Translate the following verbal statement into an algebraic equation and then solve:
Use x for your variable.
The difference of four times a number and seven is ten times the number.

Answers

Answer 1

If the statement is "The difference of four times a number and seven is ten times the number." then an algebraic equation is 4x-7= 10+x and the solution is -7/6.

Given the statement "The difference of four times a number and seven is ten times the number." We have to translate the statement in an algebraic equation and then solve it.

Let, the number be x.

This difference of four times a number and seven is 4x-7 and ten times the number is 10x

According to the question, the equation is,4x-7= 10x

4x-7=10x

6x=-7

x=-7/6

x=-7/6

Hence the value of the x is -7/6.

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Related Questions

answer must be in simplest form

Answers

The trigonometric ratios shows that the cos M is 4/5.

RIGHT TRIANGLE

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: [tex]hypothenuse^2=(leg_1)^2+(leg_2)^2[/tex] . And the main trigonometric ratios are: sin [tex]\alpha[/tex],  cos [tex]\alpha[/tex] and tan [tex]\alpha[/tex], where:

[tex]sin \alpha =\frac{opposite\;leg}{hypotenuse} \\ \\ cos \alpha =\frac{adjacent\;leg}{hypotenuse} \\ \\ tan \alpha =\frac{opposite\;leg}{adjacent\;leg}[/tex]

For finding the cos M, firstly, you should find the side MN from Pythagorean Theorem.

[tex]hypothenuse^2=(leg_1)^2+(leg_2)^2\\ \\\ 30^2=18^2+(MN)^2\\ \\ 900=324+(MN)^2\\ \\(MN)}^2=900-324\\ \\ (MN)^2=576\\ \\ MN=24[/tex]

If MN=24, the cos M will be

[tex]cosM =\frac{adjacent\;leg}{hypotenuse} =\frac{24}{30} =\frac{4}{5}[/tex]

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Determine the measure of each indicated angle.

Answers

Answer:

∠ABC =   52°

∠BCA =  48°

∠CAB = 80°

Step-by-step explanation:

Angle sum property of triangle: Sum of all the angles of a triangle is 180.

13x² + 12x² + 20x² = 180

Combine like terms,

                 45x²  = 180

                     x² = 180 ÷ 45

                     x² = 4

                     x = √4

                     x = ± 2

x = 2 ; -2

∠ABC = 13x² = 13*4 = 52°

∠BCA = 12x² = 12 *4 = 48°

∠CAB = 20x² = 20 *4 = 80°

The value of x is +2 and -2 and the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.

What is trigonometry?

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

Given that:-

∠ABC = 13x² ∠ACB = 12x² and ∠CAB = 20x²

The angles will be calculated as follows:-

13x² + 12x² + 20x² = 180

45x²  =  180

x²  =  4

x   =  ±2

The angles will be:-

∠ABC = 13x²  = 13 x ( 2² ) = 52

∠ACB = 12x²  = 12 ( 2² )    = 48

∠CAB = 20x²  = 20 ( 2² )  = 80

Therefore value of x is +2 and -2 the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.

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A ship is stationary at sea.
A tugboat is 36 km away at a bearing of 130°, and a yacht is 27 km from the tugboat at a bearing of 260°.
Draw a scale diagram showing the positions of the three vessels.
Use a scale of 1 : 450,000.
Measure the distance from the ship to the yacht to the nearest km.

Answers

Bearing is a topic that deals with the distance and location of a given object with respect to a reference point. Thus in the given question, the ship is 57.23 km to the yacht.

Bearing is a topic that considers the distance and position of a given object with respect to a reference point. Thus the angles are usually measured with reference to the north pole.

Thus to solve the given question, let the required distance be represented by x.

Applying the cosine rule, we have;

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos C

The angle C between the line from ship to tugboat and from tugboat to yacht can be determined as;

C = [tex]10^{o}[/tex] + [tex]40^{o}[/tex]

C = [tex]50^{o}[/tex]

Thus,

[tex]c^{2}[/tex] = [tex]36^{2}[/tex] + [tex]27^{2}[/tex] + 2(36 x 27) Cos [tex]50^{o}[/tex]

  = 1296 + 729 + 1944(0.6429)

  = 2025 + 1249.8

[tex]c^{2}[/tex] = 3274.8

c = [tex]\sqrt{3274.8}[/tex]

  = 57.2259

c = 57.23

Therefore, the distance from the ship to the yacht is 57.23 km.

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Kindly contact a 1-on-1 tutor if more explanations are needed.

A bike store rents bikes for $9 an hour in addition to a helmet rental fee of $15. If
Emmanuel paid $51, for how many hours did he rent the bike?

Answers

Answer:

4 hours

Step-by-step explanation:

First we need to subtract the one pay fee (the helmet rental fee, $15)

So 51 - 15 = 36

Then we need to divide 36 by the amount of money it costs for each hours to find how many hours he rented the bike

So 39/9 = 4


A similarity transformation maps AABC to AJKL The measure of ZA of prelmage AABC Is 105°. The scale factor of the dilation in the similarity
transformation is 1.5. If ZA In the prelmage corresponds to ZJ in the image, what is m
a 70°
b 140°
c 105°
d 35°
its reserved.

Answers

Answer:

The answer is 105.

Step-by-step explanation:

Which of the following terms is defined as 1/sin?

Answers

Answer: D) cosecant

• cosec θ = 1/sin θ
• sin θ = 1/cosec θ

Answer: cosecant

Formula's are:

Secant:

1/cos(x) = sec(x)

Cosecant:

1/sin(x) = cosec(x)

Cotangent:

1/tan(x) = cos(x)/sin(x) = cot(x)

Describe the correlation in terms of strength (weak or strong) and direction positive or negative).

Answers

The description of the correlation in terms of strength (weak or strong) and direction positive or negative) is as explained below.

How to Interpret Correlation Problems?

A correlation coefficient, is expressed as r and it indicates a measure of the direction and strength of a relationship between two variables.

Now, in terms of strength, Correlation strength ranges from -1 to +1. Thus, The closer the correlation is to 0, the weaker it is while the closer it is to ±1, the stronger it is.

Now, in terms of direction;

A correlation of +1 indicates a perfect positive correlation which tells us that both variables move in the same direction together.

A correlation of –1 indicates a perfect negative correlation, which tells us that as one variable goes up, the other goes down.

A zero correlation suggests that the correlation statistic does not indicate a relationship between the two variables.

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Need help with this math question (pic included)

Answers

Answer:

8

Step-by-step explanation:

If the only zero for this function is at x = - 4 it looks like this:

f(x)  = (x+4)(x+4)        =    x^2 +8x + 16         so j = 8

Answer:

Step-by-step explanation:

x² +jx +k = 0

If there is only one root ( - 4 ), then (x + 4)² = 0

or

x² + 8x + 16 = 0

j = 8 and k = 16

Using Newton-Raphson method to find the approximate root of the equation x log_{10}x=1.2
( Carry out three iterations ). [tex] \\ \\ [/tex]
Thank uh!

Answers

Answer:

[tex]x \approx 2.740646096[/tex]

Step-by-step explanation:

Given:

[tex]x\log_{10}x=1.2[/tex]

Rewrite so that it's equal to zero:

[tex]\implies x\log_{10}x-1.2=0[/tex]

Therefore:

[tex]\implies f(x)=x\log_{10}(x)-1.2[/tex]

Differentiate the function:

Use the product rule to differentiate [tex]x\log_{10}(x)[/tex]:

[tex]\textsf{Let }u=x \implies \dfrac{du}{dx}=1[/tex]

[tex]\textsf{Let }v=\log_{10}(x) \implies \dfrac{dv}{dx}=\dfrac{1}{x \ln 10}[/tex]

[tex]\begin{aligned}\implies \dfrac{dy}{dx} & = u\dfrac{dv}{dx}+v \dfrac{du}{dx}\\& = \dfrac{x}{x \ln 10}+\log_{10}(x)\\& = \dfrac{1}{\ln 10}+\log_{10}(x)\end{aligned}[/tex]

[tex]\implies f'(x)=\dfrac{1}{\ln 10}+\log_{10}(x)[/tex]

[tex]\implies f'(x)=\dfrac{1+\ln 10 \log_{10}(x)}{\ln 10}[/tex]

Newton-Rhapson iteration formula

[tex]x_{n+1}=x_n-\dfrac{f(x_n)}{f'(x_n)}[/tex]

Substitute the function and its derivative into the formula, replacing x with [tex]x_n[/tex]:

[tex]\implies x_{n+1}=x_n-\dfrac{x_n\log_{10}(x_n)-1.2}{\dfrac{1+\ln 10 \log_{10}(x)}{\ln 10}}[/tex]

[tex]\implies x_{n+1}=x_n-\dfrac{x_n\ln 10\log_{10}(x_n)-1.2\ln 10}{1+\ln 10 \log_{10}(x_n)}[/tex]

Therefore, the iteration formula is:

[tex]x_{n+1}=x_n-\dfrac{x_n\ln 10\log_{10}(x_n)-1.2\ln 10}{1+\ln 10 \log_{10}(x_n)}[/tex]

Let [tex]x_0=3[/tex]

Substitute this into the formula and carry out 3 iterations:

[tex]\implies x_{1}=3-\dfrac{3\ln 10\log_{10}(3)-1.2\ln 10}{1+\ln 10 \log_{10}(3)}=2.746149035[/tex]

[tex]\implies x_2=2.740648841[/tex]

[tex]\implies x_3= 2.740646096[/tex]

If 5 hours at a computer terminal costs $25, what is the cost of 6 hours?

A. $30
B. $45
C. $150
D. $12

Answers

Answer:

30 dollars

Step-by-step explanation:

25/5 = 5 dollars per hour

so 6 hours would be 5 * 6 = 30 dollars

Answer:

It would be B

Step-by-step explanation:

First, we need to find out the unit rate

5/25=1/5

Therefore, that means in one hour the cost would be $5

Since you are going from one hour to 6 hours you need to multiply both numbers by 6

Since 5x6=30, it would be 30$ :)

Which graph shows h(x) = f(x)g(x)

Answers

The attached graph represents the function h(x), where h(x) = f(x)g(x)

Complete question

Consider the functions f(x) = x - 6 and g(x) = x + 6. Which graph shows h(x) = f(x)g(x)?

How to determine the graph of h(x)?

We have

f(x) = x - 6

g(x) = x + 6

The equation h(x) = f(x)g(x) means

h(x) = f(x) * g(x)

So, we have:

h(x) = (x - 6) * (x + 6)

Expand

h(x) = x² - 36

See attachment for the graph of function h(x)

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Answer:

A on edg. 2020

Step-by-step explanation:

Which graph shows h(x) = f(x)/g(x)

Which function is graphed below?

Answers

Answer: The second option, y = 3(1/3)^x

Step-by-step explanation: Input each equation into a graphing calculator (preferably GeoGebra online) and check the answer. I linked the equation, but make sure to check anyway just in case :)

The scatter plot shows the number of households, in millions, that have cable television over eight consecutive years. Which of the following is an appropriate line of best fit?

Answers

The equation of the appropriate line of best fit is y = 1.25x + 2

How to determine the line of best fit?

Start by drawing a line through the points (see attachment)

From the attached graph, we have:

(x, y) = (0,2) and (4,6.5)

Calculate the slope (m) using:

m = (y2 - y1)/(x2 - x1)

This gives

m = (6.5 - 4)/(2 - 0)

Evaluate

m = 1.25

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = 1.25(x - 0) + 2

Expand

y = 1.25x + 2

Hence, the equation of the appropriate line of best fit is y = 1.25x + 2

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Which equation completes the system that is satisfied by the solution (1, 1)?
02x+y = 2
O4x - 2y = 2
02x - 2y = 2
Ox+y = 4

Answers

Answer: B. 4x-2y=2

Step-by-step explanation:

We will work this out one by one. Plug in the x and y values of the solution to the equations and you will see which one is true or false.

A. [tex]2(1)+y(1)=2\\2+1\neq 2[/tex]     B. [tex]4(1)-2(1)=2\\4-2=2[/tex]

C. [tex]2(1)-2(1)=2\\2-2\neq 2[/tex]     D. [tex]x(1)+y(1)=4\\1+1\neq 4[/tex]

With this information, we see that B is the correct answer.

I hope this helped!! Pls mark brainliest!! :))

I believe the answer is B) 4x - 2y = 2

3(2x − 8) – 11x ......

Answers

Answer:

-5x-24

Step-by-step explanation:

3(2x-8)-11x

Use distributive property.

6x-24-11x.

Combine like terms.

6x-11x-24=-5x-24

-5x-24

Hope this helps!

If not, I am sorry.

Answer:

-5x - 24

Step-by-step explanation:

3(2x − 8) – 11x =

Distribute the 3, then combine like terms.

= 6x - 24 - 11x

= -5x - 24

Probability of Next Candy
Fill in the chart below with the probability of choosing the next candy.

Answers

Answer:

8 is correct.

Mark as brainlist, thanks me, and rate. Hope it helps you!!!

w and x are whole numbers
w>60
x<50
Work out the smallest possible value of x-z

Answers

Using the given information, the smallest possible value of x - z is 12

Evaluating an expression

From the question, we are to determine the smallest possible value of x - z

From the given information,

w and x are whole numbers

and

w > 60

x < 50

∴ w = 61, 62, 63, 63, 65, ...

x = 49, 48, 47, 46, 45, ...

Then,

The smallest possible value of x - z is

x - z = 61 - 49

x - z = 12

Hence, the smallest possible value of x - z is 12

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Please help fast!!

Multiply and reduce to lowest terms. Convert into a mixed number if necessary.

[tex]3 \times \frac{2}{5} [/tex]

Answers

Answer:

[tex]1\frac{1}{5}[/tex]

Step-by-step explanation:

3 = 3/1

(multiply top and bottom separately for fractions)

[tex]\frac{3}{1}[/tex] × [tex]\frac{2}{5}[/tex] = [tex]\frac{6}{5}[/tex]

[tex]\frac{6}{5} = \frac{5}{5}+\frac{1}{5}= 1\frac{1}{5}[/tex]

Answer:

1 1/5

Step-by-step explanation:

3×2/5

multiplying three (3) and two(2) and express the product of three and two over five.

6/5

five can enter in six three times , remainder 1

The fraction in lowest terms is one whole number , one over five.

1 1/5

Teresa is factoring this polynomial by grouping. Which common factors should be used in the next step of factoring?

10x3+3x2−20x−6

(10x3+3x2)+(−20x−6)

x2 and −2x
2x2 and −2x
x2 and −2
2x2 and −2

Answers

Answer:  [tex]x^2[/tex]  and  [tex]-2[/tex]

Step-by-step explanation:

original :

[tex](10x^3+3x^2)+(-20x-6)[/tex]

factored :

[tex]x^2(10x+3)+-2(10x+3)[/tex]

Answer :

[tex]x^2[/tex]  and  [tex]-2[/tex]

Find the distance between -6.77777 and 3.55555.
O 10.3
O 10.33332
O 10.3333332
13.33332

Answers

Answer:

10.33332

Step-by-step explanation:

-6.77777 is 6.77777 units away from 0. So there's 6.77777+3.55555 which is 3.55555 units away from 0.

Add those two numbers together and it's 10.33332

Answer:

10.33332

Step-by-step explanation:

distance between -6.77777 and 3.55555 is 10.33332

Determine the values for the pronumerals that make the following piece-wise functions continuous. (I really need help please).​

Answers

Step-by-step explanation:

A function is continuous at x is

Limit as x approaches c= f(c).

Step 1: Find f(4).

4 is defined for 2x-1 so plug in. 4 for x.

[tex]2(4) - 1 = 7[/tex]

Note that what we just calculated was not only f(4) but also the left sided limit of f(x).

Step 2: Make sure the left sided and right sided limit are equal to 7.

[tex]a + 5x = 7[/tex]

Plug in 4 for x

[tex]a + 5(4) = 7[/tex]

[tex]a = - 13[/tex]

On a farm, there is a grain silo.The silo is cylindrical with a tile roof. The silo has a diameter of 8 metres and is 6 metres tall. The farmer wants to paint the curved surface of the silo.Each can of paint will cover 20m². The paint costs $11.75 per can. How much will it cost the farmer to paint the silo?​

Answers

The paint that the farmer needs to paint his Silo will cost $152.75.

How to calculate the price of the paint that the farmer will require?

To calculate the value of the total paint that the farmer will require, we must carry out the following procedure:

1. Identify the area you need to paint

2πrh + 2πr²2 * 3.14 * 4m * 6m + 2 * 3.14 *4m² = 251.32m²

2. Find how many cans of paint he needs.

251.32m² ÷ 20m² = 12.56

That is, he will need 13 cans of paint.

3. Find the price of 13 cans of paint.

$11.75 × 13 = $152.75

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Which is mostly likely to be the first step in solving a system of nonlinear equations by substitution

Answers

Answer: To solve a system of equations by substitution, we can rewrite a two-variable equation as a single variable equation by substituting the value of a variable from one equation into the other. Let’s start by solving the system of equations that we looked at above: x=4 x = 4 y+x=12 y +x = 12

Step-by-step explanation:

Answer:

Isolating a variable in one of the equations.

Step-by-step explanation:

Triangle ABC has vertices at A(1,2), B(4,0) and C(1,-4) Find the area of triangle ABC.
PLEASE EXPLAIN HOW YOU DID IT

Answers

The area of triangle ABC from the given vertices is gotten as; 7.5

How to find the area of a triangle?

We are given the vertices of the triangle as;

A(1, 2)

B(4, 0)

C(1,-4)

The formula for area of a triangle with 3 vertices is;

Area = ¹/₂[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]

Thus;

Area = ¹/₂[1(0 + 4) + 4(-4 - 1) + 1(1 - 0)]

Area = ¹/₂(4 - 20 + 1)

Area = -7.5

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The product (

Answers

[tex](a+b)(a-b) = a^2 - ab + ba - b^2 = a^2 - b^2[/tex]

Since the middle terms cancel each other out, what is left is the difference of two squares.

In your example (x+6)(x-6) = x² -36

if x=p+2 and y=p-3, show that x+y+1=2p and x-y-5=0​

Answers

If [tex]x=p+2[/tex] and [tex]y=p-3[/tex], then

[tex]x+y = (p+2) + (p-3) = 2p - 1 \implies x+y+1=2p[/tex]

and

[tex]x-y = (p+2)-(p-3) = 5 \implies x-y-5=0[/tex]

as required.

MARKING BRAINLIEST TO FIRST CORRECT ANSWER If quadrilateral JKLM had a translation where all the vertices were in the third quadrant, what would be the coordinates of the vertices?

Answers

If quadrilateral JKLM were in third quadrant then the coordinates will be (-1,0),(-4,-1),(-4,-2)(-1,-2)

Given Quadrilateral JKLM is in fourth quadrant and coordinates (1,0),(4,-1),(4,-2)(1,-2)

We know that the coordinates of x used to negative in third quadrant and positive in fourth quadrant. Coordinates of y used to negative in third and fourth quadrant.

So in order to change the coordinates from fourth to third we need to change the coordinates of x axis to negative and the coordinates will be :

Coordinates of J will change from (1,0) to (-1,0)

Coordinates of  K will change from(4,-1) to (-4,-1)

Coordinates of L will change from (4,-2) to (-4,-2)

Coordinates of M will change from (1,-2) to (-1,-2).

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Trey graphs the equations y = –x2 + 2x + 3 and y = x2 – 2x + 3 to solve the equation –x2 + 2x + 3 = x2 – 2x + 3. His graph is shown below.

What are the solution(s) of –x2 + 2x + 3 = x2 – 2x + 3?

Answers

The solution of the equation -x^2 + 2x + 3 = x^2 - 2x + 3 are the x-coordinates of common points on the graphs are x=0 and x=2.

What is a system of equations?

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

As we can see from the attached graph these graphs intersect at points (0,3) and (2,3).

The system of equation are;

[tex]y = x^2 + 2x + 3 \\y = x^2 - 2x + 3[/tex]

So,

[tex]-x^2 + 2x + 3 = x^2 - 2x + 3 \\\\2x^2 - 4x = 0\\\\2x ( x - 2) = 0[/tex]

Then the solutions of the equation are x=0 and x=2.

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Answer:

0 and 2

Step-by-step explanation:

b on edge

4
12 + 17 < -18 *
True
False

Answers

did you mean 4 multiply by -18 on your right side? if so, it would be:

12+ 17 = 29
4 * -18 = -72

so the answer would be false, since 29 is greater than -72
False! Because -18 is definitely not greater

John bought 8 watches for $56 and his friend victor bought 7 watches for $63. whose watch is expensive ?

Answers

John=$7 each watch
Victor =$9 each watch
Victors was more because if I were to buy the same amount of each (56).
63*8= 504
56*7=382.

John bought 56 for 382
Victor bought 56 for 504.
Other Questions
[39/(15-2)|-(2*9)please solve and show steps! thx! Does the chart below represent a proportional relationship? What is the rate of change?x y1 42 83 124 16 In this excerpt, Randolph was in favor of which of the following?Select one:a.Retaining the Articles of Confederationb.Declaring independence from Great Britainc.Developing a new constitution with adequate power for the governmentd.Securing the Bill of Rights The creation of which of the following allowed merchant firms to hold money on accountinstead of carrying precious metals as a form of payment for trade goods?Select one:a. Bank of Amsterdamb. Transfer merchandizingc. International Company of Bankersd. Bank of Genoa Construct a square inscribed in a circle. Please help asp. Find six rational numbers between -2 and 5 Read the following excerpt from a speech made by a national leader duringwartime:It has been a difficult few weeks. Progress has been slow.But there have been promising signs. I encourage you notto look at what has been, but what is to come, becausewith your dedication at home and our soldiers' dedicationin the field, things are beginning to turn around.Which is one likely purpose of the speech, based on the excerpt above?A. To persuade citizens to sacrifice moreB. To challenge citizens who oppose the warC. To provide hope for citizensD. To explain a difficult decision Mahek owns a holiday tree farm. There are currently 800 trees on the property. Each year 20% of the trees are harvested and sold, and 200 seedlings are planted. Write a recursive definition for the number of trees on the farm at the beginning of the nth year.1. a1 = 800, an = 0.20an-1 +2002. a1 = 200, an = 0.80an-1 + 8003. a1 = 800, an = 0.80an-1 + 2004. a1= 0.20, an=0200an-1 what mass of aluminium is required to produce 500g of aluminium chloride?2Al + 3Cl --> 2AlCl the equation is 6a+3b when a=4 and b=1 Given that 2x^2-5 = a(x+2)^2 _ b(x+1)+x for all values of X, find the value of a, of b and of c 3. What mathematical symbol is appropriate to use given theword?4. What word is appropriate to use given the symbol? modern observations have shown that the geometry of the universe is ____. please help!!!!picture below In an article about foods that have a lot of vitamin C, which image would connect most with the text?A. A picture of someone drinking orange juiceB. A picture of a big vitamin that has "C" written on itOC. A picture of someone eating an orangeD. A picture of all the fruits and vegetables that have a lot of vitaminC What wrong of "old nepal" does the poet wants to amend? Explain . Software that functions as an electronic version of a filing cabinet? The graph shows the function f(x).On a coordinate plane, a cube root function goes through (8, 2), has an inflection point at (0, negative 1), and goes through (8, negative 3).Which equation represents f(x)?f(x) = Negative RootIndex 3 StartRoot x EndRootf(x) = Negative RootIndex 3 StartRoot x minus 1 EndRootf(x) = Negative RootIndex 3 StartRoot negative x EndRoot minus 1f(x) = Negative RootIndex 3 StartRoot negative x EndRoot in which area of the galaxy would you find stars with fairly circular orbits about the galactic center? Please help!!! Thanks so much