this case $20 per hour).

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Further Explanation:

Recall that,

[tex]\text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}[/tex]

The rise tells us how much to go up or down, depending if the rise is positive or negative. The run tells us how much to go to the right. Always move to the right.

In this problem, the change in y is the change in price. The change in x is the change in hours. Dividing the two items gives cost per hour, aka unit cost.

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

Example:

Let's pick two points from this line and use the slope formula. I'll pick (1,60) and (3,100) as they are the only two points with coordinate labels.

So,

[tex](x_1,y_1) = (1,60) \text{ and } (x_2,y_2) = (3,100)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{100 - 60}{3 - 1}\\\\m = \frac{40}{2}\\\\m = 20\\\\[/tex]

The slope is 20, or 20/1

It says that each time the number of hours x goes up by 1, the cost variable y goes up by 20.

Put simply: The hourly fee is $20 per hour.

This matches what it says in the instructions when your teacher wrote "A roofer charges $60 for the first hour and $20 per hour for each additional hour".

Answer:

105

Step-by-step explanation:

Supplementary angles are two angles that add up 180 degrees.

if one is 75, then the other would be 105

hope this helps :)

(i made a mistake so i edited it, thanks for the reminder in the comments)

Answer:

105 degrees

Step-by-step explanation:

Supplementary Angles are angles whose measurements equal 180 degrees

To find the supplement subtract this known measurement angle A

180 - 75 = 105 degrees

Answer:

[tex] \sf \rightarrowtail \: \frac{x}{4} = \frac{2}{5} \\ \sf \rightarrowtail \: 4 \times 2 = 5x \\ \sf \rightarrowtail \: 5x = 8 \\ \sf \rightarrowtail \: \boxed{ \bf \: x = \frac{8}{5} }[/tex]

The correct answer is "C" - a decrease in personal income tax is most likely to result in an increase in consumer demand.

Taxes are compulsory payments made by a government organization, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools.

A value-added tax, often referred to as a goods and services tax in some nations, is a kind of tax that is imposed gradually. At every stage of manufacture, distribution, or sale to the final customer, it is added to the cost of a good or service.

There is an increase in consumer demand when personal income taxes are cut because people have more money that they can spend on products and services.

On the other hand, a rise in personal income taxes would reduce the amount of disposable money that consumers have, which will result in a drop in demand from consumers.

In a similar vein, a rise in company tax would result in higher business costs and lower profits, both of which would reduce consumer demand. Conversely, a drop in corporate tax would not directly influence consumer spending.

So the correct answer is C.

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Answer:

D. 29°

Step-by-step explanation:

Triangle ACB is an isosceles triangle so the two base angles are the same(61° and 61°). A triangle's angles must add up to 180, so take 180-61-61.

180-61-61 = 58

Divide by 2 to find angle ACB:

58/2 = 29

Answer:

Option D; 29°

Step-by-step explanation:

ΔAOB is isosceles triangle: so ∠B = ∠A, ∠A = 61, therefore:

∠O = 180 - (61 + 61)

∠O = 58

and ∠C = 58 / 2

∠C = 29

Hope this helps!

Answer:

24 pounds

Step-by-step explanation:

48 quarts of raisins divided by 6 is equal to 8.

So 3 pounds of cookie dough times 8 = 24.

24 pounds of cookie dough.

Log₁₀ is an expression used to represent logarithmic functions with a base of 10. To write log₁₀ in Microsoft Word, you can use the “Insert Equation” feature.

To access this, select Insert on the top menu bar, followed by Equation. In the new window that appears, select the Greek and Math Symbols tab. In this tab you will find the log₁₀ symbol that looks like an upside-down “y”. You can then click on the symbol and it will be added to your document.

If you need to type out the equation, you can type “log₁₀” and it will automatically be converted to the log₁₀ symbol.  You can also use the shortcut CTRL+Alt+L to insert the log₁₀ symbol directly into your document.

If you are using a Mac, you can use the shortcut Command+Shift+L.  The log₁₀ symbol is commonly used in mathematics and science, particularly in algebra and calculus. It is used to represent the logarithm of a particular number to the base 10.

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ok um 213=89Step-by-step explanation:ummmmmmmmmm

Answer:

5.5

Step-by-step explanation:

180/3 =60 (60/1 hr)

330/60 =5.5

Answer: first u have to find the perimiter for each side

Step-by-step explanation:

the answer is 100 d z

Answer: obtuse

Step-by-step explanation:

Answer:

$0.62

Step-by-step explanation:

1.24/2=0.62

1 gallon- 4 pint

0.5 gallon- 2 pint

Answer:

637 in^3

Step-by-step explanation:

V=(BxH)/2

V=((13x7) x 14)/2

V=(91x14)/2

V=1274/2

V=637 in^3

Answer:

8

Step-by-step explanation:

Answer:

A regular octagon has eight sides.

Step-by-step explanation:

Octagon = Octa + gon where octa means eight and gon means sides.

Answer:

y = 2x - 1

Step-by-step explanation:

Point 1: (0, -1); Point 2: (1, 1)

           (x₁, y₁)              (x₂, y₂)

y₂ - y₁      1 - (-1)       1 + 1       2

---------- = --------- = -------- = ------ = 2

x₂ - x₁      1 - 0           1          1

y - y₁ = m(x - x₁)

y - (-1) = 2(x - 0)

y + 1 = 2x - 0

   -1          -1

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

y = 2x - 1

I hope this helps!

Answer:

the expression can be factored into (x+4)(23x + 7) and it is a product of two binomials.

Step-by-step explanation:

The expression 23x² + 6x + 7 is in the form of a quadratic equation. A quadratic equation is an equation in the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. In this case, the coefficients of the x², x, and the constant term are a = 23, b = 6, c = 7.

One way to factor a quadratic equation is by using the factoring by grouping method, where we group the terms in pairs and factor out the greatest common factor (GCF) from each group.

Here is one way to factor this equation:

23x² + 6x + 7 = (23x² + 6x) + 7

= (23x² + 6x) + 7

= (23x² + 6x + 6x) + 7

= (23x² + 12x) + 7

= (23x(x) + 3x(4)) + 7

= (23x(x+4) + 7)

= (x+4)(23x + 7)

So the expression can be factored into (x+4)(23x + 7) and it is a product of two binomials.

It's important to note that the above expression factors into a product of two binomials and not two factors of 23x² + 6x + 7

You can also use Quadratic formula to solve the above expression if this method seems confusing.

Answer:

Jo turned around and walked back to the starting point

8 km/hr

Step-by-step explanation:

4 km/one-half hr = 8 km/hr

Step-by-step explanation:

A)

If we look at the graph at 10 mins its evident that there has been some movement meaning Joes has moved 1km (as we can see in the graph) away from the starting point.

B)

For the last 30 mins of the graph we can see some changes.

so Joe started at 30 mins and ended at 60mins so there is a difference of 30 mins. In those 30 mins Joe moved from 0km to 4km. Meaning that Joe moved at 4km in 30 mins.

We are going to work this out in KPH. Since we have 30 mins and the unit we are using to measure his speed is measured in hours, we need to double it along with the kilometres he moved so it stays fair and constant. so we will have 8km and 60 min (1 hour). Therefore Joe moved at 8kph.

Hope this helps

Area of the middle rectangular section = length x width = 35 x 20 = 700 square cm.

The radius of the circular sections is 25 cm

Area of a full circle is pi x r^2 = 3.14 x 25^2 = 1962.5 square cm.

There are two quarter circles which is 1/2 of a circle. The area of those would be 1962.5/2 = 981.25 square cm.

Total area of the figure = 700 + 981.25 = 1681.25 square cm

Solutions refers to the answer to the problem, Real Solutions are realistic and practical whereas ideal solutions are the best cases for the solutions.

In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.

In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.

Ideal Solutions - Best cases, Usually not possible.

Real Solutions - Practical and possible to attain.

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Answer:

-5.026

Step-by-step explanation:

-9.23 + 4.204

= -5.026

Answer:

The zeros are {-2, 3}

Step-by-step explanation:

Set each of these factors equal to zero, in turn, set each factor = to 0 and solve the resulting equation for x:

x + 2 = 0 yields x = -2;

x - 3 = 0 yields x = 3

The zeros are {-2, 3}

Answer:

10 and 24units

Step-by-step explanation:

Pythagoras' Theorem applies to right angle triangles with the formula:

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

where c is the longest side, with a and b the shorter ones (interchangable)

With the parameters given from the question and the formula given as well, we can find the value of x and therefore the side lengths.

By Pythagoras' Theorem,

[tex] {26}^{2} = ( {5x)}^{2} + ( {12x)}^{2} \\ 676 = 25 {x}^{2} + 144 {x}^{2} \\ 169 {x}^{2} = 676 \\ {x}^{2} = 676 \div 169 \\ {x}^{2} = 4 \\ x = \sqrt{4} \\ = 2[/tex]

Now we can find the side lengths.

[tex]5x = 5(2) = 10units \\ 12x = 12(2) = 24units[/tex]

Therefore the side lengths are 10 and 24 units.

The steps to solve two polynomial equations are given below.

What is polynomial?

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

x^2 + 4x + 7 is an illustration of a polynomial with a single indeterminate x.

Apply the Zero Factor Property to an Equation Solving.

ZERO. FACTOR, write the equation with one side equal to zero. the expression by a factor.

PROPERTY. Solve the equation by setting each factor to zero.

Check by adding substitutes to the initial equation.

Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero once it has reached zero. The original equations' solutions are the solutions to the resulting equations. Factoring cannot always be used to solve polynomial equations.

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Answer:

100π sq. ft

Step-by-step explanation:

Given,

Radius ( r ) = 10 ft

To find : Area ( circle ) = ?

Formula : -

Area ( circle ) = π r^2

Area ( circle )

= π x 10^2

= π x 100

= 100π sq. ft

Answer:

area of circle : πr^2

                      = π(10)^2

                      = 314.1592654

                      ≈ 314.16 cm2

Answer:

[tex]v=48 cm^3[/tex]

Step-by-step explanation:

→ [tex]v=(l)(w)(h)[/tex]

→ [tex]v=(4)(2)(6)[/tex]

→ [tex]v=48 cm^3[/tex]

[tex]-------------[/tex]

hope it helps...

have a great day!!

Therefore, one mole of any substance is equal to its molar mass in grams.

Mass per mole is a definition of molar mass. In other terms, molar mass is the total mass of all the atoms in a material that makes up a mole. It is measured in gram-per-mole units.

A chemical element is uniquely defined by its atoms, which are tiny pieces of substance. An atom is made up of a core nucleus and one or more negatively charged electrons that orbit it. The positively charged, comparatively hefty protons and neutrons that make up the nucleus may be present.

The molar mass of a substance is the mass of one mole of that substance and is usually expressed in grams per mole (g/mol).

For example, the molar mass of carbon is 12.01 g/mol, so one mole of carbon weighs 12.01 grams.

Therefore, one mole of any substance equals its molar mass in grams.

It is essential to mention that the molar mass is the weight of one mole of a substance and is determined by the atomic or molecular weight of the substance.

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Answer:

m= -2 , c=3

Step-by-step explanation:

equation of a straight line is given by y= mx+c

y + 2x = 3

or, y = -2x + 3

(m) (c)

Answer:

Step-by-step explanation:

y + 2 x = 3 is almost but not quite in the slope-intercept form y = mx + b.  We need to rewrite y + 2 x = 3 in that form:

y = -2x + 3

Comparing this to y = mx + b, we get:

slope = m = -2

y-intercept = b (or c) = 3

Answer:

8.25cm²

Step-by-step explanation:

the area of the triangle = (half x base x height )=

(1.5x3)÷2= 2.25cm²

the area of the rectangle= length x width = 3x2= 6cm²

total = 2.25+6= 8.25cm²

7 students failed the examination out of 28 students who appeared for the examination.

What is the Proportion?

A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls)

When we say that a proportion is two ratios that are equal to each other, it means this in the sense of two fractions being equal to each other.

For instance, 5/10 equals 1/2.

If 3/4 of the students passed the exam, this means that 1 - 3/4 = 1/4 of the students failed the exam.

We can use this information to find the number of students who failed the exam by multiplying the total number of students who appeared for the exam by the proportion of students who failed:

Number of students who failed = Total number of students * Proportion of students who failed

Number of students who failed = 28 students * 1/4 = 28 students * 0.25 = 7 students

Hence, 7 students failed the examination out of 28 students who appeared for the examination.

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x + 2y = 3x + 4

2y = 3x + 4 - x

y = (2x + 4)/2

y = x + 2

Answer: y=x+2

Step-by-step explanation:

you subtract x on the left on both sides then you'll have 2y=2x+4 we have to get y by itself so divide it by 2 on both side and when you do that on the right you divide both 2x and 4 by 2 thus giving y=x+2