A $1508 award is shared equally by 8 people. What is each persons share of the award

Answer:

[tex]10.3\ mi[/tex]

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]A(10,8)\\B(1,3)[/tex]

substitute the values

[tex]d=\sqrt{(3-8)^{2}+(1-10)^{2}}[/tex]

[tex]d=\sqrt{(-5)^{2}+(-9)^{2}}[/tex]

[tex]d=\sqrt{25+81}[/tex]

[tex]d=\sqrt{106}[/tex]

[tex]d=10.3\ mi[/tex]

Answer:

(2z - 3)(15z - 4)

Step-by-step explanation:

To factor the quadratic

Consider the factors of the product of the coefficient of the z² term and the constant term which sum to give the coefficient of the z- term

product = 30 × 12 = 360 and sum = - 53

The factors are - 45 and - 8

Use these factors to split the z- term

30z² - 45z - 8z + 12 ( factor the first/second and third/fourth terms )

= 15z(2z - 3) - 4(2z - 3) ← factor out (2z - 3)

= (2z - 3)(15z - 4) ← in factored form

Answer:

8y^3 + 6y^2 - 29y + 15

Step-by-step explanation:

8y^3 + 12y^2 - 20y - 6y^2 - 9y + 15

then

8y^3 + 6y^2 - 29y + 15 is the product

Best regards

Answer:

=8y^3+6y^2−29y+15

Step-by-step explanation:

(4y−3)(2y^2+3y−5)

=(4y+−3)(2y^2+3y+−5)

=(4y)(2y^2)+(4y)(3y)+(4y)(−5)+(−3)(2y^2)+(−3)(3y)+(−3)(−5)

=8y^3+12y^2−20^y−6y^2−9y+15

=8y^3+6y^2−29y+15

Answer:

53 miles per hour

Answer:

53 miles

Step-by-step explanation:

Total Distance: 265

Then, take that number and divide by 5. 265/5

= 53

Answer:

y= 3      

  --- X +1

   4

Step-by-step explanation:

-4y=-3x-12+8

-4y=-3x+4

---      ---  -

4        4    4

y= 3      

  --- X +1

   4

Answer:

[tex]x-1<n<3x+5.[/tex]

Step-by-step explanation:

If a, b and c are the lengths of the triangle's sides, then

[tex]a+b>c,\\ \\a+c>b,\\ \\b+c>a.[/tex]

Since

[tex]a=2x+2,\\ \\b=x+3,\\ \\z=n,[/tex]

then

[tex]2x+2+x+3>n\Rightarrow n<3x+5,\\ \\2x+2+n>x+3\Rightarrow n>1-x,\\ \\x+3+n>2x+2\Rightarrow n>x-1.[/tex]

Thus,

[tex]x-1<n<3x+5.[/tex]

Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The correct option is A, 3x + 5 > n > x - 1.

Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.

Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,

(a+b) > c

(b+c) > a

(c+a) > b

Given the three sides of the triangle 2x + 2 ft, x + 3 ft, and n ft. Now using the triangle inequality theorem we can write,

2x + 2 + x + 3 > n  → 3x + 5 > n

2x + 2 + n > x + 3 → n > -x + 1

x + 3 + n > 2x + 2 → n > x - 1

Since x can not be a negative term therefore, we can write,

3x + 5 > n > x - 1

Hence, the correct option is A, 3x + 5 > n > x - 1.

Learn more about Triangle Inequality Theorem:

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Answer:

c

Step-by-step explanation:

I think its c but I could be wrong

Answer:

7/12 - 1/12 = 6/12

Step-by-step explanation:

Answer:

The answer should be 6/12 or 1/2

Answer:

A

Step-by-step explanation:

Parallel lines have the same slope. Find the slope by converting the equation x + 5y = 10 into y = mx+b form. It becomes y = -1/5x + 2. The slope is -1/5.

Substitute -1/5 and the point (1,3) into the point slope form.

[tex]y - y_1 = m(x-x_1)\\y - 3 = -\frac{1}{5}(x - 1)\\y - 3 = -\frac{1}{5}x + \frac{1}{5}\\y = -\frac{1}{5}x + \frac{16}{5}[/tex]

Answer:

It's aaaaaaaaaaaaaaaaaaaaaaa!!!

Step-by-step explanation:

Answer: Simplifying

4x = 4x

Add '-4x' to each side of the equation.

4x + -4x = 4x + -4x

Combine like terms: 4x + -4x = 0

0 = 4x + -4x

Combine like terms: 4x + -4x = 0

0 = 0

Solving

0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

Answer:

True

Step-by-step explanation:

It was correct on my quiz

Answer:

D) [tex]y\:<\:2x+2[/tex], [tex]y\:>\:-x[/tex]

Step-by-step explanation:

The blue boundary line has a y-intercept of 2 and a slope of  2.

It has equation : [tex]y=2x+2[/tex]

Since the boundary line is not solid and the lower half plane of this line is shaded, its inequality is

[tex]y\:<\:2x+2[/tex]

The blue boundary line passes through the origin and has slope [tex]-1[/tex].

Its equation is [tex]y=-x.[/tex]

Since the boundary line is not solid and the right half-plane is shaded, its inequality is [tex]y\:>\:-x[/tex]

The correct choice is D.

The correct choice is D: y < 2x + 2, y > -x.

The blue boundary line is represented by the equation y = 2x + 2.

Since the lower half-plane is shaded, the inequality is y < 2x + 2.

The blue boundary line also passes through the origin and has a slope of -1, which gives it the equation y = -x.

Since the right half-plane is shaded, the inequality is y > -x.

So, the correct choice is D: y < 2x + 2, y > -x.

for such more question on boundary line

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Answer:

11/15

Step-by-step explanation:

If you convert them to a decimal 11/15 would be more

Answer:

[tex]9\sqrt{6}[/tex]

Step-by-step explanation:

Multiply the numbers outside of the radicand, which is 3 x 3 = 9.

Then multiply the numbers inside of the radicand, which is 2 x 3 = 6.

Therefore the answer is [tex]9\sqrt{6}[/tex].

Edit:

Is this what the problem looks like?

[tex]3\sqrt{2}[/tex] x [tex]3\sqrt{3}[/tex]

[tex]\huge\boxed{22:7}\ \huge\boxed{29:22}[/tex]

First, we need to find the number of yellow pencils in the basket. We'll represent the number of green pencils with [tex]g[/tex] and the number of yellow pencils with [tex]y[/tex].

[tex]\begin{aligned}7+y&=29&&\smash{\Big|}&&\text{Start with what we already know.}\\y&=22&&\smash{\Big|}&&\text{Subtract 7 from both sides.}\end{aligned}[/tex]

Our first ratio is [tex]y:g[/tex], or [tex]\boxed{22:7}[/tex].

The second ratio is [tex](g+y):y[/tex]:

[tex]\begin{aligned}(g+y)&:y\\(7+22)&:22\\29&:22\end{aligned}[/tex]

6r -4 +8(15-r) + 23

expand brackets

6r -4 +120 -8r + 23

collect like terms

120 + 23 - 4 = 139

6r - 8r = -2r

139 - 2r

139 - 2r = -3r + 137

-137 from both sides

-2r = -3r -2

add 3r

R = -2

sub in both equations and see if you get the same value

-3r + 137

-3 (-2) + 137

6 +137 = 143

139 - 2r

139 - 2(-2)

139 + 4

143

yes they are equal

Final answer:

After simplifying the given expression by combining like terms and using the distributive property, we find that the simplified form is indeed -3r + 137, which means it is equivalent to the original expression.

Explanation:

To determine if the expression -3r + 137 is equivalent to the given expression 6r – r + 8(15 – r) + 23 – 6, we need to simplify the given expression.

Let's simplify the given expression step-by-step:

Therefore, the simplified form of the given expression is indeed -3r + 137, which means it is equivalent to the given expression.

Answer:

m= -5/4

Step-by-step explanation:

Slope can be translated to "rise over run". You go down 5 spaces and then move over 4 spaces.

Answer:

p²-q²

Step-by-step explanation:

(p+q)×(p-q)

=p×(p-q)+q×(p-q)

=p×p-p×q+p×q-q×q

=p²-p×q+p×q-q²

=p²-q²

Answer:

1) Factor the denominator and the numerator of each fraction.

2) Simplify.

3) Find the Least common denominator (LCD).

4) Rewrite the LCD. Divide it by the denominator of the first fraction and multiply the result of the division by its numerator (The LCD is the same denominator of the second fraction, so its numerator stays the same).

5) Apply Distributive property on the numerator and on the denominator.

6) Add like terms.

Step-by-step explanation:

The steps required to determine the sum of the two expressions are:

1) Factor the denominator and the numerator of each fraction:

[tex]\frac{3x+6}{x^2-x-6}+\frac{2x}{x^2+x-12}=\frac{3(x+2)}{(x-3)(x+2)}+\frac{2x}{(x-3)(x+4)}[/tex]

2) Simplify (Remember that [tex]\frac{(x+2)}{(x+2)}=1[/tex]):

[tex]\frac{3}{(x-3)}+\frac{2x}{(x-3)(x+4)}[/tex]

3) Find the Least common denominator (LCD). In this case this is:

[tex]LCD=(x-3)(x+4)[/tex]

4) Rewrite the LCD. Divide it by the denominator of the first fraction and multiply the result of the division by its numerator. As the LCD is the same denominator of the second fraction, its numerator stays the same:

[tex]=\frac{3(x+4)+2x}{(x-3)(x+4)}[/tex]

5) Apply Distributive property on the numerator and on the denominator:

[tex]=\frac{3x+12+2x}{x^2+x-12}[/tex]

6) Add like terms:

[tex]=\frac{5x+12}{x^2+x-12}[/tex]

Answer:

x-5 edg

Step-by-step explanation:

Answer:

25/216 or 0.1157

Step-by-step explanation:

The probability of getting a 6 is 1/6.  

The probability of not getting a 6 is 5/6

We roll a die 4 times and want 2 sixes, and 2 not sixes.  

We want a combination of 2 sixes from 4 rolls, so we can use the binomial formula to solve this...

(4C2)(1/6)²(5/6)² = 6(1/36)(25/36) = (1/6)(25/36) = 25/216 = 0.1157

The long hand way of solving this is to list the 6 ways we can roll our desired result along with their probabilities...

We could get

6, 6, not 6, not 6      (1/6)(1/6)(5/6)(5/6) = 25/1296

6, not 6, 6, not 6       (1/6)(5/6)(1/6)(5/6) = 25/1296

6, not 6, not 6, 6       (1/6)(5/6)(5/6)(1/6) = 25/1296

not 6, not 6, 6, 6       (5/6)(5/6)(1/6)(1/6) = 25/1296

not 6, 6, not 6, 6       (5/6)(1/6)(5/6)(1/6) = 25/1296

not 6, 6, 6 not 6        (5/6)(1/6)(1/6)(5/6) = 25/1296

There are 6 different way this can happen, each having a probability of 25/196.  We add up the probabilities, getting 150/1296, which reduces to

25/216

Answer:

11.6%

Step-by-step explanation:

[tex]\frac{4!}{2!\left(4-2\right)!}\left(\frac{1}{6}\right)^2\left(\frac{5}{6}\right)^2 = 0.116 = 11.6[/tex]

Answer:

x = 1.56  or x = -2.56

Step-by-step explanation:

From the equation;

x2 +x − 4 = 0

a = 1 , b = 1, and c = -4

x = (-b ± √(b² -4ac))/2a

  = (-1 ± √(1²- 4×1×-4))/2

  = ( -1 ± √(17)/2

  = (-1 ± 4.12)/2

  = (-1 + 4.12)/2 or (-1 - 4.12)/2

  x = 1.56  or x = -2.56

To rewrite f(x) = x^2 - 6x - 60 by completing the square, you add and subtract (6/2)^2 within the equation and refactor to get f(x) = (x - 3)^2 - 69, with the vertex at (3, -69).

To rewrite the function f(x) = x^2 - 6x - 60 by completing the square, follow these steps:

The function is now in the completed square form. The vertex of this parabola is at (3, -69).

Answer:

Simplifies to:

748.245949x

Answer:

x       y

15     -1

12     0

9       1

6       2

3       3

0       4

Step-by-step explanation:

This is a function table. For a linear function, find the average rate of change between the listed points called slope. Then use the slope to fill in other inputs and outputs for the function.

[tex]m = \frac{y_2-y_1}{x_2-x_1}=\frac{4-0}{0-12} =\frac{4}{-12} =- \frac{1}{3}[/tex]

This means for every 3 units made in the input, the function moves down 1 output.

x       y

15     -1

12     0

9       1

6       2

3       3

0       4

Answer:

i did this question b4 but completely forgot the answer ://

Step-by-step explanation:

Answer:

I think they are all correct but 2 and 4 might be wrong. (I don't see the shapes very well.)

I can't see that well but on #2, can't you half it? If you can, it has 1 line of Symmetry. If you can't, it has no lines of symmetry  

On #4, you might be able to half it from the lower left corner and the upper right corner. If it works, there is 1 line of symmetry, if it doesn't it has none

Answer:

12.5

Step-by-step explanation:

25/200

Answer:

50

Step-by-step explanation:

0.25 x 200 = 50

Mode: the number that occurs the most in a set of data.

Although it's optional, I always like to order the numbers from least to greatest so it makes it easier to see what number repeats more than anything else.

Least to greatest - 40,41,42,43,44,45,46,47,48,49,49

The mode for this set of data is 49. The mode is 49 because 49 is the only number that occurs more than once. No other numbers in this set of data appear twice except 41.

it went to the right 4 units and up 2 units

Answer:

[tex]\large\boxed{\dfrac{7-x}{x-7}=-1}[/tex]

Step-by-step explanation:

[tex]\dfrac{7-x}{x-7}=\dfrac{-(x-7)}{x-7}\\\\\text{cancel}\ (x-t)\\\\\dfrac{7-x}{x-7}=\dfrac{-1}{1}\\\\\dfrac{7-x}{x-7}=-1[/tex]

Answer:

-1

Step-By Step:

The Answer on Ed