An equation is shown below:
3 (2 x - 7) = 3
Part A: How many solutions does this equation have?
Part B: What are the solutions to this equation? Show your work

Answers

Answer 1

The solution of the equation 3(2x - 7) = 3 is x = 4. The equation has only one solution.

What is an equation?

An equation is a mathematical expression that shows that two mathematical expressions are equal. Equation shows the relationships between variables, numbers and constant.

Therefore, let's solve the equation 3(2x - 7) = 3 as follows

3(2x - 7) = 3

Open the parenthesis

3(2x - 7) = 3

6x - 21 = 3

add  21 to both sides of the equation

6x - 21 = 3

6x - 21 + 21 = 3 + 21

6x = 24

divide both sides of the equation by 6

6x / 6 = 24 / 6

x = 4

Therefore, the equation has one solution which is x = 4.

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Related Questions

Function A and Function B are linear functions

Answers

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below for Function A.

[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-5)}}}{\underset{\textit{\large run}} {\underset{x_2}{10}-\underset{x_1}{(-8)}}} \implies \cfrac{4 +5}{10 +8} \implies \cfrac{ 9 }{ 18 } \implies \cfrac{1 }{ 2 }\impliedby \stackrel{\textit{slope of}}{A} \\\\[-0.35em] ~\dotfill[/tex]

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{5}x-1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \stackrel{\textit{slope of}}{B} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} \stackrel{A}{\cfrac{1}{2}} ~~ < ~~ \stackrel{B}{5} \end{array}}~\hfill[/tex]

what is the smallest even consecutive number such that their sum is at most 90?


SOLVE PLEASE

Answers

To find the smallest even consecutive numbers whose sum is at most 90, we can start with the smallest even number, which is 2. Then, we can add 2 to it to get the next even number, which is 4. We can keep adding 2 to get the next even numbers, and keep track of their sum. We can stop as soon as the sum exceeds 90.

The smallest even consecutive numbers whose sum is at most 90 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90

The first 20 even consecutive numbers sum 90.

A set of elementary school student heights are normally distributed with a mean of 105 centimeters and a

standard deviation of 10 centimeters. Faisal is an elementary school student with a height of 103. 1 centimeters.

What proportion of student heights are lower than Faisal's height?

You may round your answer to four decimal places

Answers

Answer:

  0.4247

Step-by-step explanation:

You want to know the proportion of heights less than 103.1 cm if the population is normal with a mean of 105 cm and a standard deviation of 10 cm.

Proportion

The proportion can be found using a suitable probability calculator. The one shown in the attachment tells us ...

  the proportion of heights less than 103.1 cm is about 0.4247.

__

Additional comment

The height of interest is less than the mean by approximately 0.2 times the standard deviation. This suggests the proportion will be close to, but less than, 0.5000.

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Joseph took a taxi from his house to the airport. The taxi company charged a pick-up

fee of $3. 10 plus $2 per mile. The total fare was $21. 10, not including the tip. Write

and solve an equation which can be used to determine m, the number of miles in the

taxi ride.

Answers

The equation is 2m + 3.10 = 21.10

And, the number of miles in the taxi ride is m = 9.

Now, According to the question:

Joseph took a taxi from his house to the airport. The taxi company charged a pick-up fee $3.10 plus $2 per mile. The total fare was $21.10.

Now,

The equation is written as,

2m + 3.10 = 21.10

Subtract 3.10 from both sides

2m = 18

Divide 2 from both sides

m = 9

Hence, The equation is 2m + 3.10 = 21.10

And, the number of miles in the taxi ride is m = 9.

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Please help with this problem!!!

Answers

At 11.5 hours, the red turtle pass the blue turtle. The red turtle won the race. The solution has been obtained by studying graph of the functions.

What is graph of the function?

The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. The graph of f is also known as the graph of

y = f(x).

In the graph, it is seen that from 6 to 13 hours, the blue turtle is at the same place whereas the red turtle is moving.

Therefore, at 11.5 hours the red turtle passes the blue turtle.

The red turtle won the race in 16 hours because in the graph it is observed that the blue turtle did not complete the entire km. The graph of blue turtle is a little less than that of red turtle.

Hence, at 11.5 hours, the red turtle pass the blue turtle and wins the race.

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Since there are multiple questions, so the question answered above is attached below.

Francine had six times the money Tommy had, but after Francine gave Tommy $33 to help him purchase a baseball cap, Tommy had twice as much as Francine. How much did they each start with?

Answers

For the relation of times of money , Francine and Tommy start with the amount of money equals to $18 and $3 respectively.

Let 'x' represents the amount of money with Francine .

And 'y' represents the amount of money with Tommy.

In the first condition:

x = 6y __(1)

To purchase baseball cap Francine gave $33 then the given relation is :

y - 33 = 2( x - 33 )

⇒ y - 33 = 2x - 66

⇒y = 2x -66 + 33

⇒ y = 2x -33 __(2)

Substitute the value of 'x' from (1) in (2) we get,

y = 2(6y) - 33

⇒y = 12y - 33

⇒ 12y - y = 33

⇒ 11y = 33

⇒ y = $3

⇒ x = 6(3)

⇒ x = $18

Therefore, the amount of money Francine and Tommy start with is equal to $18 and $3 respectively.

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the roof of a clock tower is a pentagon pyramid. each side of the base is 7ft long. the slant is 9. what is the area of the roof

Answers

The area of the roof is 157.5 .

It is given that the roof of a clock tower is a pentagonal pyramid.

Each side of the base is 7 ft long.

The slant height is 9 ft.

we know that, to find area we have,

Area=1/2 × 7 × 9 × 5

= 315/2

= 157.5

Hence, 157.5 square feet is the area of the roof.

Pentagonal pyramid

A pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point.

It is a three  dimensional figure, it is a solid figure or an object or shape that has three dimensions—length, width, and height.

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Willow is driving on the freeway. She just passed mile marker 325. The fastest she will drive is 75 miles per hour, though, there is a bit of traffic that might slow her down a bit, but she doesn’t know exactly how much. The mile markers are increasing on her route.


The expression 325 + 2y represents what mile marker she’s at after 2 hours, depending on traffic. Which inequality describes the mile marker she would be at this point?

Answers

The inequality describes the mile marker she would be at this point is:

325 + 2y ≤ 475

Now, According to the question:

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We have,

The fastest driving speed of Willow is 75 miles per hour,

There is a bit of traffic on her route that might slow her speed down,

So, the inequality which represents the speed of the willow is:

y ≤ 75

Hence, the inequality which represents the speed of the driving of willow is y ≤ 75.

Now, the expression 361 + 2y represents what mile marker he is at after 2 hours. We know that the fastest he will drive is 75, so we could replace y=75 in the last expression to know what mile marker he would be seeing at that point. This is:

325 + 2(75) => 325 + 150 = 475

Now, we know that the inequality would be:

325 + 2y ≤ 475

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2. Consider this excerpt from chapter 39: "Something is discomforting about a sun that gives no

heat but keeps shining. " In this comparison, who is the sun?

O The tour guide

Maxine

Jade's mother

The symphony members

Answers

Jade's mother is the sun of Jade because she motivated Jade against race and gender, class and privilege, and fear and courage. Something is discomforting about a sun that gives no heat but keeps shining. " In this comparison, Jade's mother is the sun. So the option 3 is correct.

While expressing the complicated emotions of an aspirational, devoted girl, Jade's narrative voice offers riveting insights on the intricacies of race and gender, class and privilege, and fear and courage. Watson's story, which brims with empathy and wisdom, extols the ability of creative expression to reimagine and transform the world.

The many individuals who find themselves in the world looking for themselves are addressed in Watson's exquisitely written book. Piecing Me Together is a novel about how young people deal with the struggles and pain of daily life while remaining entire and true to themselves. It is both timely and timeless.

The reason why Jade's mother is said to as the sun of Jade is because she inspired Jade to overcome prejudices related to class, privilege, and fear.

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The complete question is:

Consider this excerpt from chapter 39:

Something is discomforting about a sun that gives no heat but keeps shining. " In this comparison, who is the sun?

1. The tour guide

2. Maxine

3. Jade's mother

4. The symphony members

Tell whether the two rates form a proportion.

-0. 4 kilometer for every 15 minutes

-0. 6 kilometer for every 20 minutes

Answers

As the value of the ratio of both the quantities are NOT same so the given values .

No, The two rates not form a proportion.

Now, According to the question:

Two ratios are equivalent, if the fractions corresponding to them are equivalent. Four quantities are said to be in proportion, if the ratio of the first and the second quantities is equal to the ratio of the third and the fourth quantities.

A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows:

1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)

Now,

0. 4 kilometer for every 15 minutes equals to (0.4/15) = 0.026

So for every minute they travel 0.026km.

0. 6 kilometer for every 20 minutes equals (0.6/20) =  0.03

So for every minute they travel 0.03km.

Here, as the value of the ratio of both the quantities are NOT same so the given values .

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Find the lateral area, and surface area of the figure.


Round your answers to the nearest thousandth, if necessary

Answers

Lateral Area = 108 square km

Surface Area = 120 square km

Think of the triangles as the floor and ceiling of this 3D room. The walls are three rectangular sides.

We have a 9 by 4 wall with an area of 9*4 = 36 square km

We have a 9 by 3 wall with an area of 9*3 = 27 square km

We have a 9 by 5 wall with an area of 9*5 = 45 square km

The lateral area is 36+27+45 = 108

The two triangles form the base faces of this prism.

Let's find the area of one of the triangles

area=0.5*base*height = 0.5*3*4 =6

One triangle has an area of 6, so both triangles in total have an area of 2*6 = 12 square km.

The total surface area is therefore 108+12 = 120 square km.

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Multiple. Write your answer as a fraction or as a whole or mixed number.
3/4 x 8

Answers

Answer:

6

Step-by-step explanation:

3/4 x 8 = 3 x 8 / 4 x 1 = 24/4 = 6

A new Lexus sells for $56,000. Use 2 depreciation models and desmos to answer the following questions.

Model A: The car depreciates 12% per year.

Model B. Use straight line depreciation - the car has a value of $0 in 12 years.

Use desmos and attach a screenshot to show the following.

1. Use the wrench tool to label your x an y-values, change your x and y-value to appropriate numbers. Remember to lock the viewpoint.

2. Write on your screenshot and label the point where the linear model and the exponential model are equal.

3. Attach a screenshot to this ssignment.

Justgive me the equations

Answers

The time in years for which the values are the same is given as follows:

7.25 years.

How to obtain the models?

A decaying exponential model is given as follows:

y = a(1 - r)^t.

For which:

a is the initial value.r is the decay rate, as a decimal.

The parameters for this problem are given as follows:

a = 56000, r = 0.12.

Hence the exponential model is given as follows:

y = 56000(0.88)^x.

The linear model is given as follows:

y = b - mx.

In which:

b is the initial value.m is the yearly depreciation rate.

The parameter values for this problem are given as follows:

b = 56000, m = 56000/12 = 4666.67.

Hence the linear model is:

y = 56000 - 4666.67.

The point of intersection of the two graphs is at a time of 7.25 years.

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Please help me <3 Thanks :)

Answers


The Answer is: The slope is 7/4

The length of the minute hand of a clock i 6cm. Find the area wept by it when it move from 7:05 p.m. to 7:40 p.m.

Answers

Area swept by minute hand of a clock is 66cm².

Given that length of the minute hand of clock is 6cm.

We know that, total angle covered by the minute hand of clock is 360° in 60 minutes.

Total time interval = 7:45 PM – 7:05 PM = 35 minutes

In 60 minutes 360° angle covered

Then, in 1 minute 360/60 angle covered

So, in 35 minutes

total angle covered = 360/60 * 35 = 210°

Total area covered = sectional area of circle with radius 6cm

Total area covered = Ф/360 * πr²

= 210/360 * 22/7 * 6² = 66 cm²

Therefore, total area swept by minute hand of a clock is 66cm².

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a cell phone company has three different production sites. five percent of the phones from site 1, 7% from site 2, and 9% from site 3 have been recalled due to unexpected shutdown issue. suppose that 60% of the phones are produced at site 1, 30% at site 2, and 10% at site 3. if a randomly selected cell phone has been recalled, what is the probability that it came from site 3 (write it up to second decimal place)?

Answers

So, the probability that a randomly selected cell phone that has been recalled came from site 3 is 2.5 or 25%.

We can use Bayes' theorem to calculate the probability that a phone that has been recalled came from site 3. Bayes' theorem states that:

P(A|B) = P(B|A) * P(A) / P(B)

where:

P(A|B) is the probability of event A occurring given that event B has occurred (in this case, the probability that a phone came from site 3 given that it has been recalled)

P(B|A) is the probability of event B occurring given that event A has occurred (in this case, the probability that a phone has been recalled given that it came from site 3)

P(A) is the prior probability of event A occurring (in this case, the probability that a phone came from site 3)

P(B) is the prior probability of event B occurring (in this case, the probability that a phone has been recalled)

So, in this case, we have:

P(site 3 | recalled) = P(recalled | site 3) * P(site 3) / P(recalled)

We know that:

P(recalled | site 3) = 9%,

P(site 3) = 10%

We also know that:

P(recalled) = P(recalled | site 1) * P(site 1) + P(recalled | site 2) * P(site 2) + P(recalled | site 3) * P(site 3)

= (5% * 60%) + (7% * 30%) + (9% * 10%) = 3% + 2.1% + 0.9% = 6%

So, we can now calculate the probability that a phone that has been recalled came from site 3 as:

P(site 3 | recalled) = (9% * 10%) / 6% = 0.15 / 0.06 = 2.5

So the probability that a randomly selected cell phone that has been recalled came from site 3 is 2.5 or 25%.

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Shirley can choose between peanut butter pretzels and caramel coated popcorn for her evening snack. According to economists, her _____ cost of consuming caramel coated popcorn would be the forgone peanut butter pretzels. Group of answer choices internal opportunity average transaction social

Answers

According to economists, her opportunity cost of consuming caramel-coated popcorn would be the forgone peanut butter pretzels.

Opportunity costs are the possible advantages that a person, investor, or company forgoes while deciding between two options. Opportunity costs are by definition invisible, making it simple to ignore them.

Better choices can be made by being aware of the opportunities that might be lost when a company or person chooses one investment over another. It is necessary to weigh the advantages and disadvantages of each choice offered in order to correctly assess opportunity costs.

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All sides of a lawn are expanded by the same amount so that it’s dimension are now 100 feet by 60 feet. If x is the same amount of length added to each side, write a function of x giving the length of each of the original sides. Use these functions to make a function for the area of the original lawn.

Answers

The function of x giving the length of each of the original sides would be  [tex](x + 100) * (x + 60) = x^2 + 160x + 6000[/tex].

What is Function of x?

A function is a formula that expresses one variable in terms of another. The statement "y is a function of x" (denoted y = y(x)) states that y changes depending on the value of x.

The original length of each side of the lawn can be represented by the function x + 100, and the original width can be represented by the function x + 60.

To find the area of the original lawn, we can multiply the length and width functions.

So, the function for the area of the original lawn is:

         [tex](x + 100) * (x + 60) = x^2 + 160x + 6000[/tex]

This is a quadratic function in x, whose leading coefficient is 1, and the value of x is the same amount of length added to each side of the lawn.

Hence, The function of x giving the length of each of the original sides would be  [tex](x + 100) * (x + 60) = x^2 + 160x + 6000[/tex].

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What is the solution of the system of equations
Y=1/8x-1
-5x+4y= - 13

Answers

Answer:

(2.57, -0.07)

Step-by-step explanation:

To solve the system of equations, we can substitute the expression for y in the second equation:

-5x + 4(1/8x - 1) = -13

We can then simplify and solve for x:

-5x + (1/2)x - 4 = -13

-3.5x = -9

x = 2.57

We can then substitute this value of x back into the first equation to find the value of y:

y = 1/8(2.57) - 1

y = -0.07

So the solution of the system of equations is (x, y) = (2.57, -0.07)

Which even number is not a composite number?
A) 6
B) 4
C) 2
D) 8

Answers

ithe answer will be a
kills ksksmslsls
im positive the answer is A6

Given a rope 10 units in length, if side lengths must be in whole units, how many different triangles can be made?​

Answers

A per the measurement, there is only form exactly 1 unique triangle.

The term triangle in math is known as a two-dimensional shape with three sides, three interior angles, and three vertices.

Here we have know that a rope 10 units in length, if side lengths must be in whole units.

And we need to find the number of different triangles can be made.

Here we know that length is 10 units, and the side length are whole units.

Which means that here we have 3 distinct value.

So as we all know that all of the triangles you make are the same triangle. Which means that if your three side lengths can form a triangle, then they can only form exactly 1 unique triangle.

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PLEASE HELP ASAP

Find the value of r so that the line through (r,5) and (6,r) has a slope of 5/8

Answers

Answer: 70/13

Step-by-step explanation:

Slope = rise/run

(r-5)/(6-r) = 5/8

30-5r = 8r-40

70 = 13r

70/13 = r

Jason is closing on a $430,000 home. He made a 13% down payment and is borrowing the rest. What is the approximate range of costs that he might expect to pay at the closing?

Answers

Answer:

$8,600 - $31,100

Step-by-step explanation:

Hope this helps :)

Ayúdenme a encontrar el valor de los ángulos la medida de A) es 48 grados y E) es 136 grados y con eso encuentra los valores de los demás

Answers

eeeeeAnswer:

Step-by-step explanation:

se que g=136 t=48 los demás no los se

Write the missing angle measure next to each
letter.
65°
a, b, c, d, e
The angle relationship I used to find Angle a is...
The angle relationship I used to find Angle b is...
The angle relationship I used to find Angle c is...
The angle relationship I used to find Angle d is...
The angle relationship I used to find Angle e is...


Answers

The missing angle measure for the following letters are:

a - 65°

b - 115°

c - 115°

d - 65°

e - 65°

The angle relationship I used to find Angle a is the Corresponding Angle (a = 65°)The angle relationship I used to find Angle b is Angles on a Straight line (b = 180 - 65)The angle relationship I used to find Angle c is the Corresponding Angle (b = c)The angle relationship I used to find Angle d is Angle on a straight line (d = 180 - 65) = 115°The angle relationship I used to find Angle e is. Corresponding angles. d = e and e = d.

What is a corresponding angle?

Corresponding angles are generated when two parallel lines are crossed by a transversal.

Opening and closing a lunchbox, completing a Rubik's cube, and endless parallel railway tracks are all examples of equivalent angles.

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relative frequency distributions are generally more useful than frequency distributions when

Answers

Relative frequency distributions are generally more useful than frequency distributions when comparing data sets of different sizes.

Frequency distributions can show the actual number of observations falling in each range or the percentage of observations. In the latter sample, the distribution is called a relative frequency distribution.

Frequency distribution tables can be utilised for both categorical and numeric variables. Continuous variables should only be used with class intervals, which will be described shortly.

A relative frequency distribution displays the proportion of the total number of observations associated with each value or class of values and is related to a probability distribution, which is extensively used in statistics.

--This question is incomplete; the complete question is

"Relative frequency distributions are generally more useful than frequency distributions when _____."--

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Solve for kkk.

20-6+4k=2-2k20−6+4k=2−2k20, minus, 6, plus, 4, k, equals, 2, minus, 2, k

k =k=k, equals

Answers

The value of k is -2

Now, According to the question:

The given equation is:

20 - 6 + 4k = 2 - 2k

We have to solve for the value of k.

Now,

20 - 6 + 4k = 2 - 2k

Combine the like terms;

20 - 6 - 2 = -2k - 4k

Calculate the sum or difference:

20 - 8 = -6k

12 = -6k

Calculate the product or quotient:

k = -12/6

k = -2

Hence, The value of k is -2

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A recipe states that chicken needs to be cooked for 15 minutes per kg plus an extra 40 minutes. Express the relationship between mass and cooking time using function notation, and define the domain and range.

Answers

For the given statement, the domain and range are - Domain : x ,Range : f(x)  40.

What does a notation in mathematics mean?

In mathematical notation, symbols are used in expressions and formulas to represent operations, unnamed numbers, relations, and any other mathematical objects. In mathematics, science, and engineering, mathematical notation is frequently used to communicate complicated ideas and properties in a clear, unambiguous manner.

A notation is a set of clear guidelines for using symbols to describe numbers and actions.

The sum of numerous linked terms is frequently represented by the sign (capital sigma) in shorthand notation. In statistics, sigma notation is frequently employed.

For each dividend number, the extended notation division method merely repeats the division, multiplication, and subtraction operations.

Given data :

x is the mass of the chicken (in kg)

f(x) : the cooking time ( in minutes )

Domain : x

Range : f(x)  40

f(x) = 15x + 40 - 15 minutes per kg (x) plus 40 more minutes

f (1) = 15 x 1 + 40 = 55

A 1 kg chicken needs 15 min + 40 min = 55 min

f (2) = 15 x 2 + 40 = 70

A 2 kg chicken needs 30min + 40 min = 70 min

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Help please!!! (3x² - 4xy + y²)(4x + 3y)

Answers

The simplified form of the expression (3x² - 4xy + y²)(4x + 3y) is 12x³ - 7x²y + 8xy²  + 3y³.

What is the simplified form of the expression?

Given the expression in the question;

(3x² - 4xy + y²)(4x + 3y)

To simplify, apply distributive property by multiplying each term in the first expression by each term in the second expression.

(4x + 3y)(3x² - 4xy + y²)

4x (3x² - 4xy + y²) + 3y(3x² - 4xy + y²)

3x² × 4x - 4xy × 4x  + y² × 4x  + 3x² × 3y - 4xy × 3y  + y² × 3y

12x³ - 16x²y + 4xy²  + 9x²y - 12xy²  + 3y³

Collect like terms

12x³ - 16x²y + 9x²y + 4xy²  - 12xy²  + 3y³

Add -16x²y and 9x²y

12x³ - 7x²y + 4xy² - 12xy²  + 3y³

Add 4xy²  and -12xy²

12x³ - 7x²y + 8xy²  + 3y³

Therefore, the simplified form is 12x³ - 7x²y + 8xy²  + 3y³.

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Give f(x)=3-|2x-5| find f(0)+f(-4)

Answers

The value of the function f(0) + f(-4) is -12

How to determine the value of the function?

From the question, we have the following equation that can be used to solve the question

f(x) = 3 - |2x - 5|

Also, we have the function values to be

f(0) and f(-4)

When these values are calculated, we have

f(0) = 3 - |2(0) - 5| = -2

f(-4) = 3 - |2(-4) - 5| = -10

substitute the known values in the above equation, so, we have the following representation

f(0) + f(-4) = -2 - 10

Evaluate

f(0) + f(-4) = -12

Hence, the solution is -12

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