Mr Smith halves a certain number and then adds 8 to the result. He finds that he obtains the same answer if he doubles his original number and then subtracts 8 from the result. What is Mr Smith’s original number?

The **original number **is 32/3.

A branch of mathematics known as **algebra **deals with **symbols **and the mathematical **operations **performed on them. **Variables **are the name given to these **symbols **because they lack set values. We frequently observe constant change in specific variables in our day-to-day situations. But the **need **to depict these **shifting **values is **ongoing**. These values are frequently represented in **algebra **by symbols such as x, y, z, p, or q, and these symbols are known as **variables**.

let the **number **be x

So, halves a certain **number **and then **adds** 8 to the **result**

=1/2 x + 8

and, same answer if he **doubles **his **original **number

= 2x

2x - 8 = 1/2x + 8

2x - 1/2 x =8 + 8

3/2 x = 16

x = 32/3

Hence, the **original** **number **is 32/3.

Learn more about **algebra **here:

https://brainly.com/question/24875240

#SPJ1

4x^-x/x^3-2 how much

**Answer:**

4x^-x-1

**Step-by-step explanation:**

4x^-x/x^3-2

= 4x^-x/x

= 4x^-x-1

In a math class with 23 students, a test was given the same day that an assignment

was due. There were 14 students who passed the test and 15 students who completed

the assignment. There were 12 students who passed the test and also completed the

assignment. What is the probability that a student chosen randomly from the class

did not complete the homework?

**Answer: 8/23**

**Step-by-step explanation:**

**Make a two-way table**

** Did Assignment Didn't do Assignment**

**Passed 12 2**

**Did not pass 3 6**

**Total 15 8 = 23**

**2+6=8**

**8/23 **

Question 8A: Mr. Sowers wants to purchase expo markers for his classroom. He has a budget of $35. A four pack of markers costs $5.49, including tax. Write and solve an inequality, using x for the variable, to solve for the number of packs of markers Mr. Sowers can purchase. Copy/paste one of the following inequality symbols to help you write your inequality: ≤ < ≥ >

The number of** packs of markers** that Mr. Sowers can purchase is 6.

The** maximum amount **that Mr. Sowers can spend is $35. This means that the amount can either by $35 or less than $35. Thus, the **inequality sign **that would be used is the less than or equal to sign, ≤ .

total amount spent on the packet of **markets** ≤ budget

(cost of one packet x number of packets) ≤ $35

$5.49x ≤ $35

In order to determine the value of x, divide both sides of the equation by 5.49

x ≤ $35 / 5. 49

x ≤ 6.38

x ≤ 6

To learn more about **inequality, **please check: https://brainly.com/question/5031619

#SPJ1

Question

Refer to the Newsela article, "Doctoral Student Played a Big Part in First Black Hole Photo."

How does Bouman contribute to taking the first photograph of a black hole?

Responses

Bouman is the first person to suggest that black holes exist in space.

Bouman invents a telescope that can gather images taken by eight telescopes located around the world.

She and her team create an algorithm that makes it possible to collect data and combine it into one image.

Her TED talks on black holes inspire other scientists to figure out how to photograph them.

Bouman contributed to taking the first **photograph** of a **black hole** as she and her team created an **algorithm **that makes it possible to collect data and combine it into one image.

The article highlighted the importance of **Katie Bouman **in leading her team who created a computer software capable of using an **algorithm **that analyzes data and creates an image based on it. Its elaboration took about two years to complete but the results were very promising and promoted a great advance for science.

In conclusion, Bouman and the team were able to develop series of algorithms that converted **telescopic data **into the historic photo shared by the world's media.

Read more about **Bouman impact**

brainly.com/question/28744190

#SPJ1

Both Felipe and Enzo forgot to study for their science test. The probability of Felipe passing the test is 0.190.190, point, 19. The probability of Enzo passing the test is \dfrac14 4 1 start fraction, 1, divided by, 4, end fraction. Which of these events is more likely? Choose 1 answer: Choose 1 answer: (Choice A) A Felipe passes the test. (Choice B) B Enzo passes the test. (Choice C) C Neither. Both events are equally likely.

The **more likely** event is (B) Enzo passes the test , the correct option is (B).

In the question ,

it is given that

the** probability** that Felipe will pass the test is 0.19

Converting 0.19 to percent , we get

0.19 = 0.19/100 = 19%

the probability that Enzo will pass the test is 1/4 ,

Converting 1/4 to percent , we get

1/4 = 1/4 * 100 = 100/4 =25%

hence , the **probability** of **Felipe** passing the test is 19% and the probability that **Enzo** passes the test is 25% ,

On comparing we see that 25% > 19% , which means Enzo has **higher **chance of passing the test than Felipe .

Therefore , the more **likely event** is (B) Enzo passes the test , the correct option is (B).

The given question is incomplete , the complete question is

Both Felipe and Enzo forgot to study for their science test. The probability of Felipe passing the test is .19 , the probability of Enzo passing the test is 1/4.

Which of these events is more likely?

(A) Felipe passes the test.

(B) Enzo passes the test.

(C) Neither. Both event are equally likely.

Learn more about **Probability** here

https://brainly.com/question/13915418

#SPJ1

prove that (a - b)2 = (b - a)2

**Answer:**

**Step-by-step explanation:**

* (a - b)²* =

(a - b)(a - b) =

[(- 1)(b - a)] × [(- 1)(b - a)] =

(- 1)(- 1)(b - a)(b - a) =

**(b - a)²**

At the beginning of the year, Salma had $35 in savings and saved an additional $8 each week thereafter. Henry started the year with $95 and saved $5 every week. Let SS represent the amount of money Salma has saved tt weeks after the beginning of the year and let HH represent the amount of money Henry has saved tt weeks after the beginning of the year. Write an equation for each situation, in terms of t,t, and determine the number of weeks after the beginning of the year until Salma and Henry have the same amount of money saved.

The **number of weeks** when Salma and Henry would have the same amount of money is 20 weeks.

The form of the **equations **that represent the total amount of money saved is :

Total amount in the account = initial amount in the account + (amount added each week x number of weeks)

SS = $35 + ($8 x tt)

SS = $35 + $8tt

HH = $95 + ($5 x tt)

HH = $95 + $5tt

When they have the same amount in their account, the two** equations **woud be equal.

HH = SS

$95 + $5tt = $35 + $8tt

$95 - $35 = $8tt - $5tt

$60 = $3tt

tt = $60 / 3

tt = 20 weeks

To learn more about **linear equations, **please check: https://brainly.com/question/25711114

#SPJ1

you’ve asked for a survey of your property and the surveyor has just sent you a drawing of your property boundary. you show it to your neighbor and he says that the boundary between your two properties is wrong. he says his legal description says that that boundary bears n49°31’56.37""w at 363.591’. he says you shouldn’t pay the surveyor and get him back out to re-survey that line. who is right?

**"Seven Year Rule,"** which is derived from Section 157(4) of the Planning and Development Act 2000, is not the same as this.

**What does the seven-year time limit mean?**

Learn more about** Seven year rule'**

**brainly.com/question/14114285**

**#SPJ9**

James had pizza delivered. James tips $5 for deliveries or 10% of the purchase, whichever is higher. The pizza delivered cost $69.50.

How much will James tip?

**Answer:**

**Step-by-step explanation:**

$4.69

Timmy is working with 2 sets of numbers.

Set A has all the odd number from 1-10.

Set B has all the even numbers from 2-20.

What is the ratio that represents the prime

numbers in Set A to the prime numbers in Set B?

(HINT: Think about what prime numbers are.)

**Answer:**

there's no ratio, or maybe u can help me out

Evaluate the Expression when x is -9

When is -9, x^2 is [ ]

(Simplify your answer)

**Step-by-step explanation:**

that only means we need to put the given values into every place, where the variable is used in the expression.

this is straight forward.

x² for x = -9 means

(-9)² = 81

you remember, a² = a×a.

and when a is negative, this is then the multiplication of a negative number with a negative number, and that result is positive.

so, a square operation always delivers a positive result for real numbers as input, no matter if the input was already positive or negative.

Given f(x)=√(3x-12)+2 what is the range in set notation? {y|y ∈ R, y ≥ }

The **function **f(x)=[tex]\sqrt{3x-12} +2[/tex]. The **Domain **of the **function **is 4, we can also write {y|y∈R,y≥4}

Given that,

The **function **f(x)=[tex]\sqrt{3x-12} +2[/tex]

We have to find the range of the **function**.

Range is nothing but y but in the equation we have x so we find **domain**.

The **domain **is the set of inputs that a **function **will accept is known as the **domain **of the **function **in mathematics. It is occasionally indicated by dom(f), where f is **function**.

More specifically, f:X--->Y the **domain **of f is X given a **function**. It should be noted that in contemporary mathematical terminology, a **function's domain **is a component of its definition rather than a quality.

Take the **function **

f(x)=[tex]\sqrt{3x-12} +2[/tex]

Now,

3x-12≥0

3x≥12

x≥12/3

x≥4

Therefore, The **Domain **of the **function **is 4, we can also write {y|y∈R,y≥4}

To learn more about **domain **visit: https://brainly.com/question/28135761

#SPJ1

**Answer:**

2

**Step-by-step explanation:**

2

HELPP ONBB- I just realized this is due today!!

The **rate of change** (m) = 9

The **starting number **(b) = 100

The **equation** is: y = 9x + 100

(0, 100) is the ordered pair for the **starting number**.

See the image for the **graph** of y = 9x + 100.

To create the **equation** of a **line**, we need to determine the following:

**Y-intercept/starting value** = b

**Slope** of the **line/rate of change** = m

The ordered pair of the **y-intercept** or **starting value** is represented as (0, b), where b is the value of y on the y-axis where the **line **intercepts the **y-axis** and x = 0 at this point.

These values can be substituted into y = mx + b, which represents the **equation** of the **line** in **slope-intercept form**.

From the information given, we have:

**Y-intercept/starting value** (b) = 100

**Slope** of the **line/rate of change** (m) = 9

To write the **equation** of the **line**, substitute m = 9 and b = 100 into y = mx + b:

y = 9x + 100

The ordered pair for the **starting number **would be: (0, 100).

The image below shows the **graph** of y = 9x + 100.

Learn more about the **equation of a line** on:

https://brainly.com/question/13763238

#SPJ1

20 POINTS!

Please Help Me!

What is the equation of the line perpendicular to -2x + 3y = -12 and which passes through the point (2, -5)? Write your answer in slope-intercept form. Show all your work.

Explanation:

the equation of a line in

slope-intercept form

is.

∙

x

y

=

m

x

+

b

where m is the slope and b the y-intercept

rearrange

2

x

−

3

y

=

12

into this form

subtract 2x from both sides

⇒

−

3

y

=

−

2

x

+

12

divide all terms by

−

3

⇒

y

=

2

3

x

−

4

←

in standard form

with

m

=

2

3

given a line with slope m then the slope of a line

perpendicular to it is

∙

x

m

perpendicular

=

−

1

m

⇒

m

perpendicular

=

−

1

2

3

=

−

3

2

⇒

y

=

−

3

2

x

+

b

←

is the partial equation

to find b substitute

(

2

,

6

)

into the partial equation

6

=

−

3

+

b

⇒

b

=

6

+

3

=

9

⇒

y

=

−

3

2

x

+

9

←

equation of perpendicular line

rewrite 5+3/4x=3/8 so it doesn't have fractions

**Answer:**

40 + 6x = 3

**Step-by-step explanation:**

Multiple all the way through by 8

8( 5 + [tex]\frac{3}{4}[/tex] x) = ([tex]\frac{3}{8}[/tex])8

8(5) + [tex]\frac{8}{1}[/tex][tex](\frac{3}{4})[/tex]x = [tex]\frac{3}{8}[/tex][tex](\frac{8}{1})[/tex]

40 + 6x = 3

What is the shape of the base of the figure?

16 km

8 km

**Answer: rectangle**

**Step-by-step explanation: brainliest please? i could really use it**

**Answer:**

most likely 16 if its a long object or 8 if its a short one

**Step-by-step explanation:**

if u provided a graph it could help alot

Answer these question

Hannah needs to build two wall, One has a height of 1024 feet and the other of 672 feet. If hannah has to use bricks of equal sizes for both wall, what is the biggest size of each brick she can use. ( Answer in feet)

There are now x cans stacked on a shelf that hold 36 cans when full, If 4 of these cans were removed, the shelf would be half full. Find x

1. The biggest size of each **brick** that Hannah can be able to use is 32.

2. The value of x when there are now x **cans** stacked on a shelf that hold 36 **cans** when full is 22 cans.

From the information, **Hannah** needs to build two wall, one has a height of 1024 feet and the other of 672 feet and she has to use bricks of equal sizes for both wall. It should be noted that this implies that we've to calculate the highest common **factor** for 672 and 1024. This is 32.

2. The value of x will be:

= (36/2) + 4

= 18 + 4

= 22

Therefore, x is 22. This means that there are 22 **cans**.

Learn more about **factor** on:

brainly.com/question/25829061

#SPJ1

Two cars leave from a place at the same time they travel in opposite directions one at 62 KM per hour the other at 48 KM per hour how long will it take before they are 550 KM apart

If two cars leaves from a place at the same time they travel in opposite directions and the** speed** of the first and second cars are 62 km per hour and 48 km per hours respectively , 5 hours will take before they are 550 km apart

The speed of the first car=62 km per hour

The speed of the second car=48 km per hour

Two cars leave from a place at the same time they travel in **opposite directions**

**The relative speed** of the car = Speed of the first car - (- Speed of the second car )

=62-(-48)

=110 km per hour

**Time take** = Distance between the two cars / Relative speed of the two care

=550/110

=5 hours

Hence, if two cars leaves from a place at the same time they travel in opposite directions one at 62 km per hour the other at 48 km per hour, 5 hours will take before they are 550 km apart

Learn more about **relative speed **here

brainly.com/question/14362959

#SPJ1

What value of x would result in the numerical value of zero in the expression -10+11+x

**Answer:**

-1

**Step-by-step explanation:**

-10+11+x = 0

1+x = 0

x = -1

Ivan was at the beach. He wanted to spend $12 or less on a beach bike rental. The company he chose

to rent from charged an initial fee of $5 and an additional $0.45 per mile he rode.

a. Write an inequality for this situation. Let x represent the number of miles ridden.

b. What is the greatest number of whole miles Ivan can ride without going over his spending

limit?

Using a **linear function**, it is found that:

**a.** The inequality for this situation is: 5 + 0.45x ≤ 12.

**b. **He can ride at most 15 miles without going over the limit.

A linear function, in **slope-intercept** format, is modeled according to the following rule:

y = mx + b

In which the **coefficients **are described as follows:

For the context of this problem, the **slope **and the **intercept **are defined as follows:

Hence the **cost function**, considering x miles, is given as follows:

C(x) = 0.45x + 5.

He wanted to spend $12 or less on a beach bike rental, hence the **inequality **that models this situation is given by:

C(x) ≤ 12.

5 + 0.45x ≤ 12.

The inequality is solved similarly to an equality, isolating the variable and finding the range of values, hence the **solution **is found as follows:

0.45x ≤ 7

x ≤ 7/0.45

x ≤ 15.6 miles.

The greatest **whole number** of miles is of 15 miles, as for 16 miles, the cost would be above $12.

A similar problem, also about** linear functions**, is given at https://brainly.com/question/24808124

#SPJ1

ngth of the third side. If necessary, write in simplest radical form.

5

V11

**Pythagoras theorem - **The length of the **third side** is 6.71unit

**What is Pythagoras theorem ?**

The **Pythagorean theorem**, sometimes known as **Pythagoras**' **theorem**, is a key **relationship** in** Euclidean geometry **between a right **triangle's** three sides. According to this **statement**, the areas of the **squares** on the other two sides add up to the size of the** square **whose side is the **hypotenuse.**

The **Pythagoras theorem's **equation is as follows:

H² = P² + B²

The **triangle's** third side will be the following length:

Let x represent the **triangle's** third side's length.

9² = 6² + x²

81 = 36 + x²

x² = 45

x = 6.708

x = 6.71 units

Hence, the third side of the **triangle **is 6.71unit

To learn more about **Pythagoras theorem's **click on the link

https://brainly.com/question/343682

#SPJ9

Point C is on line segment \overline{BD} BD . Given CD=11 CD=11 and BD=17,BD=17, determine the length \overline{BC}. BC

**Answer:**

draw the diagram out

**Step-by-step explanation:**

BC=17-11

= 6

Solve for x: 4x + 1/2 (2x+4) > 12

a. x > 14/5

b. x < 14/5

c. x > 2

d. x < 2

**Answer:**

**c. x > 2.**

**Step-by-step explanation:**

4x + 1/2 (2x+4) > 12

4x + x + 2 > 12

5x > 10

x > 2.

Segment addition and midpoints

In the figure below, B is between A and C, and C Is between B and D. If AC=8, BC=5, and BD=9, find AD.

The **line segment **AD is 12 units.

The** midpoint** is the middle point of a line **segment**.

It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.

The **midpoint** is halfway between the two end points:

Therefore, B is between A and C.

C is between B and D.

Hence,

AC = 8

BC = 5

BD = 9

AD = ?

Therefore,

AD = AB + BC + CD

AB = AC - BC

AB = 8 - 5

**AB = 3 units**

CD = BD - BC

CD = 9 - 5

**CD = 4 units**

Therefore,

AD = 3 + 5 + 4

**AD = 12 units**

learn more on **segment** and **mid point** here: https://brainly.com/question/18422288

#SPJ1

Make a table of ordered pairs for the equation.

y=−13x+4

Then plot two points to graph the equation.

PLEASE ANSWER QUICKLEY, I WILL GIVE YOU 90 POINTS IF IT IS CORRECT and maybe brainleist

Table of **ordered pair** for the **equation **y =-13x +4 is given by **(0,4)** and **(1,-9).**

As given in the question,

Given **equation** is equal to :

y = -13x + 4

Substitute x =0 in the given equation

y = -13 (0) + 4

⇒ y = 0 +4

⇒ y = 4

**Ordered pair** is (0,4)

Substitute x=1 in the given equation

y = -13(1) +4

⇒ y = -9

Ordered pair is (1,-9)

Table of the ordered pair is

x : 0 1

y : 4 -9

Graph of the two plot points A(0,4) and B(1,-9) attached.

Therefore, table of **ordered pair** for the equation y =-13x +4 is given by (0,4) and (1,-9).

Learn more about **ordered pair **here

brainly.com/question/28874341

#SPJ1

help please with this question

About **Nevada** state, it is **true** that "**The rural air pollution level for this state is much higher or much lower than the rest of the states in the data set.**"

To learn more about **outliers**, visit :

https://brainly.com/question/26958242

#SPJ1

The slope of the trend line is 15 what does that mean in regards to the data of the scatter plot? Check all that apply

The correct options are-

1. The **slope** represents the rate of change of the data.

3.** Sales** increase $1,000 as ads increase by $1,000.

5. A positive slope infers a positive correlation.

What is defined as the slope?The slope of a line measures its steepness as well as direction.The**Positive correlation**:

From the** scatter points **on graph, its clear that the slope which is 15 is a positive correlation.

Now, to find the slope we see the change in y with respect to x.

Thus, the change in sales increase $1,000 as ads increase by $1,000.

To know more about the **positive correlation**, here

**https://brainly.com/question/28093548**

**#SPJ10**

The complete question is-

The slope of the trend line is 15. What does that mean in regard to the data of the scatterplot? Check all that apply.

1. The slope represents the rate of change of the data.

2. Advertising costs increase $1,000 as sales increase by $1,000.

3. Sales increase $1,000 as ads increase by $1,000.

4. A positive slope infers a negative correlation.

5. A positive slope infers a positive correlation.'

Draw the graph of f(x)=[[x - 4]] - 2

**Answer:**

See attachment.

**Step-by-step explanation:**

Given absolute value function:

[tex]f(x)=|x-4|-2[/tex]

The **parent **absolute value function is f(x) = |x|.

**Graph **of the parent absolute value function:

Translations

[tex]\textsf{For $a > 0$}:[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]

The graph of the given function is a **transformation **of the parent function by:

Therefore, the **vertex **of the given function is (4, -2).

Find two further **points **on the graph by inputting x-values either side of the x-value of the vertex into the given function:

[tex]\begin{aligned}\implies f(8)&=|8-4|-2\\&=|4|-2\\&=4-2\\&=2\end{aligned}[/tex]

[tex]\begin{aligned}\implies f(0)&=|0-4|-2\\&=|-4|-2\\&=4-2\\&=2\end{aligned}[/tex]

To **draw **the **graph **of the given function:

Rearrange the equation

a= 1/4 b

to make b the subject.

**b = 4a **is the answer.

Given,

a= 1/4 b

To find:

**Make b the subject,** the given equation

**Solution:**

Take 4 to the side of a

4a = 1b

Therefore,

**b = 4a**

To learn more about **algebra,** refer

https://brainly.com/question/4344214

#SPJ13

Where does the graph of y= -2x + 1 intersect the x-axis?

The graph intersects the** x-axis** at ( 1/2 , 0) .

A **cartesian coordinate** system, which uses signed distances between two fixed perpendicular oriented **lines **and the point measured in the same unit of length, uniquely identifies any point in a plane by a pair of numerical coordinates.

We know that at the** x-axis** the value of y is 0 .

Now substituting the value of y in the **equation **of the **graph **we get :

y = - 2x + 1

at y = 0 ,

0 = -2x + 1

or, -1 = -2 x

or, x = 1 / 2

Hence the co-ordinate of the point where the **graph **passes through **x-axis** is ( 1/2 , 0 ) .

to learn more about **x-axis** visit:

https://brainly.com/question/1442188

#SPJ1

zayn boards the big rock metro to ride downtown to his job. zayn gives his money to the driver and takes his seat. neither the driver nor zayn says anything. zayn and the bus driver: have an implied contract. have no contract. have an express contract. have a formal contract.
What is the conjecture? 1,1,2,3,5,8 _, _, _, _, _,
Please help with this
Which is a benefit that we get frombiodiversity?A. over-hunted animalsB. production of oxygen by plantsC. deforestation of rainforestsD. air pollution
Rewrite 7 8 using the additive inverse and display the new expression on a number line.
select 3 statements one for Cosine one for Tangent and one for sine
Rewrite -I usually visit my grandpa on friday (Now)
Send the answer's please.
Suppose you identify a new element, Pivotium. Pivotium has two isotopes: Pivotium-423 and Pivotium-417. In the mixture, 22% of the mixture is Pivotium-423; the rest of the mixture is Pivotium-417.What is the relative atomic mass for Pivotium?
TRUE OR FALSE? The Transitive property on N states that: For any two natural numbers a and b, either a > b or a = b or b> a.
The change in the value of a stock is represented by the rational number -6.50 describe in words what this means
The stemplot displays 26 students' scores on a 90-pointstatistics test. The lowest possible passing grade on the test was a 54 out of 90. What percentage of students passed this test ? A. 23%B. 54%C. 77%D. 96%
A factory produces sweatshirts for a sports team, and packages the sweatshirts in boxes of 20. Everyhour, the factory produces 9,284 sweatshirts.How many full boxes of sweatshirts are packaged in 1 hour?
Question 10 of 10Primary sources are valuable because they:A. reflect generally accepted conclusions about the past.B. combine many different sources to draw conclusions about thepast.C. provide firsthand information about a historical event.D. offer corroborated evidence about important events.SUBMIT
Prey animals are...A. mutualistic.B. carnivores.C. captured and eaten.
From the graph below, how much money will be saved after 5 weeks?Question 4 options:$55$50$60$30
please help im not sure how this works
Find a vocabulary word to replace the underlined word or phrase1. My souvenir from my trip to Paris is a model of the Eiffel TowezSummer2. Founders' Day is a day to pay tribute to the people who established our cityacelebration3. My trip to camp was the most unforgettable.experience of the summer.
URGENT!! please help me figure this out :)
Let sets A and B be defined as follows. A is the set of integers greater than -8 and less than -4.B={b,h,i,l,r,s}