**Answer:**

[tex]\sf 12-5x+6x=4[/tex] (Given)

[tex]\sf 12+x=4[/tex] (Combine like terms)

[tex]\sf x=-8[/tex] (Subtraction property of equality)

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

Hope this is what you're looking for!

**Answer:**

1. given

2. combine like terms,

3. subtraction property of equality

**Step-by-step explanation:**

A bicycle has cash price $16 319.50. It can be bought on hire purchase with a deposit of $6

900 and ten monthly installments of $1 224.50 each.

a. What is the total hire purchase price for the bicycle? [3 marks]

b. Find the difference between the hire purchase price and the cost price for the bicycle.

[1 mark]

c. Express your answer in (b) above as a percentage of the cash price.

The **total cost **of the **hire purchase **for the **bicycle **is $19,145.

The difference between the **hire purchase price** and the** cost price **for the bicycle is $2,825.50

The **difference **as a percentage of **cash price **17.31%.

The **total cost **of the **hire purchase **is the sum of the deposit and the total monthly instalment.

**Total cost **of the **hire purchase **= amount deposited + total instalment paid

Total instalment paid = number of month x payment per month

$1224.50 x 10 = $12,245

**Total cost **of the **hire purchase **= $6,900 + $12,245 = $19,145

The difference = cost of hire purchase + cash price

$19,145 - $16 319.50 = $2,825.50

The **difference **as a percentage of **cash price **= (2,825.50 / $16,319.50) x 100 = 17.31%

To learn more about** percentages, **please check: https://brainly.com/question/25764815

#SPJ1

What is the slope of a parallel line whose equation is x-2y=-18. Fully simplified answer.

**Answer:**

slope of 1/2

**Step-by-step explanation:**

x-2y=-18

First, get the equation in **slope intercept form**

y = mx+b where m is the slope and b is the y-intercept

-2y = -x -18

Divide each side by -2

y = 1/2 x + 9

The slope is 1/2

**Parallel lines** have the same slope, so lines that are parallel will have a slope of 1/2

4

Choose the conjecture that describes how to find the 7th term in the sequence 4, 20, 36, 52,

OA) Multiply 52 by 9.

O B) Multiply 16 to 32..

OC) Add 32 to 52

OD) Add 48 to 52.

...

The correct option D) Add 48 to 52 is the** conjecture** that describes for the 7th term in the **sequence.**

For the given question, the sequence is given as;

4, 20, 36, 52,

Where, the first term a₁ is 4.

Second term a₂ is 20 and,

Third term a₃ is 36

Common difference d for each case is;

d = a₂ - a₁

d = 20 - 4 = 16

d = a₃ - a₂

d = 36 - 20 = 16

as,** common difference** is same, the sequence is said to be in **AP**.

Then, the formula for finding the **7th term** is -

a₇ = a₁ + 6d

a₇ = 4 + 6×16

a₇ = 100

Now, this 7th term from the options can be found as;

Add 48 to 52 = 100.

Thus, the** conjecture** that describes for the 7th term in the **sequence **is add 48 to 52.

To know more about the **arithmetic progression**, here

**https://brainly.com/question/6561461**

**#SPJ13**

ABCDE is a circle centre O. The diameter, AC, is extended to the point F so that CF = 16 cm. The line BF is the tangent to the circle at B and FDE is a straight line such that FD = 18 cm and DE = 14 cm. The radius of the circle is r

**Answer:**

**Step-by-step explanation:**

*It is assumed you are looking for the ** missing value of r*.

Use the **intersecting secants** theorem:

**Substitute **known values and **solve for r**:

**Answer:**

(a) FB = 24 cm

(b) r = 10

**Step-by-step explanation:**

Find the length, in cm, of FB.

Intersecting Secant and Tangent Theorem

When a **secant segment** and a **tangent segment** meet at an exterior point, the **square **of the measure of the tangent segment is equal to the **product **of the measures of the **secant segment** and its **external secant segment**.

Given:

Tangent segment = FBSecant segment = FE = 18 + 14 = 32 cmExternal secant segment = FD = 18 cm[tex]\begin{aligned}\implies FB^2 & =FE \cdot FD\\FB^2&=32 \cdot 18\\FB^2&=576\\\sqrt{FB^2}&=\sqrt{576}\\FB&=24\end{aligned}[/tex]

Therefore, the length of FB is 24 cm.

Part (b)Find the value of r.

Triangle FBO is a **right triangle** with side lengths:

Pythagoras Theorem

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

where:

a and b are the legs of the right triangle.c is the hypotenuse (longest side) of the right triangle.Therefore, substitute the side lengths of triangle FBO into **Pythagoras Theorem** and **solve for r**:

[tex]\begin{aligned}\implies BO^2+FB^2&=OF^2\\r^2+24^2&=(r+16)^2\\r^2+576&=r^2+32r+256\\576&=32r+256\\32r&=320\\r&=10\end{aligned}[/tex]

Therefore, the value of r is 10.

Please help me with parts C and D, I’m struggling with them

**ANSWER**

**EXPLANATION**

Given;

[tex]\begin{gathered} sin\theta=\frac{6}{7} \\ 0<\theta<\frac{\pi}{2} \end{gathered}[/tex]c) Hence;

[tex]\begin{gathered} sin\frac{\theta}{2}=\sqrt{\frac{1}{2}(1-\frac{\sqrt{13}}{7}}) \\ \end{gathered}[/tex]In decimal form;

[tex]sin\frac{\theta}{2}=0.49[/tex]d)

[tex]\begin{gathered} cos\theta=\frac{\sqrt{13}}{7} \\ cos\frac{\theta}{2}=\sqrt{\frac{1}{2}(\sqrt{\frac{13}{7}+1})} \\ decimal=0.87 \end{gathered}[/tex]A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.(b) If the water is rising at a rate of 3/8 inch per minute when h = 2.1, determine the rate at which water is being pumped into the trough. ft3/min

Given:

A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.

The volume of the trough will be as follows:

[tex]undefined[/tex]The graph of a linear function IS shown.

Which word describes the slope of the line?

positive

negative

zero

undefined

your answer will be positive

Question 3 options:

Premises:

If you have a cat, then it will chase mice.

You have a cat.

Conclusion:

Your cat will chase mice.

The Law of ___________________________makes this argument true.

This is the Law of Syllgism

The law of **syllogism **makes this argument true if you have a cat, then it will chase **mice **and your cat will **chase **mice.

**Legal** syllogism is a **legitimate** concept that deals with the **law **and how it is applied, specifically a type of **argument **that uses deductive **reasoning **to determine whether a given act is legal.

It is given that:

The statement is:

If you have a cat, then it will chase mice.

As we know, from the definition of the **Law **of Syllogism, the **legitimate** concept that deals with the** law **and how it is applied, specifically a type of **argument **that uses deductive reasoning to determine whether a given **act** is legal.

Your cat will **chase** mice.

The Law of **syllogism **makes this argument true.

Thus, the law of **syllogism **makes this argument true if you have a cat, then it will chase **mice **and your cat will **chase **mice.

Learn more about the **law of syllogism **here:

https://brainly.com/question/11306409

#SPJ5

14.14 / 14 Is what ? Please show work ┐( ∵ )┌

**Answer:**

1.01

**Step-by-step explanation:**

14.14/14

14/14=1

0.14/14=0.01

1+0.01=1.01

What is the value of this expression.

Answer:46

Step-by-step explanation:

From a 128-foot tree, an object is thrown straight up into the air then follows a trajectory. The height S(t) of the ball above the building after t seconds is given by the function S(t) = 96t - 16t^(2). How long will it take the object to reach maximum height?

**Answer:**

**3 seconds**

**Step-by-step explanation:**

We can solve this in either of two ways: Graphing or taking the first derivative, I'll use both,

**Graphing**

Plot the equation. My DESMOS graph is attached. One can find the vertex of this curve at 3 seconds. Bonus: It reaches a height of 144 units at this point.

**Derivative**

The first derivative of this function will produce an equation that returns the slope of the line at any point x.

S(t) = 96t - 16t^(2)

S'(t) = 96 - 2*16t

S'(t) = 96 - 32t

The slope of the curve will be 0 when the ball reaches it's maximum height and begins to fall. Since we want the time it takes to reach a slope of zero, we can set S'(t) to 0 and solve:

S'(t) = 96 - 32t

0 = 96 - 32t

32t = 96

t = 3 seconds

50 POINTS!!!

Decide whether inductive reasoning or deductive reasoning is used to reach the conclusion. Explain

1. even numbers are divisible by 2. odd numbers are not divisible by 2 so 4 is an even number

2. all photosynthetic organisms produce oxygen. phytoplankton and photosynhetic organisms. So phytoplankton produces oxygen.

3. Each time you clean your room, you are allowed to go out with your friends. So, the next time you clean your room, you are allowed to go out with your friends

**Answer:**

1. Deductive reasoning, because it is testing the ecisting theory that odd numbers are not divisible by 2 and gives an example that 4 is an even number and is divisible by 2.

2. This statement would be deductive reasoning because the person stating this is establishing the truth that all photosynthetic organisms produce oxygen, they are not creating a theory, just stating facts.

3. This would be inductive reasoning because they have given good reasons to base their theory however it is not simple fact.

**Step-by-step explanation:**

Hope i helped explain

What is 10+409 bc I really need help

=419

Hope this helps you :)

Hope this helps you :)

The total is 419! Add 1 + 0 and 0 + 9.

NEED HELP ASAP - 100 POINTS

When solving quadratic equations, there are benefits to utilizing one method over the other. In your own words, explain what the advantages may be of using the method of completing the square to solve quadratic equations.

The **advantages **may be of using the method of **completing **the square to solve **quadratic equations **to estimate the values of x and y roots without calculating them.

A **quadratic equation **is the second-order degree algebraic expression in a variable. the standard form of this **expression **is ax² + bx + c = 0 where a. b are **coefficients **and x is the variable and c is a constant.

Using **Completing **the square.

1. First of all we can find the **minimum **or **maximum **of the equation immediately.

2. **Second **is to cuts out the need to use the given ones (a, b, c) in the **quadratic formula**.

3. It allows estimating the **values of **x and y roots without calculating them.

Then **Estimating **on a test is a very valuable asset.

Learn more about **quadratic equations**;

https://brainly.com/question/17177510

#SPJ1

I need some help with my math please

8g+11h+14f since permitted is each side added up

Aiyana wrote the ratio 3:5 to compare a number of Paris of shorts that she owns to the number of pairs of jeans that she owns which ratio is equivalent to Aiyana’s ratio

** 3:5 **is equivalent to Aiyana’s **ratio**

Since 3 and 5 are both** prime numbers**, you must multiply them by the **same number** (or any other integer) in order to have a **ratio **that is the same as Aiyana's. Ex 3:5=6:10=9:15 etc. The three ratios are **identical**.

A** ratio **displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, while the ratio of **lemons to oranges** is 6:8.

To know more about **ratios **refer to https://brainly.com/question/12024093

#SPJ1

what is the 2nd ponit of x = -3

0 because if x=-3 then it would be written as (-3,0)

5(4x - 1.5)+12=4x - 2

(if you’re solving for x)

Answer: -0.406

Explanation:

5(4x - 1.5) + 12 = 4x - 2

first, distribute the 5 into the parenthesis

20x - 7.5 + 12 = 4x - 2

then, simplify like terms

20x + 4.5 = 4x - 2

then, put the x terms together

16x + 4.5 = -2

put the constants together

16x = -6.5

solve for x.

x = -0.406

Answer: -0.406

Explanation:

5(4x - 1.5) + 12 = 4x - 2

first, distribute the 5 into the parenthesis

20x - 7.5 + 12 = 4x - 2

then, simplify like terms

20x + 4.5 = 4x - 2

then, put the x terms together

16x + 4.5 = -2

put the constants together

16x = -6.5

solve for x.

x = -0.406

Determine which integers in the set S: {−2, −3, −4, −5} will make the inequality 2p − 8 < 5p + 4 true.

S:{−2, −3}

S:{−3, −4}

S:{−4, −5}

S:{−2, −5}

**Answer:**

s:[-2,-3] is the answer

The **set **S:{ - 2 , - 3 } will make the **inequality **2p - 8 < 5p + 4 true

**What is an Inequality Equation?**

**Inequalities **are the mathematical expressions in which both sides are not equal. In **inequality**, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an **inequality**, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

The **set **S : { - 2 , - 3 , - 4 , - 5 }

The **inequality relation** is 2p - 8 < 5p + 4

Now , **substituting **the value from **set **S in the **inequality **, we get

When p = - 2 :

2p − 8 < 5p + 4

2(-2) − 8 < 5(-2) + 4

-4 − 8 < -10 + 4

-12 < -6 **TRUE**

When p = - 3

2p − 8 < 5p + 4

2(-3) − 8 < 5(-3) + 4

-6 − 8 < -15 + 4

-14 < -11 **TRUE **

When p = - 4

2p − 8 < 5p + 4

2(-4) − 8 < 5(-4) + 4

-8 − 8 < -20 + 4

-16 < -16 **FALSE**

When p = - 5

2p − 8 < 5p + 4

2(-5) − 8 < 5(-5) + 4

-10 − 8 < -25 + 4

-18 < -21 **FALSE**

Therefore , the value of p = - 2 , - 3 will satisfy the given inequality relation

Hence , the **set **S:{ -2,-3 } is the **solution**

To learn more about **inequality equation **click :

https://brainly.com/question/11897796

#SPJ2

Determine if the following representations or functions or not? Explain your reasoning.

The three **relations** given all represent **functions** because each has exactly one y-value that corresponds to each x-value.

A **relation** can be defined as a **function** if the x-values (input/domain element) each has exactly one y-value (output value/range element) that is related to or it corresponds to.

A **function** can have two x-values that have the same y-value but cannot have two y-values that corresponds to one x-value.

In the first **relation** showing a graph, each x-value on the graph has exactly one y-value it corresponds to. Therefore, it is a **function**.

In the second **relation** that is represented by the set of ordered pairs, every x-value also have only one y-value it is related to. Therefore, it represents a **function**.

The third **function** given shows a table of values of a **relation** that has exactly only one y-value that is assigned or related to each x-value. This also is a **relation **that represents a **function**.

Therefore, all three **relations** represent **functions**.

Learn more about **function** on:

https://brainly.com/question/10439235

#SPJ1

PLS HURRYYYYY

Think about what you know about ratios and comparisons. Fill in each box. Use

words, numbers, and pictures. Show as many ideas as you can.

I don’t get it like we’re is the ratios

6. Given the area of the rectangle is 52 ft², find

the value of x.

(4x - 2) ft

2 ft

Answer:x=7

Step-by-step explanation: 2(4x-2)=52

8x-4=52

8x=56

x=7

Write an equation in point-slope form of the line that passes through (-4,1) and (4,3) The equation is ?

**Answer:**

y = 4x+2

**Step-by-step explanation:**

To find an equation that runs through (-4,1) and (4,3) first find the difference between the two y numbers and x number to find the slope. between the two y numbers you go left or right 8 units, and difference between the two x numbers, which is 2. making the slope 4. looking at a graph and marking the two points, draw a line connecting the two given points, find the y intercept. the y intercept is at coordinates (0, 2) making the y intercept 2. making that into an equation is y = 4x + 2

Casho went shopping for a new pair of sneakers because of a sale. The price on the tag was $25, but Casho paid $22.50 before tax. Find the percent discount

The percentage **discount **for the pair of **sneakers **is 10%.

A percentage is a value per **hundredth**. Percentages can also be fractions and **decimals **by decimals by dividing by 100 and vice versa. To obtain a percentage of a given value we divide the given percentage by a hundred and **multiply** the value with it.

The **percentage **discount can be determined by putting the discounted value upon the price multiplied by a hundred and **subtracting **the obtained percentage from the hundred percentage.

∴ The percentage discount on the pair of sneakers is,

= (22.50/25)×100.

= 0.9×100.

= 90%.

So, the **percentage discount **is (100 - 90)% = 10%.

learn more about **percentages** here :

https://brainly.com/question/28269290

#SPJ1

a college professor hands out a list of 10 questions, 5 of which will appear on the final examination for the course. one of the students taking the course is pressed for time and can prepare for only 9 of the 10 questions on the list. suppose the professor chooses the 5 questions at random from the 10.

one of the students taking the course is pressed for time and can prepare for only 9 of the 10 questions on the list. then the **probability **of all 5 questions prepared for appears is 2

Recall : nCr = n! ÷ (n-r)!r!

The total possible **outcome **; 5 questions out of 10

10C5 = 10! ÷ 5!5! = (10*9*8*7*6)÷(5*4*3*2*1) = 252

Required outcome :

All 5 questions set being from the 9 questions covered and 0 from the 1

left uncovered

9C5 * 1C0

9C5 = 9! ÷ 4!5! = (9*8*7*6) ÷ (4*3*2*1) = 126

1C0 = 1! ÷ 1!0! = 1

**Probability **= required **outcome **/ Total possible outcomes

P(All 5 questions prepared for appears) :

[9C5 * 1C0] ÷ 10C5

(126 * 1) / 252

= 126/ 252

=2

learn more about of **probability **here

https://brainly.com/question/23308939

#SPJ4

Answer each part. If necessary, round your answers to the nearest hundredth.

(a) It takes 51 pounds of seed to completely plant a 9-acre field.

How many acres can be planted per pound of seed?

acres per pound

(b) Christine runs 4 miles in 22 minutes.

How many minutes does she take per mile?

minutes per mile

**Answer:4**

**Step-by-step explanation:**

**Answer:a) Given :**

**51 pounds of seed can be planted in = 9 acre field.**

**Per pound of seed = **

**We can convert 9/51 in simplest fraction by dividing top and bottom by 3.**

**We get**

**Therefore, 3/17 of an acrs can be planted per pound of seed.**

**b) $10 amount = 16 pounds of sugar.**

**$1 amount = 16/10 = 1.6 pounds of sugar.**

**Therefore, 1.6 pounds of sugar she got per dollar.**

**Step-by-step explanation:**

After 4 months of a new nutrition program, Rashid has lost 16% of his original weight. he lost 36 lb. What was Rashid's original weight?

225 is his original weight.

36*100/16

36 times 100 then divide by 16

36*100/16

36 times 100 then divide by 16

**Answer:**

225 lb

**Step-by-step explanation:**

Let x be Rashid's original weight.

If 16% of Rashid's original weight is 36 lb then:

[tex]\implies 0.16x=36[/tex]

To find Rashid's original weight solve for x:

[tex]\implies \dfrac{0.16x}{0.16}=\dfrac{36}{0.16}[/tex]

[tex]\implies x=225[/tex]

Therefore, Rashid's original weight is 225 lb.

On a map, Elmwood Drive passes through R(4,-11) and S(0,-9) and Taylor Road passes through

J(6,-2) and K(4,-5). If the streets are straight lines, determine if the streets are parallel or

perpendicular.

The streets where Elmwood and Taylor drive are **neither perpendicular nor parallel.**

Elmwood Drive passes through R(4,-11) and S(0,-9)

**Slope** of this line is (y₁-y₂)/(x₁-x₂)

Here (x₁,y₁) is (4,-11) and (x₂,y₂) is (0,-9)

slope of this line is (-11 - (-9))/(4-0)

= (-11 + 9)/4

= -2/4 = -1/2

Taylor Road passes through J(6,-2) and K(4,-5)

Slope of this line is (y₁-y₂)/(x₁-x₂

Here (x₁,y₁) is (6,-2) and (x₂,y₂) is (4, -5)

slope of this line is (-2 - (-5))/(6 - 4)

= (5 - 2)/2

= 3/2

The slopes of both the line is not same, so they are **not parallel**.

The **product of slopes** of both the lines is equal to 1, then it can be said as perpendicular lines.

The product of slope of streets passed by Elmwood and Taylor is

- 1/2 x 3/2 = -3/4

The result is not equal to 1, so they are **not perpendicular lines.**

Therefore, the streets where Elmwood and Taylor drive are **neither perpendicular nor parallel.**

To learn more about** parallel lines** refer here

https://brainly.com/question/13763238

**#SPJ1**

A stack of 12 sheets of gypsum board are 10.5 inches thick. If all the boards are uniform, how thick is each board?

**Answer:**

0.875 inches

**Step-by-step explanation:**

Pretty easy. Just divide how many inches thick the boards are by how many there are: inches-thick/amount

Now substitute 10.5/12 and find your answer

0.875 inches thick per board

Which answer choice correctly shows 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 in

exponential notation?

OA) 811

OB) 118

OC) 11⁹

OD) 1111

Answer:

it would be 11^8

Step-by-step explanation:

i dont see this as an option but i believe that there was a mistake i dont believe that any of theese are correct

Suppose these accounts had been written by a visitor from a competing European power eager to remove the Spanish from the Americas and takeover the land for itself.what might be that author's audience and purpose
Convert 1.54 x 10^25 molecules of water into moles.
A fast food restaurant wants the average number of total carbohydrates in their items to be less than 50g. How can they use formulas to know if they have met this goal?
20. Many energy drinks contain aO A. prescriptionOB. toleranceC. proprietary blendD. herbal blendof ingredients and don't list the actual amount of each ingredient on the label.B
Translate Pre Image coordinates using the rule (x + 18) and (y - 12).
An operating cycle is the length of time it takes to convert inventory to accounts receivable plus the time it takes to convert the account receivable back to cash. This statement is.
which of the following statements about karl marx is not true? a. he analyzed 19th-century industrial production capitalism. b. he viewed socioeconomic stratification in terms of several classes with different but complementary interests. c. he called the owners of the means of production the bourgeoisie. d. he called the people who sold their own labor the proletariat. e. he emphasized class consciousness.
Please help asap! Thanks!
What is the slope of the line represented by 4x-2y=10?
please help this is for my study guide thanks! (no rounding)
Which of the following is true when the kinetic energy of the particles in a sample of matter is lowered?The temperature increases.bThe temperature decreases.cThe sample will absorb less heat.dMore heat flows away from the sample.
From the Odysseus, what *line number* can this be found? I'm so confused. Please help!! -- "Nevertheless I longI pine, all my days to travel home and see the dawn of my return. And if a god will wreck me yet again on the wine-dark sea, I can bear that too, with a spirit tempered to endure. Much have I suffered, labored long and hard by now in the waves and wars. Add this to the total bring the trial on!"
In 330, Constantine moved the capital of the Roman Empire
A group of 45 people attended a ball game. There were twice as many children as adults in the group. Set up a system of equations that represents the numbers of adults and children who attended the game and solve the system to find the number of children who were in the group. A. system15 adults, 30 children B. system30 adults; 22 children C. system22 adults; 30 children D. system30 adults, 15 children
What is the end behavior of the graph of the polynomial function f(x) = -x5 + 9x4 - 18x?O As x-co, Yco and as xco, y -00As x-co, Y and as xco, y .O As x-co, Yco and as xco, y 0O As x-co, y co and as xco, y co
where are the tiny invaders arriving and why
1. Which details in this passage hint at events to come?2. Do you think that Jason has any reason to be afraid? Explain.3. Based on this passage, do you think the bell will be important in the story?Explain why or why not.
Question 3 (10 points)
the person who has the most powerful position in the senate, who articulates the majority party's legislative priorities, and works to pass them, is known as the
This excerpt is from the Bhagavad Gita. This passage is talking about the soul.Pierce means "stab.Singe means "burn.Wither means "wilt.All-pervading means "affecting everything.What does this passage reveal about Hindus belief in the soul?They believe that the soul is a weapon.They believe that the soul is everlasting.They believe that the soul can be harmed.They believe that the soul can be a burden.