The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 53 minutes of calls is $12.03 and the monthly cost for 65 minutes is $13.59. What is the monthly cost for 57 minutes of calls?

According to the solving the value of the Quadratic equation are as follows:

x = 0

x = 2

We can answer any quadratic equation using the quadratic formula. The first step is to change the equation's form to ax2+bx+c=0, where a, b, but instead c are the coefficients. The formula (-b(b2-4ac))/(2a) is then used to enter these coefficients. View instances of the formula being used to solve various equations.

Make a video of the pupils utilizing one technique to solve a quadratic equation. Allowing pupils to pick is an option, but you can also direct them to utilize the quadratic equation, factoring, or square-rooting.

f(x) = 2x² – 3x

x- (2x² – 3x) = 0

x - 2x² + 3x = 0

4x - 2x²= 0

x = 0

x = 2

According to the solving the value of the Quadratic equation are as follows:

x = 0

x = 2

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Answer:

okkokokokokokoookkijoiig

The image of R after a reflection over the x-axis is the point S(-2, -1).

To reflect a point over the x-axis, we simply negate its y-coordinate while keeping its x-coordinate the same.

Starting with point R(-2, 1):

The x-coordinate remains the same: -2

The y-coordinate is negated: -1

So the image of R after a reflection over the x-axis is the point S(-2, -1).

To graph the reflection, we can plot the original point R and then draw a dashed line to represent the x-axis. Finally, we can plot the reflected point S on the other side of the x-axis.

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A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

The midpoint of MN is (7,1)

Add the x coordinates 7+7=14 then you divide that by 2 giving you 7.

Then you add the y coordinates together 6+(-4)=2 then divide by 2 and that gives you 1. Therefore the answer is (7,1)

Answer:

The mean and standard deviation of the corrected pH measurements are 6.63 and 3.8025 respectively.

Step-by-step explanation:

We can correct the values of the mean and standard deviation using the properties of the mean and the variance.

To the original value X we have to add 0.2 and multiply then by 1.3 to calculate the new and corrected value Y:

\(Y=1.3(X+0.2)\)

The mean and standard deviation of the original value X are 4.9 and 1.5 respectively.

Then, we can apply the properties of the mean as:

\(E(Y)=E(1.3(X+0.2))=1.3E(X+0.2)=1.3E(X)+1.3*0.2\\\\E(Y)=1.3E(X)+0.26\\\\E(Y)=1.3*4.9+0.26=6.37+0.26=6.63\)

For the standard deviation, we apply the properties of variance:

\(V(Y)=V(1.3(X+0.2))\\\\V(Y)=1.3^2\cdot V(X+0.2)\\\\V(Y)=1.69\cdot V(X)\\\\V(Y)=1.69\cdot 1.5^2=1.69\cdot 2.25=3.8025\)

The properties that have been applied are:

\(1.\,E(aX)=aE(X)\\\\ 2.\,E(X+b)=E(X)+b\\\\3.\,V(aX)=a^2V(X)\\\\4.\,V(X+b)=V(X)+0\)

Growth Rate: According to the problem the bob will be approximately 6'3 when he is 19.

Growth rate is the rate at which a company’s revenue expands over time. It is typically measured by comparing the company’s current revenue to its previous revenue. Growth rate can be calculated using the formula (Current Revenue – Previous Revenue)/Previous Revenue. It can be used to gauge the success of a company’s sales or marketing efforts. Companies with higher growth rates are usually seen as more successful and attractive investments.

This is because his growth rate of 1 1/2 every 2 years is equivalent to 3/4 inch per year.
So we can calculate his height at 19 by multiplying 3/4 by 19, which is 14 1/4.
Adding this to his original height of 2'3 gives us a total of 6'3.

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Step-by-step explanation:

the answer is the image above

Answer:

x=3  and x=7

Step-by-step explanation:

x2 - 10x + 21=0

a=1, B=-10, c=21

delta= b2 - 4(ac)

if delta >0 => have two answer

x1= -b - _/delta / 2a = -(-10) - _/16 / 2.1 = 3

x2= -b + _/delta /2a = -(-10) + _/16 / 2.1= 7

Answer:

Diana finshed playing volleyball at 8am

Step-by-step explanation:

So we know she started at 5:35 AM

And she hiked for an hour and 30 minutes

so 5:35+1 hour is 6:35

and 6:35+35 is 7:05

So before playing volley ball, the time is 7:05 am

Now volley ball was 55 minutes

so 7:05+55 is 8

So 8am

Answer:

She finish playing valleyball at 8:00 am

Step-by-step explanation:

Hike at 5:30 => 1h 30 min => 7:05

valleyball at 7:05 => 55 min => 8:00

To express the function \(\displaystyle\sf h(x) = (x+4)^{3}\) in the form \(\displaystyle\sf f(g(x))\), where \(\displaystyle\sf f(x) = x^{3}\) and \(\displaystyle\sf g(x)\) is the inner function, we need to determine \(\displaystyle\sf g(x)\).

Notice that \(\displaystyle\sf h(x)\) is the cube of \(\displaystyle\sf (x+4)\). This suggests that \(\displaystyle\sf g(x)\) is equal to \(\displaystyle\sf x+4\).

So, \(\displaystyle\sf g(x) = x+4\).

Now, to express \(\displaystyle\sf h(x)\) as \(\displaystyle\sf f(g(x))\), we substitute \(\displaystyle\sf g(x) = x+4\) into \(\displaystyle\sf f(x) = x^{3}\):

\(\displaystyle\sf h(x) = f(g(x)) = f(x+4) = (x+4)^{3}\).

Therefore, \(\displaystyle\sf h(x)\) can be expressed as \(\displaystyle\sf f(g(x))\), where \(\displaystyle\sf f(x) = x^{3}\) and \(\displaystyle\sf g(x) = x+4\).

Answer: x>-18

Step-by-step explanation:

simplify

9x-24-12x<30

-3x-24<30

-3x>54

-x>18

x>-18

Answer: 4 BTUs/ft^3

Step-by-step explanation:

i just did a test and this was the right answer

The expressions that are equivalent to 3^8 are:

We have to solve these out

3^8. = 6561

From the options

A. 3^2x3^4

= 9 x 81

= 729

B  3²x3^6

= 9 x 729

= 6561

C.  3^16/3^2

= 43046721/9

= 4782969

d. 3^12/3^4

= 531441 / 81

= 6561

E.  (3^4)²

= 3⁴ x 3⁴

= 3⁴⁺⁴

= 3⁸

= 6561

F. (3¹)^7

= 3⁷

= 2187

The expressions that are equivalent to 3^8 are:

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Answer:

Step-by-step explanation:

You need JL. Use the Pythagorean Theorem to get it.

a^2 + b^2 = c^2

a = 9

b = 40

c = ?

9^2 + 40^2 = c^2

c^2 = 1681

sqrt(c^2) = sqrt(1681)

c = 41

Cos(j) = adjacent / hypotenuse

adjacent = 9

hypotenuse = 41

Cos(J) = 9 / 41

Where's the system? I can't answer your question without it.

Answer:

x = 5

Step-by-step explanation:

If it is equilateral, that means all sides are equal

30 = 4x+10

Subtract 10 from each side

30-10 =4x

20 = 4x

Divide by 4

20/4 = 4x/4

5 = x

Answer:

36 < (x - 2)² + (y + 3)² and 16 > (x - 4)² + y²

Step-by-step explanation:

This is because the shaded area is inside the first circle (centered at (4, 0) with a radius of 4) but outside the second circle (centered at (2, -3) with a radius of 6). The inequalities reflect these conditions by setting the inequality signs accordingly. The inequality with "<" for the first circle ensures that the shaded area is within the circle, and the inequality with ">" for the second circle ensures that the shaded area is outside the circle.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

-6.4 is GREATER.

The number closest to 0 is greater.

Answer:− -19s

Step-by-step explanation:

Move  

Answer:

\(\huge\boxed{(-19)^{-8}=19^{-8}}\)

Step-by-step explanation:

Use

\(a^n\times a^m=a^{n+m}\)

\((-19)^{-12}\times(-19)^4=(-19)^{-12+4}=(-19)^{-8}\)

Answer:

They r correct lol

Step-by-step explanation:

\(\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(\log(x)=2\hspace{5em}\log(y)=3\hspace{4em}\log(2)\approx 0.3\hspace{4em}\log(3)\approx 0.48 \\\\[-0.35em] ~\dotfill\\\\ \log\left(\sqrt[3]{x^4\cdot y^2} \right)\implies \log\left(\left( x^4\cdot y^2 \right)^{\frac{1}{3}} \right)\implies \cfrac{1}{3}\log(x^4 y^2) \\\\\\ \cfrac{1}{3}[\log(x^4)~~ + ~~\log(y^2)]\implies \cfrac{1}{3}[4\log(x)~~ + ~~2\log(y)]\implies \cfrac{1}{3}[4(2)~~ + ~~2(3)] \\\\\\ \cfrac{1}{3}[8~~ + ~~6]\implies {\Large \begin{array}{llll} \cfrac{14}{3} \end{array}}\)

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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answer:

\((3x+5)(x+1)\)

explanation:

\(3x^2 +8x + 5\)

\(3x^2 +3x+5x + 5\)

\(3x(x+1)+5(x+1)\)

\((3x+5)(x+1)\)

\(3x² + 8x + 5\)

\(3x² + 3x + 5x +5\)

\(3x(x + 1) +5(x + 1)\)

\((3x + 5) (x + 1)\)

Answer :— \((3x + 5) (x + 1)\)

Answer:

65.22% probability that it is in compliance of both safety and sanitary standards

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Number of restaurant in compliance of both safety and sanitary standards.

First I will find those not in compliance, using a Venn's set.

Set A: Violation of sanitary standards.

Set B: Violation of safety standards.

5 were in violation of sanitary standards, a total of 6 were in violation of safety standards, and 3 were in violation of both.

This means that \(A = 5, B = 6, (A \cap B) = 3\)

At least one:

\(A \cup B = A + B - (A \cap B)\)

So

\(A \cup B = 5 + 6 - 3 = 8\)

8 are in violation of at least one of these standards.

So 23-8 = 15 are in compliance of both safety and sanitary standards.

What is the probability that it is in compliance of both safety and sanitary standards?

15 out of 23

15/23 = 0.6522

65.22% probability that it is in compliance of both safety and sanitary standards

Answer:

Step-by-step explanation:

x-intercept is where the line cuts the x-axis. That is, when y=0.

Substitute y=0 and we get:

       \(0=\frac{1}{3} x-1\)

       \(1=\frac{1}{3} x\)

       \(x=3\)

So x-intercept is the point (3,0).