Complete the point-slope equation of the line (6,4) and (7,2).

y-2=________

The solution for 4+√5x+66=x+10 is x=3 (option 2)

Given equation: 4+sqrt5x+66=x+10

Subtract 4 from both sides;

[tex]\sqrt(5x+66) = x+6[/tex]

Square both sides:

[tex]5x+66 = (x+6)^2[/tex]

Simplify further, we get:

[tex]5x + 66 = x^2 + 12x + 36[/tex]

[tex]x^2 + 12x - 5x + 36 - 66 = 0[/tex]

[tex]x^2 + 7x - 30 = 0[/tex]

Factor the equation to get:

[tex](x + 10)(x - 3) = 0[/tex]

[tex]x - 3 = 0[/tex]

[tex]x = 3[/tex]

Therefore, the solution of 4+√5x+66=x+10 is x=3 (option 2)

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Complete question:

What is the solution of 4+√5x+66=x+10?

1.x=-10

2.x=3

3.x=-10 or x=3

4.no solution

Total distance of a typical running track  = [tex]402 \frac{1}{4} meters[/tex].

Let us convert it into impoerper fraction first, we get

[tex]\frac{402\times4+1}{4}=\frac{1609}{4}meters.[/tex]

Total number of maps in a day = 10 maps.

Number of days of running = 5 days.

Total number of maps of 5 days = 10 × 5 = 50 maps.

Total number of meters in 50 maps = [tex]50\times\frac{1609}{4}=\frac{80450}{4}=20112\frac{1}{2}\ meters.[/tex].

To find the sum of 7+9 using the make a ten strategy, start with the larger number, add 1 to it to make it 10, subtract 1 from the other number, and then add the resulting numbers together.

So, the sum of 7 + 9 is 16.

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The answer is 23 beats

Step-by-step explanation:

P = 2l + 2w --> w = 1/2·P - l = 1/2·42 - 15 = 6 feet

The width of the rectangular garden will be 6 feet.

The rectangle is defined as a quadrilateral having four sides and the angle suspended by all the sides is equal to 360 degrees. The perimeter is the sum of all the sides of the rectangle.

Given that the perimeter of a garden is 42 feet. The length is 15 feet.

The width of the rectangular garden will be calculated as:-

P = 2l + 2w

w = 1/2·P - l

w= 1/2·42 - 15

w= 6 feet

Therefore, the width of the rectangular garden will be 6 feet.

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Yes square meters is a type of surface area.

Answer:

1 7/50

Step-by-step explanation:

2 6/25= 2 12/50

1 1/10= 1 5/50

2 12/50-1 5/50= 1 7/50

Step by Step:

[tex]2\frac{6}{25}  - 1\frac{1}{10}[/tex]

Subratact whole numbers 2-1: 1

Combine fractions [tex]\frac{6}{25} - \frac{1}{10}[/tex]: [tex]\frac{7}{50}[/tex]

1 + /frac{7}{50}

Answer:

A = 1/frac{7}{50}

Notes:

N/A

side one is 5 side two is 10 and the third side is 13. 28 is not divisible by three so if one side i 5 ft longer and another side is 8 ft longer then you add them 5+8=13 then subtract 13 from the perimeter 28-13=15 then divide 15 by 3 and get 5 5 5. add 5 (5+5) (5+8).

The lengths of the sides of the triangle are 5 feet, 10 feet, and 13 feet.

Let's assume the second side of the triangle has a length of x feet.

According to the given information, the first side of the triangle is 5 feet longer than the second side, so its length would be x + 5 feet.

Similarly, the third side is 8 feet longer than the second side, so its length would be x + 8 feet.

The perimeter of a triangle is calculated by adding the lengths of all three sides, so we can write the equation:

x + (x + 5) + (x + 8) = 28

Now let's solve this equation to find the value of x:

3x + 13 = 28

3x = 28 - 13

3x = 15

x = 15 / 3

x = 5

So, the second side of the triangle has a length of 5 feet.

Using this value, we can find the lengths of the other two sides:

First side: x + 5 = 5 + 5 = 10 feet

Third side: x + 8 = 5 + 8 = 13 feet

Therefore, the lengths of the sides of the triangle are 5 feet, 10 feet, and 13 feet.

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[tex]\dfrac{3}{4}x+5-\dfrac{1}{2}x=3\qquad|\text{multiply both sides by 4}\\\\\not4^1\cdot\dfrac{3}{\not4_1}x+4\cdot5-\not4^2\cdot\dfrac{1}{\not2_1}x=4\cdot3\\\\3x+20-2x=12\\\\(3x-2x)+20=12\qquad|\text{subtract 20 from both sides}\\\\x=-8[/tex]

The number of the bills will be 100 to equate to $100 bills.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a $1 bills are the same as one $100 bill. the number of the bills will be calculated as:-

Number = 100 x 1 = 100

Therefore, the number of bills will be 100 to equate to $100 bills.

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Keiko has a total of $5200

x is the amount of money in larger account

y is the amount of money in smaller account

x - y = $900

and x + y = $5200

This creates two simultaneous equations:

x - y = $900 ... (i)

x + y = $5200 ... (ii)

Adding (i) and (ii) :

2x = $6100 , x = $3050

y = x - $900 = $3050 - $900 = $2150

The amount of money in larger account (x) = $3050

The amount of money in smaller account (y) = $2150

To solve the problem, we set up and solved a system of equations using the given information. We find that Keiko has invested $2150 in the smaller account and $3050 in the larger account.

Keiko has $5200 that she invested in two accounts. We're told the larger account is $900 more than the smaller one. Since we let x represent the amount of money in the larger account and y represent the amount of money in the smaller account, we can establish the following system of equations:

Substituting the second equation into the first, we get:

Solving for y from this equation, we obtain y = $2150, representing the smaller account. Substituting y into the original second equation, we find x = $3050, which is the larger account. Hence Keiko has $2150 in the smaller account and $3050 in the larger account.

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Answer:

Green: [tex]\bf~\frac{3}{20}[/tex]

Blue: [tex]\bf~\frac{5}{20}[/tex] or [tex]\bf~\frac{1}{4}[/tex]

Combined probability of a green or a blue: [tex]\bf~\frac{8}{20}[/tex] or [tex]\bf~\frac{2}{5}[/tex]

Step-by-step explanation:

The probabilty of you getting a marble of a given colour is the amount of marbles of the given colour divided by the total amount of marbles.

By using that rule, we get a probabilty o [tex]\frac{3}{20}[/tex] for a green marble, a probabilty of [tex]\frac{1}{4}[/tex] for a blue marble, or if we sum those two and find the probabilty of getting a marble that is either green or blue, we get [tex]\frac{2}{5}[/tex]

[tex]\frac{3}{20} + \frac{5}{20} = \frac{8}{20} = \frac{4}{5}[/tex]

Hope it helped,

BioTeacher101

Answer:

C:  {4, -12/5}

Step-by-step explanation:

Let's actually solve |-4+5x|=16:  Divide all 3 terms by 5.  Then:  |-4/5 + x| = 16/5.

If we were to graph this, the center (on a number line) would be at -4/5.  Now if we add 16/5 to -4/5, we get 12/5, the larger solution; if we subtract 16/5 from -4/5, we get -20/5, the smaller solution, equivalent to -4.  Correct answer choice is C.

This corresponds to option C.

The solution set for the absolute value equation |-4+5x|=16 can be found by considering both the positive and negative scenarios since an absolute value represents the distance a number is from zero on the number line, without regards to direction (positive or negative).

To find the solution set, we need to split the absolute value equation into two possible linear equations:

Solving the first equation gives us:

Solving the second equation gives us:

However, x = 2.4 does not make sense in the context of our original problem, because we are looking for the negative solution when we consider the equation -4 + 5x = -16. The correct step is:

Therefore, the correct solution set is {4, -12/5}, which corresponds to option C.

90 is approximately 37.5 percent of 240.

To find the number that 90 is 37.5% of, we can set up the following proportion:

90 is to x as 37.5 is to 100

This can be expressed as:

90/x = 37.5/100

To solve for x, we can cross-multiply:

37.5 * x = 90 * 100

Now, divide both sides of the equation by 37.5 to isolate x:

x = (90 * 100) / 37.5

Simplifying the expression on the right side:

x = 9000 / 37.5

Dividing 9000 by 37.5:

x ≈ 240

37.5% of 240 is 90.

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90 is 37.5% of 240.

Part = (Percentage / 100) * Whole

In this case, we are given the part (90) and the percentage (37.5%), and we need to find the whole.

Whole = Part / (Percentage / 100)

Substituting the given values:

Whole = 90 / (37.5 / 100)

Whole = 90 / 0.375

Whole = 240

So, 90 is 37.5% of 240.

5.6 * (7 / 5) = 7.84

G = George's age

G = 3(P+1) - 3

G = 3P + 3 - 3

G = 3P

Hey there!!

Let's take the number as ' n '

Three times the difference of a four and number.

... 3 ( 4 - n )

Eight more than the expression.

... 8 + 3 ( 4 - n )

' n ' is given as ' 3 '.

Plugging in :

... 8 + 3 ( 4 - 3 )

... 8 + 3 ( 1 )

... 8 + 3

... 11

The required answer is 11.

Hope my answer helps!!  

The actual area of the game room is 150 square yards.

To find the actual area of the game room, we need to convert the dimensions on the blueprint to actual measurements. The scale on the blueprint is 1 foot to 5 yards, so we can convert the length and width of the room by multiplying by 5. The room measures 3 feet by 2 feet on the blueprint, so the actual dimensions are 3 feet x 5 yards and 2 feet x 5 yards. Thus, the actual area of the game room is (3 feet x 5 yards) x (2 feet x 5 yards), which simplifies to 15 yards x 10 yards or 150 square yards.

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Hey there!!

Given equation :

... { ( 500 + n ) - 50 }5 = c

... { 500 + n - 50 }5 = c

... { 450 + n }5 = c

... 2250 + 5n = c

Hope my answer helps!!

94*27=2538

90*20+4*7+20*4+90*7=2538

1800+28+80+630=2538

2538=2538

he subtracted both numbers and got 49

I assume the underlined digit tells you to round off to that place. In this case, the 3 is in the tenths place, so you need to round off 2.348 to the nearest tenth.

2.348

The 3 is in the tenths place. If you are asked to round off to the nearest tenth, then first, drop the digits to the right of the 3. Now you have 2.3, but we need to look at the next digit in the original number. The original number was 2.348, with a 4 to the right of the 3. Since 4 is less than 5, you just keep the rounded number as 2.3.

Answer: 2.3

Answer: [tex]\frac{6}{336}[/tex]

Step-by-step explanation:

Given: The Number of different prizes = 3

The number of people entered the drawing room = 8

The number of ways to select for 3 prizes, such that  you win first prize and your mom wins second prize = You × Mom × Rest of people

[tex]1\times1\times(8-2)=1\times6=6[/tex]

The total number of ways to award the prizes = 336

Therefore, the probability that you win first prize and your mom wins second prize=[tex]\frac{6}{336}[/tex]

Convert 12 pounds to ounces which is 192 ounces.

Divide the price by the ounces. That would get $0.09765625 rounded to $0.10 per ounce.

The unit price per ounce will be equal to $0.10.

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

Given that:-

The unit price per ounce will be calculated as:-

1 pound = 16 ounces

12 pounds = 12  x  16  =  192

Cost of 192 ounces = $18

Cost of unit ounce = 18  /  192

Cost of unit ounce  =  0.095156 ≅ $0.10

Therefore the unit price per ounce will be equal to $0.10.

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Answer:

The equation will be:   [tex]y=4x[/tex]

Step-by-step explanation:

Side lengths[tex](x)[/tex] ⇒    4.5       8.5        10.25       13.75

Perimeter [tex](y)[/tex]    ⇒     18         34            41            55

First we will pick any two ordered pairs in form of point like [tex](x,y)[/tex]. So, here [tex](x_{1}, y_{1})= (4.5, 18)[/tex] and [tex](x_{2}, y_{2})= (8.5, 34)[/tex]

Now, the slope will be:  [tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}= \frac{34-18}{8.5-4.5}=\frac{16}{4}=4[/tex]

So, the equation using the point-slope form will be..............

[tex]y-y_{1}=m(x-x_{1})\\ \\ y-18=4(x-4.5)\\ \\ y-18=4x-18\\ \\ y=4x[/tex]

Thus, the equation that represents the relationship between the side length[tex](x)[/tex] and the perimeter[tex](y)[/tex] will be:  [tex]y=4x[/tex]

Answer:

y=4x

Step-by-step explanation:

88-55=33

33 second handicap

Joe must give Jake a 33 second catch up time period

1608 divided by 6 is equal to the quantity of 268.

We can verify this by multiplying 268 by 6.

268 * 6 = 1608.

16/6=2 Ramander 4

4 bring the 0 down is 40.

40/6=......... If you need it the long way.

short way

1608/6=268