How to solve a function?.

Answer:

(a + 8)(a - 5)

Step-by-step explanation:

a² + 3a - 40 =

= (a      )(        )

Find two numbers that multiply to -40 and add to 3.

They are 8 and -5.

= (a + 8)(a - 5)

solution :

a²+3a-40

find the roots (2 numbers in which you can add and multiply to give 3a and 40)

(a-5) (a+8)

substitute the roots with 3a and multiply 40 by a²

a²-5a+8a-40a²

a(a-5) +8(a-40a²)

(a-5) (a+8)

Answer:

See picture attachment.

Hope this helps :)

The length of the line segment separating two places is the measure of distance between them. Calculating the length of the line segment that connects the two points in the provided coordinates will tell you the distance between them.

The length of the section of a line connecting any two places represents their distance. Only one line connects the two places, and it passes through both.

The length of the line segment that connects the two places may therefore be used to compute the distance between them. The distance between A and B, for instance, is 10 cm if A and B are two points and [Math Processing Error] cm.

The length of the line segment connecting two places serves as the measure of their distance (but this CANNOT be the length of the curve joining them). You should be aware that a distance between two points is always positive.

The Complete Question is distance.

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Answer:The arrow diagram represents a relation between two sets of data, but it does not provide enough information to determine whether it is a function or not. A function is a relation in which each element of the first set (the domain) is related to exactly one element of the second set (the range). In order to determine if the relation shown in the arrow diagram is a function, we need to know if each element in the domain corresponds to only one element in the range. From the arrow diagram we can not determine that.

As we have a set of ordered pairs (27,39), (31,27), (60,130), (45,67) and (123,180) and there is no repetition of the x-values (domain) or y-values (range) in the ordered pairs, we can say that the relation shown in the arrow diagram is a function.

Step-by-step explanation:

To work out the value of k, we can use the given information that fg(2) = 12. We know that fg(x) is the composition of two functions f and g, so we can write fg(x) = f(g(x))

In this case, fg(2) = f(g(2)) = f(k*2^2) = f(4k)

We know that fg(2) = 12. So we can substitute this value into the equation above:

12 = f(4k)

Since we are only interested in the value of k, we can set the equation equal to 12 and solve for k.

12 = 4k

k = 12/4

k = 3

Therefore, k = 3 is the value of k in the function g(x) = kx^2

$ 240,437.74 - the balance of her fund on her 17th birthday.

His daughter turned 10 years old. Her reward was 5000.

subsequently, she began getting monthly interest compounded at a rate of 15%

She would thus have 5000 (the deposit from her birthday) + 15% = 5750 in her account at the end of the first month.

The amount would have been 5750 + 15% = 6612.50 at the conclusion of the second month.

She would have 6612.50 + 15% + 5000 (quarterly deposit) at the conclusion of the third month, which equals 12,604.38.

When she becomes 17 years old, if you keep doing these calculations, she will have a fun

$1,832,087,983.19

Only 145,000, including the 5,000 deposit made on her father's 17th birthday, would have been made by her father.

I would be grateful if someone could let me know where I can earn 15% compounded monthly.

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Answer:

75

Step-by-step explanation:

First, we solve

y - 16= 4

y = 20

Now we put 20 in for y and solve 3(y+5)

3(20+5)

3(25)

75

So, the answer is 75.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{y - 16 = 4 \rightarrow 3(y + 5)}\\\\\text{FIRST: Let us solve for the first equation}\\\mathsf{y - 16 = 4}\\\textbf{ADD 16 to BOTH SIDES}\\\mathsf{y - 16 + 16 = 4 + 16}\\\textbf{SIMPLIFY it}\\\mathsf{y = 4 + 16}}\\\mathsf{y = 20}\\\\\text{SECOND: Let us plug the value of y into our second equation}\\\mathsf{3(y + 5)}\\\mathsf{= 3(25 + 5)}}\\\mathsf{= 3(25) + 3(5)}\\\mathsf{= 75 + 15}}\\\mathsf{= 90}\\\\\huge\text{Therefore, your answer should be:}[/tex]

[tex]{\mathsf{y = 25 \ when\ we\ found\ \ the\ y-value\ we\ got \ 90 \ for \ the \ answer\ for the \ 2^{nd} \ equation}}}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

First step to solve system of equations using elimination method is to equate the coefficient of the variable you want to eliminate first in opposite sign and add both the equations.

As given in the question,

Let us consider two system of equations :

ax + by = c ___(1)

bx + ay = c ___(2)

First step to solve the system of equation by elimination method is :

To eliminate variable x:

Equate the coefficient of x by multiplying 'b' by (1) and '-a' by (2) we get,

abx + b²y = cb  __(3)

-abx - a²y = -ac __(4)

Now in second step you can add equation (3) and (4) and eliminate x-term.

Therefore, the first step while solving system of equation using elimination method is to equate the coefficient of eliminated term in opposite sign.

The above question is incomplete , the complete question is:

What is the first step in solving a system of equations by elimination method?.

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Sam' speed for the first 15 minute of her journey is 80km/hr.

Speed refers to the rate of change of an object’s position in any direction. It is measured as the ratio of distance to the time (period in which the distance was covered). It is a scalar quantity. The formula for speed is given by:

Speed = Distance/ Time

Based on the provided travel graph,

Distance d = 20 km

Time t = 15 min = 15/60 = 0.25 hr

Hence,

Speed = d/t = 20/0.25 = 80km/hr

The speed in the first 15 minutes of Sam’s journey is 80km/hr.

Note: The question is incomplete. The complete question is: Sam drives his car on a journey. The travel graph for the first 15 minutes of his journey. Work out Sam' speed for the first 15 minute of her journey. Give your answer in km/h.

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Answer:64

Step-by-step explanation:

answer is in the photo. lmk if you want the solution steps.

The zeros of polynomial 4x² - 1 are x = 1/2 and x = -1/2

Let us assume that given polynomial be p(x) = 4x² - 1

We know that from the definition of zeros , the zeros of a polynomial are nothing but the values of the variable of the polynomial that makes the polynomial value equal to 0.

To find the zeros of polynomial p(x), we need to equate p(x) to zero then solve it for x.

⇒ p(x) = 0

⇒ 4x² - 1 = 0

⇒ 4x² = 1

⇒ x² = 1/4

⇒ x = ±(1/2)

Thus x = 1/2 and x = -1/2 are zeros of given polynomial.

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The complete question is:

What are the zeros of the polynomial 4x² - 1 ?.

Answer:

For 1st triangle value of BC side =9CM

For 2nd triangle value of  EF side =6FT

For 3rd triangle  value of CE side=13.03YD

Using Pythagorean theorem which gives the formula of deriving Hypotenuse in an equilateral triangle.

Formula

c²= a² + b²

using this formula

AB= 12CM

BC=xCM

AC=15CM

AC²= AB² + BC²

BC²= AC²-AB²

x²CM= 225CM - 144CM

X²= 81CM

X=9 CM

Similarly  

EF²= GE² - GF²

x²FT= 100FT - 64FT

x²= 36 FT

x= 6FT

For the last

CE²  YD=  CD² YD + CE² YD

x² YD= 49 YD + 121 YD

x² YD= 170 YD

x YD= 13.03 YD

Step-by-step explanation:

The  expression can be used to find the total cot of the meal with the gratuity is 1.18P

A gratuity is an amount of money that customers typically give to specific service sector employees, including those in the hotel industry, in addition to the service's base charge for the work they have completed.

A party of 8 had a bill of p.

A restaurant charges an automatic gratuity of 18% on tables with more than 6 people.

Since there are 8 people so, gratuity will be applied on the bill

Since bill is of amount p

So, gratuity of 18 % of p =  18% of  P  

                                          = 18/100 ×P

                                         = 0.18P

Now the total bill after adding gratuity : P+0.18P= 1.18P

Hence the total cost of the meal with the gratuity is $1.18p.

Therefore the  expression can be used to find the total cost of the meal with the gratuity is 1.18P

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Alison spends $48 less on the five t-shirts. Typically, the rate is expressed as a percentage.

Typically, the rate is expressed as a percentage. Multiply the rate by the starting cost to determine the discount. Subtract the discount from the original price to obtain the sale price.

Therefore, a sale price of $70 will be achieved with a 30% discount on a $100 list price. The phrase can also mean simply the price at which anything sells. For instance, if a piece of art sells for $10 million, that price set a record.

Typically, the rate is expressed as a percentage. Multiply the rate by the starting cost to determine the discount. Subtract the discount from the original price to obtain the sale price.  

40% * 16 = 4.0 * 16 = 64 - 16 = 48 = $48.

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The age of the sample of the carbon material is 19042 years.

We have to note that the half life of the sample has to do with the time that it takes for us to have only half of the original amount of the isotopes that are in the sample to be present.

Using the formula;

0.693/[tex]t{\frac{1}{2} }[/tex] = 2.303/t log (No/N)

[tex]t{\frac{1}{2} }[/tex] = Half life of the sample

t = time taken

No = Number of atoms initially present

N = Number of atoms at time t

Then;

0.693/5730 = 2.303/t log (No/0.1No)

0.693/5730 = 2.303/t  * 1

1.21 * 10^-4 = 2.303/t

t = 2.303/1.21 * 10^-4

t = 19042 years

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Answer:

Answer: Option 4
The only one where m∠C = m∠D

Step-by-step explanation:

If you rotate the triangle on the right enough to align them then you will see that with the given information the third choice is the correct one.

Even without that process if m∠A = m∠E and m∠B = m∠F then for the two triangles to be similar, ∠C, the remaining angle of ABC and ∠D the remaining angle of DEF must be equal

So ∠C = ∠D is a must for the two triangles to be similar

Only the fourth option has this as one of the entries

The corresponding sides and angles are m∠C = m∠D

Similar figures are zoomed in or zoomed-out (or just no zoom) version of each other. They are scaled versions of each other, and by scale, we mean that each of their dimension(like height, width, etc linear quantities) are constant multiple of their similar figure.

Even without that process if m∠A = m∠E and m∠B = m∠F then for the two triangles to be similar, ∠C, the remaining angle of ABC,

Also, ∠D the remaining angle of DEF must be equal

Therefore, ∠C = ∠D is a must for the two triangles to be similar

Hence,  m∠C = m∠D

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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.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{ -4 }{ 4 } \implies \text{\LARGE - 1}[/tex]

Note that the answer to the above expression is c = 19.35 or x = -32.35. This is resolved using the  Quadratic Formula.

Given

(13+c) * c = 620

⇒ 13c + c² = 620

⇒ c² + 13c -620 = 0 .......................1

We now have a quadratic equation above which we shall solve as follows:

For the above expression   (1)

a = 1, b = 13 and c = -620

that is

1c² + 13c + (-620) =0

Applying the Quadratic Formula = [tex]$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$[/tex]

Rather than say c =  we say x to avoid confusion

[tex]$x = \frac{-13 \pm \sqrt{13^2 - 4(1)(-620)}}{2(1)}$[/tex]

[tex]$x = \frac{-13 \pm \sqrt{169 + 2480}}{2}$[/tex]

[tex]$x = \frac{-13 \pm \sqrt{2649}}{2}$[/tex]

Therefore

x (or c as you would recall) = (-13 + 51.7)/2 or -13 - 51.7)/2

Thus, c = 19.35 or x = -32.35.

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The triangle with the given sides is a right triangle and therefore with acute angular measures.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².

Given here: The sides of a triangle here as 24,10,26

Now we know that the hypotenuse is the greatest side of a triangle.

and thus the hypotenuse is the side 26

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given, the length of sides of a triangle are 10, 24 and 26.

We have to find whether the given triangle is the right triangle.

By pythagoras theorem,

a²+b²=c²

Substituting the values

10²+24²=26²

By further calculation

100 + 576 = 676

LHS = RHS

Therefore, the given triangle is a right triangle and a right angle triangle is a acute triangle.

Hence, The triangle with the given sides is a right triangle and therefore with acute angular measures.

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For the given data, independent variable = time in hours, dependent variable = distance traveled in miles.

An independent variable is one that is tweaked or changed to explore its effects when performing an experimental study. It is called "independent" because it is unaffected by any other study variables.

These are also referred to as independent variables:

Various justifications (they explain an event or outcome)

elements that predict (they can be used to predict the value of a dependent variable)

Those on the right side are variables (they appear on the right-hand side of a regression equation).

These expressions are particularly useful in statistics when calculating how effectively a change in one independent variable can forecast or explain changes in the dependent variable.

Given, the data is -

(0, 0), (2, 100), (3, 140), (4, 140), (5, 200), (8, 360)

time in hours = {0,2,3,4,5,8}

distance traveled in miles = {0, 100, 140, 140, 200, 360}

independent variable = time in hours

dependent variable = distance traveled in miles

Yes, the given relation is a function.

x variable represents the input of the relation

y variable represents the output of the relation

Domain = {0,2,3,4,5,8}

Range =  {0, 100, 140, 140, 200, 360}

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Answer:

1) x = 4, 2) x = 9, 3) x = 9

Step-by-step explanation:

Since you give no other context my guy I am assuming this is a similar triangles kind of thing. Comparing the triangles you can create what is known as a scale factor, (Ex: 10/2 = 5) and then multiple/divide by this scale factor to get the unknown number (Ex: 20/5 = 4)

Repeat with all three triangles

Answer:

[tex]m\angle1=2^\circ\\m\angle2=88^\circ[/tex]

Step-by-step explanation:

As both angles are complementary, meaning they add up to 90°, we can simply solve for x using this sum and find each individual angle measure:

[tex]m\angle1+m\angle2=90^\circ\\(x-9)^\circ+(8x)^\circ=90^\circ\\x-9+8x=90\\9x-9=90\\9x=99\\x=11\\\\m\angle1=(x-9)^\circ=(11-9)^\circ=2^\circ\\m\angle2=(8x)^\circ=(8\cdot11)^\circ=88^\circ[/tex]

Answer:

x-intercept: (2,0)

y-intercept: (0,-4/3)

vertical asymptote: x = -3

Step-by-step explanation:

To find the x-intercepts, we can set f(x) to 0, which is y=0:

2x-4/x+3 = 0

2x-4 = 0

2x = 4

x = 2

To find the y-intercepts, we can set x to 0:

2(0)-4/(0)+3 = y

y = -4/3

To find the vertical asymptote, we can set the denominator equal to 0:

x+3 = 0

x = -3

There are 20 pink flowers in Mr. Elliot's garden.

We can start by using the information provided to figure out how many flowers are not red or purple. We know that 1/8 of the flowers are red, and 1/4 of them are purple, so:

(1/8) * 128 flowers = 16 red flowers

(1/4) * 128 flowers = 32 purple flowers

So, 16 + 32 = 48 flowers are red or purple.

This means that 128 - 48 = 80 flowers are not red or purple.

Then we know that 1/4 of the remaining flowers are pink, so:

(1/4) * 80 flowers = 20 pink flowers

So, there are 20 pink flowers in Mr. Elliot's garden.

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To graph a two step inequality solution boundary line is dashed for > and < and solid for ≤ and ≥.

These steps will be used to graphically solve a set of linear inequalities:

1. Find y's inequality solution.

2. Represent the inequality as a linear equation and, depending on the inequality sign, graph the line as either a solid line or a dashed line.

a. Draw the line as a dashed line if the inequality symbol is missing an equals sign ( or >).

b. Draw the line as a solid line if the inequality sign contains an equals sign (or ).

3. Darken the area when the inequality is satisfied.

4. For every disparity, repeat steps 1 through -3.

5. The region where all of the inequalities intersect will be the solution set.

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391 children swam at the public pool that day and 667 - 391 = 276 adults swam.

What is algebraic equation ?

An algebraic equation or polynomial equation is an equation of the form P=0 where P is a polynomial with coefficients in some field, often the field of the rational numbers.

Let's call the number of children that swam "x". The number of adults that swam would then be 667 - x.

The total revenue from the children was 1.75x and the total revenue from the adults was 2.25(667 - x).

set up an equation to represent the total revenue from both groups of swimmers

1.75x + 2.25(667 - x) = 1312.25

Expanding the second term on the left-hand side:

1.75x + 1507.75 - 2.25x = 1312.25

Combining like terms:

-0.5x + 1507.75 = 1312.25

Solving for x:

-0.5x = -195.5

x = 391

So, 391 children swam at the public pool that day and 667 - 391 = 276 adults swam.

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199 children and 468 adults swam at the public pool that day.

Let x be the number of children and y be the number of adults. Then we have the following two equations:

x + y = 667 (the total number of people)

1.75x + 2.25y = 1312.25 (the total amount of money collected)

We can substitute the first equation into the second to eliminate x:

1.75x + 2.25y = 1312.25

1.75(667 - y) + 2.25y = 1312.25

1175 - 1.75y + 2.25y = 1312.25

1175 = 1312.25 - 1.75y + 2.25y

1175 = 1312.25 - 1.75y + 2.25y

1175 = 1312.25 - 4y/2 + 9y/4

1175 = 1312.25 - (4/2)y + (9/4)y

1175 = 1312.25 - (6/4)y + (9/4)y

1175 = 1312.25 - (15/4)y

1175 + (15/4)y = 1312.25 + (15/4)y

15/4y = 137.25

y = 468

So there were 468 adults and 667 - 468 = 199 children.

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Answer:

Let the two numbers be x and y

Given ,

[tex]x + y = 95 \: \: ...(1)[/tex]

Also ,

[tex]y = x + 15 \: \: ...(2)[/tex]

Substiting equation 2 in equation 1 ,

[tex]x + x + 15 = 95 \\ \dashrightarrow \: 2x + 15 = 95 \\ \dashrightarrow \: 2x = 95 - 15 \\ \dashrightarrow \: 2x = 80 \\ \: \: \: \: dividing \: both \: sides \: by \: 2 \: \\ \dashrightarrow \: \cancel\frac{2x}{2} = \cancel\frac{80}{2} \\ \\ \dashrightarrow \: \: \boxed{ x = 40}[/tex]

Now , y = x + 15

therefore ,

[tex] y = 40 + 15 \\ \dashrightarrow \boxed{ y = 55 } [/tex]

Hence ,

the two numbers are 40 and 55 .

hope helpful! :)

a) The probability of event occur is  [tex]\frac{1}{5}[/tex].

b) The probability of event not occur is  [tex]\frac{4}{5}[/tex].

What is probability?

The likelihood of an event happening is gauged by probability. It is difficult to provide a complete prediction for many events. We can only anticipate the likelihood of an event occurring by using it. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

Here The ratio of the odds of an event occurring are 1:4.

Then probability of that the event will occur is ,

=>P(event will occur = [tex]\frac{1}{4+1}[/tex] = [tex]\frac{1}{5}[/tex]

Now the probability of that event not will occur is ,

=> P(event will not occur) = 1 -[tex]\frac{1}{5}[/tex] = [tex]\frac{5-1}{5}[/tex] = [tex]\frac{4}{5}[/tex]

Hence the answers are a) [tex]\frac{1}{5}[/tex] and b) [tex]\frac{4}{5}[/tex].

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