Find all points of intersection of the graphs of the polynomials. f(x)=(x+5)(x-5) and g(x)=(x+1)(x-3)

The equivalent expression using the distributive property is 6(7x + 2)

From the question, we have the following expression

42x + 12

Rewrite the given expression as follows

This is represented using

(42x + 12)

Factor out 2 from the expression

So, we have the following representation

42x + 12 = 2(21x + 6)

Factor out 3 from the expression

So, we have the following representation

42x + 12 = 2 * 3(7x + 2)

Evaluate the products

42x + 12 = 6(7x + 2)

The above represents the equivalent expression

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Answer: -2.55

Step-by-step explanation:

Answer:

-2.55

Step-by-step explanation:

-1.25 + 2 1/5 + (-3.5) =

= -1.25 + 2.2 - 3.5

= 0.95 - 3.5

= -2.55

Answer:

24.359

Step-by-step explanation:

The height is opposite of the 77 so we are using sin. The length of the ladder is the hypotenuse.

sin(77°)=height/25     Set up equation sin=height/hypotenuse

25*sin(77°)=height     Multiply both sides by 25

25*.96437=height

height=24.359

The probability that first card selected has a yellow bird and second card selected has a lion both with and without replacement is 1/40 and 1/38. respectively.

Probability is the likelihood of an event or more than one event occurring. It is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.

Probability may also be described as the likelihood of an event occurring divided by the number of expected outcomes of the event. i.e.,

               P(A) = f / N

Where:

P(A) = Probability of an event (event A) occurring

f = Number of ways an event can occur (frequency)

N = Total number of outcomes possible

Here deck of 20 cards are given which implies total number of possible outcomes are 20. From these 20 cards 5 cards has lions and 5 cards has birds in which 2 are yellow and 3 are red.

Now two cards are selected randomly.

We have to find the probability that first card selected has a yellow bird and second card selected has a lion both probability that first card selected has a yellow bird and second card selected has a lion both with and without replacement.

Probability with replacement:

Probability that first card selected has a yellow bird = 2/20  ---(1)

Since replacement is allowed so the probability that second card selected has a lion = 5/20---(2)

So, the probability that first card selected has a yellow bird and second card selected has a lion with replacement = (1) * (2) = 2/20 * 5/20 = 1/40.

Probability without replacement:

Probability that first card selected has a yellow bird = 2/20  ---(3)

And since replacement is not allowed, the probability that second card selected has a lion = 5/19---(4)

So, the probability that first card selected has a yellow bird and second card selected has a lion without replacement = (3) * (4) = 2/20 * 5/19 = 1/38.

Therefore, the probability with and without replacement is 1/40 and 1/38. respectively.

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The transformation that is applied to the ΔABC to get the ΔA'B'C' is vertical translation by 6 units downwards.

The triangle has the vertices  A(-2, 3), B(2, 1), and C(1, 0)

They are transformed such that:

A(-2, 3)→A'(-2,-3)

B(2, 1)→B'(2,-5)

A(-1, 0)→A'(-2,-6)

Now if we carefully observe we can see that the y-coordinate of A' is 6 less than that of A.

Similarly for B and C the coordinates are 6 units less than that of the object, but the x-coordinate remains the same.

This proves that the graph follows a vertical transformation and since the new ordinates are 6 units smaller, so the graph is translated 6 units downwards.

A function, f, that maps to itself is known as a transformation, or f: X→X'. The pre-image X will change into the picture X' following the transformation. This transformation can use any operation, or a combination of operations, including translation, rotation, reflection, and dilation.

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The value of the expression which shows the amount he paid for lunch is 7 dollars.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and divisions.

Given that Frankie orders two hamburgers and a soda for lunch. A hamburger is $3 and a soda is $1.00.

Now here is the expression-

1+(2x3)= 2 x 3 = $6

Cost of lunch = ($3 / hamburger) (2) + ($1 / soda) (1)

Cost of lunch = $6 + $1

Cost of Frankie's  lunch = $7

Therefore, the value of the expression which shows the amount he paid for lunch is 7 dollars.

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Answer:

I am going sujshsbeba170

Answer:

21st 22nd are equal so ×=0

The value of x in the given triangle is x = 4

From the question, we are to determine the value of x.

From the given triangle,

We can write that

(9x+ 1)° + 78° + (17x - 3)° = 180° (Sum of angles in a triangle)

Now, we will solve for x

(9x+ 1)° + 78° + (17x - 3)° = 180°

9x° + 1° + 78° + 17x° - 3° = 180°

Collect like terms

9x° + 17x° = 180° - 1° + 3° - 78°

26x° = 104°

x = 104/26

x = 4

Hence, the value of x is 4

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Answer:

Soultion\left(x^2+\frac{7}{3}x-\frac{17}{3}\right)=3\left(x^2+\frac{7}{3}x+\frac{49}{36}-\frac{49}{36}-\frac{17}{3}\right)\quad :\quad x=-\frac{7+\sqrt{253}}{6},\:x=\frac{\sqrt{253}-7}{6} steps \left(x^2+\frac{7}{3}x-\frac{17}{3}\right)=3\left(x^2+\frac{7}{3}x+\frac{49}{36}-\frac{49}{36}-\frac{17}{3}\right) simplify -2x^2-\frac{14x}{3}+\frac{34}{3}=0.

Step-by-step explanation:

I got you my boy.

Answer:

On a number line, 1/6 would land in the exact middle between 0 and 2/6

Step-by-step explanation:

Not too sure what your question meant, but I hope my answer helped!

If it wasn't what you were looking for, please let me know and elaborate on your question and I'll be happy to help out! :)

Answer:

900212356

Step-by-step explanation:

The fourth coordinate of rectangular piece of material is (2.8 , -2.7)

According to the question,

Charles drew a plan for a rectangular piece of material that he will use for a blanket. Three of the vertices are (-1.4, -2.7), (-1.4,3.7), and (2.8,3.7).

As we know , the opposite sides of rectangle are equal

If we locate these coordinates in our graph and join them

Length of rectangle will be = 2.8+1.4 = 4.2cm

Breadth of rectangle will be = 3.7 + 2.7 = 6.4cm

So, the fourth coordinate should lie 6.4cm far from  (2.8,3.7)

Subtracting 6.4 from y-axis,

Fourth coordinate = 3.7 - 6.4

= -2.7

Therefore , The fourth side of rectangle = (2.8 , -2.7)

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The time it will takes for the rock to hit the ground (h=0)  given the height of 360 feet high is 3.53 seconds.

The concept that will be used in the calculation is the concept of height and time .

The formular for the  expression is given as  ℎ= 200 −16t^2

Then the height of the tower is been given as 360 feet high

ℎ= 200 −16t^2

then

t^2=200/16

t^2=12.5

t=3.53 seconds

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The cost of buying one of each of the soap and plaster is 165p.

From the information, the bar of soap cost 70p and a box of plasters cost 95p.

It should be noted that in order to find the total cost, we will have to add the. oat of each product.

This will be:

Total cost = Cost of soap + Cost of plaster

= 70p + 95p

= 165 p

The cost is 165p.

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Answer:

7

Step-by-step explanation:

15-8

Check the picture below.

The profit that the upcoming business would be making after 10 years is  $122 million.

The profit of the business in 10 years can be modelled with an exponential equation. This is because the rate of growth of profit each year would be 10% of the last year's profit.

The equation that is used to determine the profit in 10 years is:

FV = P (1 + r)^n

Where:

FV = 100 x (1 + 0.02)^10

FV = $100 million x (1.02^10) = $122 million

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The pieces of long bunting is 22.

From the question, we have

The room is 4m long and 3m wide.

perimeter of room = 2×(4+3)

=14 m = 1400 cm

she has lots of 70 cm lenghts of bunting.

1400 cm/70 cm = 20

she needs to use 50mm =5 cm of each piece of string for the knot.

20×5 = 100

100/70 ≈2

pieces of 70 cm long bunting = 20+2 =22

Divide:

Split is to divide into two or more equal sections, places, groupings, or divisions in its most basic form. To divide something simply means to provide it to a group in equal quantities or to cut it up into equal pieces. Let's imagine a diagonal divides a square into two triangles with equal areas. An integer may or may not be the result of a division operation. Sometimes the result will be expressed as decimal numbers.

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The true statements are:

The center of the circle lies on the x-axis

The radius of the circle is 3 units.

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

The standard equation of a circle is expressed as:

x²+y²+2gx+2fy+C=0

Centre is (-g, -f)

radius = √g²+f²-C

Given a circle whose equation is

x²+y²-2x-8=0

Get the centre of the circle

2gx = -2x

2g = -2

g = -1

Similarly, 2fy = 0

f = 0

Centre = (-(-1), 0) = (1, 0)

This shows that the center of the circle lies on the x-axis

r = radius = √g²+f²-C

radius = √1²+0²-(-8)

radius =√9 = 3 units

The radius of the circle is 3 units.

For the circle x² + y² = 9, the radius is expressed as:

r² = 9

r = 3 units

Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Hence we get the required answers.

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Answer:

28

Step-by-step explanation:

4,8,12,16,20,24,28. +4 every time

Answer:

The two points used to find the slope:

[tex]x_1,y_1[/tex]: 2,30

[tex]y_1,y_2:[/tex] 4,10

Final equation: y = -10x + 50

Step-by-step explanation:

From a fellow 8th grader <3

First, let's review the slope of a line: y = mx + b

Where m is the slope, and b the y-intercept

Let's find the slope. To do this I will select 2 points from this graph, and using the slope formula I will calculate it

Slope formula: [tex]\frac{rise}{run} =\frac{change- in- y}{change-in-x} =\frac{y^2-y^1}{x^2-x^1}[/tex]

To get the most accurate answer, I will be using the 2 points given that are directly on the line:

1 = (2, 30)

2 = (4, 10)

Slope: [tex]\frac{10-30}{4-2} =\frac{-20}{2} =-10[/tex]

m = -10

It makes sense that it is a negative, since the graph continues downwards.

Let's update our equation: y = -10x + b

We can see that the line intersects the y-axis at y = 50

Plug this into our b-value:

y = -10x + 50

Now, I would recommend using a graphing calculator (like a TI-83) or an online one (like desmos) to double check this. I have attached a screenshot of this line on desmos. From there we can see if this line matches up with the one seen on your graph.

Our answer is:

The two points used to find the slope:

[tex]x_1,y_1[/tex]: 2,30

[tex]y_1,y_2:[/tex] 4,10

Final equation: y = -10x + 50

Please let me know if this helped you, and if this was the correct answer! If it is incorrect I will do my best to revise my answer.

Answer: y intercept is (0,50) and Slope is -10.

Final equation is y= -10x+50

Step-by-step explanation:

Y-intercept is at what point the line intercepts the y-axis. It intersects at (0,50) coordinate point as you can see.

Slope is change in y divided by the change in x. When you change x by 1, y changes by -10. So it is -10/1 = -10. Slope is -10.

Since we know y intercept and slope equation is y=-10x+50

The probability that they two people are chosen and travel by different transport is 47/144

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.

Probability is given as sample space / total outcome

Probability to travel by car p(C)= 5/12

Probability to travel by bus P(B)= 4/12=1/3

Probability to travel by train P(T)= 3/12= 1/4

for two people chosen at random

P(C ×B)= 5/12×1/3= 5/36

P(B×T)= 1/3×1/4= 1/12

P(C×T)= 1/4×5/12= 5/48

Therefore the probability that the two chosen travel by different car is

P(C ×B)+P(B×T)+P(C×T)= 5/36+1/12+5/48

= 141/432

divide through by 3

= 47/144

Hence the get the required answer.

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Answer:

He will spend $60 on candy

Step-by-step explanation:

If the cost for one pound is $5, then just multiply.

12 x $5 = $60

Answer: C=7

Step-by-step explanation: C=12+5

the answer is c=7

Answer:

8.0 × 10^-3 ÷ 4.0 × 10^4

= 2.0 × 10^-3-4

= 2.0 × 10^-7

or 0.0000002

The fraction solve 7/15 - 6 2/5 , we get the answer -89/15.

Given,

In the question:

The Fraction is given as:

7/15 - [tex]6\frac{2}{5}[/tex]

To solve the above fraction.

Now, According to the question;

Let's know

What is fraction in math?

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.

Come to the question:

7/15 - [tex]6\frac{2}{5}[/tex]

7/15 - 32/5

Take the L.C.M

= [tex]\frac{7-96}{15}[/tex]

= -89/15

Hence, The fraction solve 7/15 - 6 2/5 , we get the answer -89/15.

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Answer:

coordinates of A are (-4.5, 2)

coordinates of B are (0, -3.5)