A family of two adults and three children went to a water park. Admission to the water park costs $18 per person. Nora used the expression 2 (18) + 3 (18) to model the total cost for the family, and Alex used the expression 5 (18). Which property of operations makes both of their expressions correct?
associative property
commutative property
distributive property
identity property

a. 2 hours = 100 to 120m

3 hrs = 150 to 180m

4 hrs = 200 to 240m

5 hrs = 250 to 300m

b. 400 to 480 miles

Bobby can drive between 50 times the number of hours and 60 times the number of hours depending on the drive duration. For an 8-hour trip with a 1-hour lunch stop, he drives for 7 hours, covering between 350 and 420 miles.

a) Bobby's driving speed varies between 50 to 60 miles per hour. Therefore:

b) For an 8-hour trip with a 1-hour stop for lunch, Bobby will effectively be driving for 7 hours. So, the minimum distance he could cover is 50*7=350 miles and the maximum distance is 60*7=420 miles.

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Im not sure it depends on the pattern? lol

The pattern described in the table is the value of b is 5 times the value of a.

A pattern is defined as a sequence of repeating objects, shapes or numbers. We can relate a pattern to any type of event or object. A pattern has a rule that tells us which objects belong to the pattern and which objects do not belong to the pattern.

Given is a table,

a - 0 1 2 3 4

b - 0 5 10 15 20,

We can see, that the values in the b row are 5, 10, 15, 20 they are the multiple of 5

And values in row a, are 1, 2, 3, 4, we can see they are the numbers which are related to row b, in a way that, values in b are 5 times the value of a,

1 × 5 = 5

2 × 5 = 10

3 × 5 = 15

4 × 5 = 20

5 × 5 = 25

Therefore, we can say that the numbers in b are 5 times the corresponding value of the a,

Hence, the pattern described in the table is the value of b is 5 times the value of a.

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The complete question is :

Which rule describes the pattern in the table?

a 0 1 2 3 4

b 0 5 10 15 20

The value of b is 5 times the value of a.

The value of b is 5 less than the value of a.

The value of b is 5 more than the value of a.

The value of a is 5 times the value of b.

Answer:

P: (3,0)

Step-by-step explanation:

AB = (9,3)

⅔(9,3) = (6,2)

(-3,-2) + (6,2) = (3,0)

the coordinates of the point P on directed line segment AB that partitions AB in the ratio 2:1 is (3,0).

P=(mx2​+nx1/m+n​​,my2​+ny1/m+n​​).

The formula can be derived by constructing two similar right triangles, as shown below. Their hypotenuses are along the line segment and are in the ratio m : n m:n m:n.

Here, given that,

Given the point A(-3,-2) and B(6, 1),

Let, (x.y) is the coordinates of the point P on directed line segment AB that partitions AB in the ratio 2:1.

Using the formula we get,

(x,y) = (nx1 + mx2)/(m + n) , (ny1 + my2)/(m + n)

P=(3,0)

hence, the coordinates of the point P on directed line segment AB that partitions AB in the ratio 2:1 is (3,0).

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Final answer:

In logic and truth tables, shifting one line correctly while the other is shifted incorrectly will result in credit for the correctly shifted line.

Explanation:

True or False: If you shift one of the lines incorrectly and the other correctly, you will receive credit for the correctly shifted line. True

The statement is true in the context of logic and truth tables. When dealing with truth tables and logical operations, if one line is shifted correctly and the other incorrectly, credit is given for the line that was correctly shifted.

Answer:

11/30

Step-by-step explanation:

P(B/A) = P(B^A)/P(A)

P(A) = 30/36 = 5/6

P(B^A) = (2+5+4)/36 = 11/36

11/36 ÷ 30/36

11/30 or 0.3667

Answer:

8n-6 = 34

Step-by-step explanation:

6 less than the product of 8 and a  number n is 34

less than means subtract from the next thing

 -6

product means multiply

8n

Now we have 8n-6

is means equals

8n-6 = 34

the value of n is 5.

Step-by-step explanation:

Given,

6 less than the product of 8 and a  number n is 34

To find the value of n

According to the problem,

n×8 - 6 = 34

or, 8n = 34+6

or, 8n = 40

or, n = 40÷8

or, n= 5

Hence, the value of n is 5.

Answer:

128 students in total

Step-by-step explanation:

25/100 = 1/4

1/4 = 32/ x

1 x 32

Answer:

your answer is A

Step-by-step explanation:

32 *4=128

4*25=100%

Final answer:

The exponential function that goes through the points (0,6) and (2,96) is y = 6 * 4^x, where 6 is the initial value (a) and 4 is the base growth rate (b).

Explanation:

The student is asking for an exponential function in the form y = ab^x that passes through the points (0,6) and (2,96).

To find this function, we must determine the values of 'a' and 'b'. Since the function passes through the point (0,6), if we substitute x = 0, we get y = a * b^0. Since any number raised to the power of 0 is 1, it simplifies to y = a. Therefore, a = 6.

Next, we substitute the second point (2,96) into the original equation with our known value for 'a': 96 = 6 * b^2. To solve for 'b', we divide both sides of the equation by 6, resulting in 16 = b^2. Finding the positive square root of 16 gives us b = 4.

Therefore, the exponential function is y = 6 * 4^x.

The exponential function that goes through the points [tex]\((0, 6)\)[/tex] and [tex]\((2, 96)\)[/tex] is [tex]y = 6 \times 4^x[/tex]

To find the exponential function in the form [tex]\( y = ab^x \)[/tex] that goes through the points [tex]\((0, 6)\)[/tex] and [tex]\((2, 96)\)[/tex], we need to determine the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex].

1. Use the point [tex]\((0, 6)\)[/tex]

When [tex]\( x = 0 \), \( y = 6 \).[/tex]

[tex]\[6 = ab^0\][/tex]

Since [tex]\( b^0 = 1 \)[/tex]

[tex]\[6 = a \times 1\][/tex]

Therefore, [tex]\( a = 6 \).[/tex]

2. Use the point [tex]\((2, 96)\)[/tex]

When [tex]\( x = 2 \), \( y = 96 \)[/tex]

[tex]\[96 = 6b^2\][/tex]

Solving for [tex]\( b^2 \)[/tex]

[tex]\[b^2 = \frac{96}{6} = 16\][/tex]

Taking the square root of both sides:

[tex]\[b = 4\][/tex]

Thus, the exponential function is:

[tex]\[y = 6 \times 4^x\][/tex]

To verify, we can check both points:

For [tex]\((0, 6)\)[/tex]

[tex]\[y = 6 \times 4^0 = 6 \times 1 = 6\][/tex]

For [tex]\((2, 96)\)[/tex]

[tex]\[y = 6 \times 4^2 = 6 \times 16 = 96\][/tex]

Answer:

1+4x

Step-by-step explanation:

Answer:

it is when the x and y intercept coordinates are changed by the same factor.

Step-by-step explanation:

Answer:

There is no solution

Step-by-step explanation:

1. y = 3/4x - 5

2. -3x + 4y = -20

-3x + 4(3/4x - 5) = -20

-3x + 3x - 20 = - 20

-20 = -20

Answer:

126

Step-by-step explanation:

The coefficient of 9(14)P = 9*14 = 126

Answer:

[tex]b) 5 (x-3)\\c) 4 x + 3 y-15- 3 y + x\\e) -20 - 3 x + 5 + 8 x[/tex]

Step-by-step explanation:

We are given the following expression in the question:

[tex]5x-15[/tex]

a)

[tex]5 (x + 15)\\=5(x) + 5(15)\\=5x + 75[/tex]

which is not equivalent to the given expression.

b)

[tex]5 (x-3)\\=5(x)-3(5)\\=5x-15[/tex]

which is equivalent to the given expression

c)

[tex]4 x + 3 y-15- 3 y + x\\=4x+x+3y-3y-15\\=5x-15\\=5(x-3)[/tex]

which is equivalent to the given expression.

d)

[tex]-7 y-6 x- 8 y + x\\=-7y-8y-6x+x\\=-15y-5x\\=-5(x+3y)[/tex]

which is not equivalent to the given expression.

e)

[tex]-20 - 3 x + 5 + 8 x\\=-3x+8x-20+5\\=5x-15[/tex]

which is equivalent to the given expression.

Answer:

219071376

Step-by-step explanation:

Answer:

219071376. Hope this helps :)

Answer:

-3 < x

Step-by-step explanation:

add the negative 3 to the other side

you get: -15 < 5x

divide by 5 on both sides

you get: -3 < x

that's the answer

Answer:

Most students spent an hour or less studying for the exam.

Step-by-step explanation:

Answer:

C on edge 2020

Most students spent an hour or less studying for the exam.

Step-by-step explanation:

I just took the assignment. Hope this helps!

Answer:

$62 per day

Step-by-step explanation:

$62 a day equals $434 a week witch turns out to be $22,568 a year

$304 a week equals $15,808 a year

Answer:

1.9 kg

Step-by-step explanation:

Empty container: 3/10 kg = 0.3 kg

Container half filled: 1 1/10 kg = 1.1 kg

Mass of water that fills it halfway: 1.1 kg - 0.3 kg = 0.8 kg

Mass of water that fills it completely: 2 * 0.8 kg = 1.6 kg

Mass of container completely filled with water: 0.3 kg + 1.6 kg = 1.9 kg

Answer:

Step-by-step explanation:

332 323 233

Answer:

233, 323, 332.

Step-by-step explanation:

Starting from 200 and count by 10 (200, 210, 220, 230.) 233 is the smallest number, repeat with each number.

Answer:

4x + 5y = 80

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 5x - 4y = 10 into this form

Subtract 5x from both sides

- 4y = - 5x + 10 ( divide all terms by - 4 )

y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{5}{2}[/tex] ← in slope- intercept form

with slope m = [tex]\frac{5}{4}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex]  = - [tex]\frac{1}{\frac{5}{4} }[/tex] = - [tex]\frac{4}{5}[/tex], thus

y = - [tex]\frac{4}{5}[/tex] x + c ← is the partial equation

To find c substitute (5, 12) into the partial equation

12 = - 4 + c ⇒ c = 12 + 4 = 16

y = - [tex]\frac{4}{5}[/tex] x + 16 ← in slope- intercept form

Multiply through by 5

5y = - 4x + 80 ( add 4x to both sides )

4x + 5y = 80 ← in standard form

The equation of line perpendicular to [tex]5x-4y=10[/tex] and passing through the point (5,12) is [tex]y=-\frac{4}{5}+16[/tex]

The line given in the problem is in Standard Form. The standard form of a linear equation is: [tex]Ax+By=C[/tex]

Where, if at all possible, A, B, and C are integers, and A is non-negative, and, A, B, and C have no common factors other than 1.

[tex]5x-4y=10[/tex]

The slope of an equation in standard form is: [tex]m=-\frac{A}{B}[/tex]. Substituting the values from the equation in the problem gives:

[tex]m=-\frac{5}{(-4)} =\frac{5}{4}[/tex]

Let's call the slope of the line perpendicular to this line [tex]m_{p}[/tex] . The slope of a perpendicular line is:

[tex]m_{p} =-\frac{1}{m} =-\frac{4}{5}[/tex]

We can now use the point-slope formula to find the equation of the line. The point-slope formula states: [tex](y-y_{1})=m(x-x_{1})[/tex]

[tex]y-12=-\frac{4}{5} (x-5)[/tex]

[tex]5(y-12)=-4(x-5)\\5y-60=-4x+20\\5y=-4x+80\\y=-\frac{4}{5}x+16[/tex]

Therefore, the equation of line perpendicular to [tex]5x-4y=10[/tex] and passing through the point (5,12) is [tex]y=-\frac{4}{5}+16[/tex]

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Answer:

k=1

Step-by-step explanation:

1. find the negative reciprocal of the slope of y=2x-5 because that is the slope perpendicular to it.

m=2 ; negative reciprocal is 1/-2

2. isolate y in the first equation

y= kx/-2 + 7/-2

3. the only value for k that would make their slopes the same would be 1

Answer:

[tex] - 7 {x}^{2} - 24 - 9 \\ - 7 {x}^{2} - 21x - 3x - 9 \\ - 7x(x + 3) - 3(x + 3) \\ ( - 7x - 3)(x + 3)[/tex]

Product is 10x² - 2x - y + 5xy

Step-by-step explanation:

(2x + y)(5x - 4 + 3) = 10x² - 8x + 6x + 5xy - 4y + 3y

                              = 10x² - 2x - y + 5xy

Hope this will help u..✌✌

The equation of the given circle is [tex](x-6)^{2}+(y+9)^{2}=100.[/tex]

Step-by-step explanation:

Step 1:

The equation of a circle with its center at (h, k) and a radius of r is given by

[tex](x-h)^{2}+(y-k)^{2}=r^{2}.[/tex]

The h value is the x coordinate and the k value is the y coordinates, so (h, k) is (6, -9).

The radius is given as 10 so [tex]r =10[/tex] and [tex]r^{2} = 100.[/tex]

Step 2:

By substituting the values we know, we get

[tex](x-h)^{2}+(y-k)^{2}=r^{2} = (x-6)^{2}+(y-(-9))^{2}=10^{2}.[/tex]

So the equation of the given circle is

[tex](x-6)^{2}+(y+9)^{2}=100.[/tex]

Answer:

2080

Step-by-step explanation:

Step 1:  Multiply

65 × 32

60*30 + 60*2 + 5*30 + 5*2

1800 + 120 + 150 + 10

2080

Answer:  2080

Answer:

2080

Step-by-step explanation:

Answer:

The first picture will have a solution a (3,4)

The second will have no solutions

The third picture will have a solution at (-4,-3)

Step-by-step explanation:

The solution is when the lines intersect you can tell in the first and third picture when they will and the second picture has parrell lines meaning they will never intersect

Answer: y=-2x+5

Step-by-step explanation:

Y+2x=5

y-2x=5-2x

y=-2x+5

then graph

Answer:

y=-2 x +5

Step-by-step explanation:

Write in slope-intercept form,  y=m x+b

Answer:

49

Step-by-step explanation:

88+(-39) is the same as 88-39 given the distributive property, so 88-39=49