Car A and car B are traveling opposite directions st the same speed. Car A drove for 17 minutes and car B drove for 32 minutes. Car B drove 12 miles more than car A. How fast were the cars driving?

Answer:

b < –2 or b > 2

Step-by-step explanation:

The given expresion is

[tex] |b| \: > \: 2[/tex]

By the definition of absolute value function.

|x|=x, if x>0

|x|=-x, if x<0

This implies that:

[tex] b \: > \: 2 \: or \: - b \: > \: 2[/tex]

Divide the second inequality by -2 and reverse the sign

[tex]b \: > \: 2 \: or \: b \: < \: - 2[/tex]

Option B is correct

The expression |b| > 2 is equivalent to b < -2 or b > 2, indicating that the value of b is either greater than 2 or less than -2.

The expression |b| > 2 is equivalent to the situation where b is greater than 2 or less than -2. The absolute value sign indicates the distance of b from 0 on a number line, without considering direction. Therefore, if |b| is greater than 2, b must lie outside the interval from -2 to 2, since anything within that interval would have an absolute value less than or equal to 2.

This means that the correct expression equivalent to |b| > 2 is b < -2 or b > 2. When b is positive, it must be greater than 2 to satisfy the inequality. When b is negative, to have an absolute value greater than 2, it must be less than -2.

1.  15t + 8t - 2t = 16

  t = 0.76

2.  24m + 24m = 96

   m = 2

3.  26 = 12n + 2n

   n = 1.86

4.  20a - 3a = 34

   a = 2

5.  170x + 4 = 64

   x = 0.35

6.  15x - 25 = 200

   x = 15

7.  5s + 3s = 42

   s = 5.25

8.  10t + 2t = 28

   t = 2.333333

9.  14s + 35s - 7s = 42

   s = 1

10.  124s - 14s + 12s = 12

   s = 0.1

Hope this helps, sorry I couldn't get to all of it.   :)

Answer:

Step-by-step explanation:

23.02 plus an additional 0.19 for each text.....x = # of texts

$ 0.19x + 23.02 = 27.77 is ur equation

Answer: B

Step-by-step explanation: i got it wrong trust me

The interior angles of each regular polygon are 60 degree, 90 degree and 108 degree respectively.

To solve the given problem, it is necessary to know about the polygon. A polygon is a closed curve that consist a set of line segments connected together, such that there is a no intersection between the segments.

For example: -

The formula for the interior angle of a regular polygon is given by,

[tex]= \dfrac{ (n-2) \times 180}{n}[/tex]

Here, n is the number of sides.

Then the calculation is given as,

For triangle ( n = 3 sides ),

[tex]= \dfrac{ (n-2) \times 180}{n}\\\\= \dfrac{ (3-2) \times 180}{3}\\\\=60 \;\rm degrees[/tex]

For square ( n = 4 sides ),

[tex]= \dfrac{ (n-2) \times 180}{n}\\\\= \dfrac{ (4-2) \times 180}{4}\\\\=90 \;\rm degrees[/tex]

For pentagon ( n = 5 sides ),

[tex]= \dfrac{ (n-2) \times 180}{n}\\\\= \dfrac{ (5-2) \times 180}{5}\\\\=108 \;\rm degrees[/tex]

Thus, we can conclude that the interior angles of each regular polygon are 60 degree, 90 degree and 108 degree respectively.

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The interior angles of each regular polygon are 60 degree, 90 degree and 108 degree respectively.

We have to determine, The measure of one interior angle in each regular polygon.

A polygon is a closed curve that consist a set of line segments connected together, such that there is a no intersection between the segments.

A regular polygon refers to a multi-sided convex figure where all the sides are equal in length and all the angles have equal degree measures.

The formula for the interior angle of a regular polygon is given by,

[tex]= \frac{(n-2)\times180}{n}[/tex]

Where, n is number of sides.

The triangle is a polygon that  has 3 interior angles.

The square is a polygon that has 4 interior angles.

The pentagon is a polygon that has 5 interior angles.

For triangle ( n = 3 sides ),

[tex]= \frac{(3-2)\times 180}{3} \\\\= \frac{180}{3} \\\\= 60degree[/tex]

For square ( n = 4 sides ),

[tex]= \frac{(4-2)\times 180}{4} \\\\= \frac{360}{4} \\\\= 90degree[/tex]

For pentagon ( n = 5 sides ),

[tex]= \frac{(5-2)\times 180}{5} \\\\= \frac{540}{5} \\\\= 108degree[/tex]

Hence, The interior angles of each regular polygon are 60 degree, 90 degree and 108 degree respectively.

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Answer:

  (4.5, 6)

Step-by-step explanation:

The distance covered is proportional to the rate, so the distance from A to C compared to the distance from B to C will have the same proportion as Phillip's and Bruce's rates.

__

  (C -A)/(B -C) = 7/5 . . . . . distance is proportional to rates

  5(C -A) = 7(B -C) . . . . multiply by 5(B -C)

  12C = 7B +5A . . . . . add 7C+5A

  C = (7B +5A)/12 = (7(7, 6) +5(1, 6))/12 = (49+5, 42+30)/12 = (4.5, 6)

Phillip and Bruce will meet at C(4.5, 6).

Answer:

he is right but the answer is (4,6) not (4.5,6)

Step-by-step explanation:

Answer:

3/10, 2/5, 1/3, 2/4

Step-by-step explanation:

the greater the denominator the lower the portion will be depending on the numerator

Answer: period=4

Step-by-step explanation: a=1,b=π/2, c=0

to calculate the period of the function,we use 2π/b

therefore,period=2π/π/2

2π×2/π=4.

Answer:

The output values of a relation are called the Range of the relation

Step-by-step explanation:

we know that

For a set of ordered pairs, the first elements of each ordered pair is called the input value or independent variable and represents the domain of the function and second elements of each ordered pair is called the output value or dependent variable and represents the range of the function.

therefore

The output values of a relation are called the Range of the relation

Answer:

16x^5

Step-by-step explanation:

use photomath it will help u with math problems if u need it.

The length of swimming course is 345.93 meters.

Step-by-step explanation:

Given,

BC = 80 m

AB = 145 m

Using pythagoras theorem to find AC.

[tex]AC^2+BC^2=AB^2\\AC^2+(80)^2=(145)^2\\AC^2+6400=21025\\AC^2=21025-6400\\AC^2=14625[/tex]

Taking square root on both sides

[tex]\sqrt{AC^2}=\sqrt{14625}\\AC=120.93m[/tex]

Length of swimming course = AB + BC + AC

Length of swimming course = 145 + 80 + 120.93 = 345.93 m

The length of swimming course is 345.93 meters.

Keywords: square root, addition

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Answer:

21.819 is the difference

The answer is 21.819

✍️(◔◡◔) hope this helps

Answer:

[tex]m=55h[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Let

m ----> the distance in miles (y-coordinate)

h ----> the time in hours (x-coordinate)

In this problem the constant of proportionality k is given and is equal to

[tex]k=55\ \frac{miles}{hour}[/tex] ----> the speed

substitute

[tex]m=55h[/tex]

Final answer:

To determine the cost of each bottle in a $3.48 six pack of soda, divide the total cost by the number of bottles, which results in each bottle costing $0.58.

Explanation:

To find out how much each bottle of soda costs when a six pack of soda costs $3.48, we need to divide the total cost by the number of bottles in a pack. Since there are six bottles in a six pack, we take the total cost of $3.48 and divide it by 6.

The calculation will look like this:

Cost per bottle = Total cost of six pack ÷ Number of bottles

Cost per bottle = $3.48 ÷ 6

Cost per bottle = $0.58

Therefore, each bottle of soda costs $0.58.

Answer:

check the photo below for the answer.

Sigma notation is used to represent series of numbers. To find the sum of the first six terms of the sequence 4, 12, 20, ..., you can use the formula Σ(4 + 8(n - 1)).

Sigma notation is a way to represent a series of numbers. In this specific case, we want to find the sum of the first six terms of the sequence 4, 12, 20, ... The sum can be represented as Σ(4 + 8(n - 1)), where n goes from 1 to 6.

Answer: 49/4

Step-by-step explanation:

3 + 1/2 = (3x2 + 1)/2 = 7/2

(7/2)² = 7²/2² = 49/4

Answer:

y-coordinate

Step-by-step explanation:

Answer:

y coordinate

Step-by-step explanation:

It takes 6 days for both of them to have same number of followers

Solution:

Let "x" be the number of days

Celebrity A has 400 followers on social media and is gaining 75 followers each day

We can frame a equation as:

Celebrity A : 400 + 75(number of days)

Celebrity A : 400 + 75x --------- eqn 1

Celebrity B has 1,000 followers on social media, but is losing 25 followers a day

We can frame a equation as:

Celebrity B : 1000 - 25(number of days)

Here we use negative sign to denote losing of followers

Celebrity B : 1000 - 25x --------- eqn 2

For both of them to have same number of followers, eqn 1 must be equal to eqn 2

[tex]400 + 75x = 1000 - 25x\\\\\text{Solve the above equation for x}\\\\75x + 25x = 1000 - 400\\\\\text{Combine the like terms }\\\\100x = 600\\\\x = 6[/tex]

Thus it takes 6 days for both of them to have same number of followers

Answer:

The 60th customer will get both a free coke and a free popcorn.

Step-by-step explanation:

i) every 10 customer gets a free coke

ii) every 12 customer gets a free popcorn

iii) therefore the first customer who will get both a free coke and a free popcorn will be given by the Lowest Common Multiple of 10 and 12 which is 60, as 10 goes in to 60 by 6 times and 12 goes into 60 by 5 times.

Answer:

The 60th customer will get both a free coke and a free popcorn.

Step-by-step explanation:

Answer:

The equation that represents the volume of a cone with the same base and height as the cylinder is [tex]\frac{1}{3}\pi t^2k[/tex]

Step-by-step explanation:

Given:

The height of the cylinder = k

The  Radius of the cylinder = t

To Find:

Equation representing the volume the cone = ?

Solution:

We know that the volume of the cone is

=> [tex]\frac{1}{3}\pi r^2 h[/tex]

where

r is the radius of the  cone

h is the height of the cone

Here the radius of the cone  =  radius of the cylinder = t

and height of the cone   = height oft the cylinder = k

then

the volume of the cone  will be

=>[tex]\frac{1}{3}\pi t^2k[/tex]

Answer:

its b

Step-by-step explanation:

i took the test

Answer:

see below

Step-by-step explanation:

y=kx

15=1.50(10)

1.50 is the cost of every coffe

10 is the amount of coffes u can get with the 15 dollars

15 is the total money u have

(hopes this helps)

Answer:

y= -1.5x+15

Step-by-step explanation:

y=mx+b

This is the formula to find the equation. M is the slope (rise over run), and b is the y-intercept. Hope this helps.

Answer:

y = 5x - 17

Step-by-step explanation:

y = mx + c

m = the gradient/slope = 5

y = 5x + c

Substitute (3, -2) into the equation above to find c.

-2 = 5(3) + c

-2 = 15 + c

-2 - 15 = c

-17 = c

y = 5x - 17

Answer:

Step-by-step explanation:

point(3, -2) and has a slope of 5

Slope m = 5

y1 = -2 and x1 = 3

The equation is

y - y1 = m(x - x1)

y + 2 = 5(x - 3)

y + 2 = 5x - 15

y = 5x - 15 - 2

y = 5x - 17

Answer:

Thymine 23

Guanine 27

Step-by-step explanation:

A DNA molecule consists of two long chains of DNA connected to each other through the bonds nitrogenous bases make one with another. However, this bonding is strictly regulated through Chargaff's rule. It basically says that adenine from one DNA chain can only bond with thymine from another chain and vice versa. Additionally, cytosine from one chain only bonds with guanine from another and vice versa:

[A] = [T]

[G] = [C]

That means that there should be an equal number of corresponding bases.

If there were 23% of adenine, there will also be 23% of thymine.

Similarly, if there were 27% of cytosine, there will also be 27% of guanine.

Also note that the sum of non-bonding bases is always 50%, in this case, adenine + cytosine was 23% + 27% = 50%.

The Answer is: Thymine 23

Then Guanine 27

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Final answer:

The missing fraction in the equation 9/10 + ?/? = 99/100 is 9/100 because 9/10 is equivalent to 90/100 and 99/100 - 90/100 equals 9/100.

Explanation:

To find the missing fraction in the equation 9/10 + ?/? = 99/100, we need to find a common denominator and then solve for the numerator of the missing fraction. The common denominator for 10 and 100 is 100, so we must convert 9/10 into an equivalent fraction with a denominator of 100, which is 90/100. Now, to find the missing numerator, we subtract 90/100 from 99/100 which gives us 9/100. Therefore, the missing fraction is 9/100.

Answer:

26

Step-by-step explanation:

Range = highest number minus lowest number.

99-73=26.

Answer:

26

Step-by-step explanation:

Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is 99−73=26.

Answer:

Option C) There is exactly one solution to this equation, and the solution is 0 is correct

That is the solution x=0

Step-by-step explanation:

Given equation is -4(x+2)+x=3x-8-5x

To find the solution to the given equation :

First to solve the given equation

-4(x+2)+x=3x-8-5x

-4x-8+x=3x-8-5x ( by using the distributive property )

-3x-8=-2x-8 ( adding the like terms )

-3x-8-(-2x-8)=-2x-8-(-2x-8)

-3x-8+2x+8=-2x-8+2x+8  ( adding the like terms )

-x=0

Therefore x=0 is the only solution to the given equation

Option C) There is exactly one solution to this equation, and the solution is 0 is correct

That is the solution x=0

After simplifying and solving the given equation, it is clear that the single solution is x = 0, which corresponds to option C.

To identify the correct statement describing the solution to the given equation, we need to solve the equation step by step:

-4[x+2]+x = 3x - 8 - 5x.

First, distribute the -4 across the terms inside the brackets:

-4x - 8 + x = 3x - 8 - 5x.

Combine like terms:

-3x - 8 = -2x - 8.

Then add 3x to both sides:

-8 = x - 8.

Finally, add 8 to both sides to solve for x:

x = 0.

The equation simplifies to x = 0, which means there is a single solution to this equation. Therefore, the correct option is: C. There is exactly one solution to this equation, and the solution is 0.

Answer:

C 14,400

Step-by-step explanation:

If a bird is chirping 10 times a min, and there are 60 min in a day you would multiply those numbers. 10×60=600.

There are 24 hours in a day so multiply 600 with that and you have ur answer. 24×600=14400. Also sorry this is probably old.

A bird chirps 14,400 times in a day.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A bird chirps 10 times a minute.

Now,

Since, A bird chirps 10 times a minute.

We know that;

1 day = 24 hours

        = 24 × 60 minutes

        = 1,440 minutes

Hence, We get;

A bird chirps in a day = 10 × 1,440

                                 = 14,400 times

Thus, A bird chirps 14,400 times in a day.

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Answer: y = -2x + 10

Step-by-step explanation:

Two lines are said to be perpendicular if the product of their slope = -1, that is , if [tex]m_{1}[/tex] is the slope of the first line and [tex]m_{2}[/tex] is the slope of the second line , if the two lines are perpendicular , then [tex]m_{1}[/tex][tex]m_{2}[/tex] = -1

The equation of the line given :

y = 1/2x - 1

comparing with the equation of line in slope intercept form

y = mx + c , where m is the slope and c is the y - intercept , it implies that

[tex]m_{1}[/tex] = 1/2

Therefore :

[tex]m_{2}[/tex] = -2

To find the equation of the line with slope -2  and passes through the point ( 3 , 4 ) we will use the formula

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

y - 4 = -2 ( x - 3 )

y - 4 = -2x + 6

y = -2x + 6 + 4

y = -2x + 10

Answer: OPTION C.

Step-by-step explanation:

In order to solve the given exercise, you can follow these steps:

1. Given the following function f(x):

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

You must substitute [tex]x=2[/tex] into the function f(x). Then:

[tex]f(2)=\frac{(2)-2}{3}[/tex]

2. Evaluating, you get:

[tex]f(2)=\frac{0}{3}\\\\f(2)=0[/tex]

3. Now, the next step is to substitute [tex]f(2)[/tex]  into the function g(x):

[tex]g (x) = 3x+2\\\\g (f(2)) = 3(0)+2[/tex]

4. Finally, evaluating, you get the following result:

[tex]g (f(2)) = 0+2\\\\g (f(2)) =2[/tex]

You can identify that it matches with the Option C.

To find the value of g(f(2)), we first calculate f(2) which equals 0, then we substitute that into g(x) to get g(0) which equals 2. Therefore, g(f(2)) is 2.

The question asks for the value of g(f(2)) given two functions g(x) = 3x + 2 and f(x) = (x - 2) / 3. To find the value, we first evaluate f(2), and then plug that result into g(x).

The answer to the given function composition g(f(2)) is 2, which corresponds to option C.

Division property of equality is used

Solution:

Given that,

If 3x = 27 then x = 9

We have to find the algebraic property used here

Division property is used here

The division property of equality is a property that tells us if we divide one side of an equation by a number, we must also divide the other side by the same number so that our equation stays the same.

Given equation is:

3x = 27

Divide both the sides by 3

[tex]\frac{3x}{3} = \frac{27}{3}\\\\x = 9[/tex]

Thus division property of equality is used

The algebraic property used in changing 3x = 27, to x = 9 is the Division Property of Equality. This property means that if both sides of an equal equation are divided by the same nonzero number, then the resulting equation remains true.

The algebraic property that applies when rearranging the equation 3x = 27, to x = 9 is known as the Division Property of Equality. This property states that when both sides of an equation are divided by the same nonzero number, the result is an equivalent equation.

To demonstrate this, in the given equation 3x = 27 we can apply the Division Property of Equality by dividing both sides of the equation by 3. This will give: 3x/3 = 27/3 which simplifies to x = 9, thus demonstrating the division property of equality.

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