Suppose that the credit remaining on a phone card (in dollars) is a linear function of the total calling time (in minutes). When graphed, the function gives a line with a slope of -0.16There is $29.00 in credit remaining on the card after 25 minutes of calls. How much credit was there after 18 minutes of calls?
Answers
The linear function there after 18 minutes of calls, then the credit was = $29
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
Given that,
Slope = -0.16
There linear function is $29.00 in credit remaining on the card after 25 minutes of calls
There after 18 minutes of calls?
Slope m = -0.16
Let us assume,
x = 25 minutes
y = $29.00 in credit
Substitute this values,
So,
We can write,
y = mx + b
$29.00 = (-0.16) (25) + b
$29.00 = -24.84 + b
b = $29.00 + 24.84
b = $53.84
We can substitute b value,
y = mx + b
y = (-0.16) x + $53.84
y = \(-0.16x\) + $53.84
y = (-0.16)(25) + $53.84
y = -24.84 + $53.84
y = $29
Therefore,
The linear function there after 18 minutes of calls, then the credit was = $29
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Related Questions
Determine the equation of the circle graphed below.
Answers
Answer:
(x - 2)² + (y + 4)² = 29
Step-by-step explanation:
Standard form
(x - h)² + (y - k)² = r²
(h, k) is the center and ris the radius
-----------------------------------
For center (2, -4)
(x - 2)² + (y + 4)² = r²
use the distance formula to find d² which is the same as r²
r² = d² = (x2 - x1)² + (y2 - y1)²
r² = (4 - 2)² + (1 - -4)²
r² = 2² + 5²
r² = 29
Now the equation becomes
(x - 2)² + (y + 4)² = 29
Solve the system of equations.
−2x+5y =−35
7x+2y =25
Answers
Answer:
The equations have one solution at (5, -5).
Step-by-step explanation:
We are given a system of equations:
\(\displaystyle{\left \{ {{-2x+5y=-35} \atop {7x+2y=25}} \right.}\)
This system of equations can be solved in three different ways:
Graphing the equations (method used)Substituting values into the equationsEliminating variables from the equationsGraphing the Equations
We need to solve each equation and place it in slope-intercept form first. Slope-intercept form is \(\text{y = mx + b}\).
Equation 1 is \(-2x+5y = -35\). We need to isolate y.
\(\displaystyle{-2x + 5y = -35}\\\\5y = 2x - 35\\\\\frac{5y}{5} = \frac{2x - 35}{5}\\\\y = \frac{2}{5}x - 7\)
Equation 1 is now \(y=\frac{2}{5}x-7\).
Equation 2 also needs y to be isolated.
\(\displaystyle{7x+2y=25}\\\\2y=-7x+25\\\\\frac{2y}{2}=\frac{-7x+25}{2}\\\\y = -\frac{7}{2}x + \frac{25}{2}\)
Equation 2 is now \(y=-\frac{7}{2}x+\frac{25}{2}\).
Now, we can graph both of these using a data table and plotting points on the graph. If the two lines intersect at a point, this is a solution for the system of equations.
The table below has unsolved y-values - we need to insert the value of x and solve for y and input these values in the table.
\(\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & a \\ \cline{1-2} 1 & b \\ \cline{1-2} 2 & c \\ \cline{1-2} 3 & d \\ \cline{1-2} 4 & e \\ \cline{1-2} 5 & f \\ \cline{1-2} \end{array}\)
\(\bullet \ \text{For x = 0,}\)
\(\displaystyle{y = \frac{2}{5}(0) - 7}\\\\y = 0 - 7\\\\y = -7\)
\(\bullet \ \text{For x = 1,}\)
\(\displaystyle{y=\frac{2}{5}(1)-7}\\\\y=\frac{2}{5}-7\\\\y = -\frac{33}{5}\)
\(\bullet \ \text{For x = 2,}\)
\(\displaystyle{y=\frac{2}{5}(2)-7}\\\\y = \frac{4}{5}-7\\\\y = -\frac{31}{5}\)
\(\bullet \ \text{For x = 3,}\)
\(\displaystyle{y=\frac{2}{5}(3)-7}\\\\y= \frac{6}{5}-7\\\\y=-\frac{29}{5}\)
\(\bullet \ \text{For x = 4,}\)
\(\displaystyle{y=\frac{2}{5}(4)-7}\\\\y = \frac{8}{5}-7\\\\y=-\frac{27}{5}\)
\(\bullet \ \text{For x = 5,}\)
\(\displaystyle{y=\frac{2}{5}(5)-7}\\\\y=2-7\\\\y=-5\)
Now, we can place these values in our table.
\(\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & -7 \\ \cline{1-2} 1 & -33/5 \\ \cline{1-2} 2 & -31/5 \\ \cline{1-2} 3 & -29/5 \\ \cline{1-2} 4 & -27/5 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}\)
As we can see in our table, the rate of decrease is \(-\frac{2}{5}\). In case we need to determine more values, we can easily either replace x with a new value in the equation or just subtract \(-\frac{2}{5}\) from the previous value.
For Equation 2, we need to use the same process. Equation 2 has been resolved to be \(y=-\frac{7}{2}x+\frac{25}{2}\). Therefore, we just use the same process as before to solve for the values.
\(\bullet \ \text{For x = 0,}\)
\(\displaystyle{y=-\frac{7}{2}(0)+\frac{25}{2}}\\\\y = 0 + \frac{25}{2}\\\\y = \frac{25}{2}\)
\(\bullet \ \text{For x = 1,}\)
\(\displaystyle{y=-\frac{7}{2}(1)+\frac{25}{2}}\\\\y = -\frac{7}{2} + \frac{25}{2}\\\\y = 9\)
\(\bullet \ \text{For x = 2,}\)
\(\displaystyle{y=-\frac{7}{2}(2)+\frac{25}{2}}\\\\y = -7+\frac{25}{2}\\\\y = \frac{11}{2}\)
\(\bullet \ \text{For x = 3,}\)
\(\displaystyle{y=-\frac{7}{2}(3)+\frac{25}{2}}\\\\y = -\frac{21}{2}+\frac{25}{2}\\\\y = 2\)
\(\bullet \ \text{For x = 4,}\)
\(\displaystyle{y=-\frac{7}{2}(4)+\frac{25}{2}}\\\\y=-14+\frac{25}{2}\\\\y = -\frac{3}{2}\)
\(\bullet \ \text{For x = 5,}\)
\(\displaystyle{y=-\frac{7}{2}(5)+\frac{25}{2}}\\\\y = -\frac{35}{2}+\frac{25}{2}\\\\y = -5\)
And now, we place these values into the table.
\(\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 25/2 \\ \cline{1-2} 1 & 9 \\ \cline{1-2} 2 & 11/2 \\ \cline{1-2} 3 & 2 \\ \cline{1-2} 4 & -3/2 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}\)
When we compare our two tables, we can see that we have one similarity - the points are the same at x = 5.
Equation 1 Equation 2
\(\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & -7 \\ \cline{1-2} 1 & -33/5 \\ \cline{1-2} 2 & -31/5 \\ \cline{1-2} 3 & -29/5 \\ \cline{1-2} 4 & -27/5 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}\) \(\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 25/2 \\ \cline{1-2} 1 & 9 \\ \cline{1-2} 2 & 11/2 \\ \cline{1-2} 3 & 2 \\ \cline{1-2} 4 & -3/2 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}\)
Therefore, using this data, we have one solution at (5, -5).
Lauren took 12 hours to read a 360 page book. At this rate, how long will it take her to read a 1200 page book?
Answers
Answer:
About 48 hours or 2 days.
Step-by-step explanation:
360 + 360 = 720 + 360 = 1080 + 360 = 1440
12x4=48
PLEASE HELP !!!! ILL GIVE BRAINLIEST !!!
Answers
Answer:
113
Step-by-step explanation:
AB and AD are tangent to circle C. Find the length of AB, if AB = 8x and AD = x + 9. Round your answer to 2 decimal places.
Answers
When a line is tangent to a circle, it forms a right angle with the radius drawn to the point of tangency. This means that triangle ABD is a right triangle with AB as the hypotenuse.
We can use the Pythagorean theorem to find the length of AB:
AB^2 = AD^2 + BD^2
Since AD = x + 9 and BD = 8x - (x + 9) = 8x - x - 9 = 7x - 9, we can substitute these values into the equation:
(8x)^2 = (x + 9)^2 + (7x - 9)^2
64x^2 = x^2 + 18x + 81 + 49x^2 - 126x + 81
64x^2 = 50x^2 - 108x + 162
14x^2 + 108x - 162 = 0
Dividing the equation by 2, we get:
7x^2 + 54x - 81 = 0
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
a = 7, b = 54, c = -81
x = (-54 ± √(54^2 - 4 * 7 * -81)) / (2 * 7)
x = (-54 ± √(2916 + 2268)) / 14
x = (-54 ± √5184) / 14
x = (-54 ± 72) / 14
Now we solve for x:
Case 1: x = (-54 + 72) / 14 = 18 / 14 = 9 / 7
Case 2: x = (-54 - 72) / 14 = -126 / 14 = -9
Since the length of a segment cannot be negative, we discard the second case and focus on the positive solution.
Therefore, x = 9/7.
Substituting this value back into AB = 8x:
AB = 8 * (9/7) = 72/7 ≈ 10.29
Rounding to 2 decimal places, the length of AB is approximately 10.29 units.
Answer:
To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:
8x = x + 9
Solving for x, we get:
x = 1.5
Therefore, AB = 8x = 8(1.5) = 12.
To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:
AB^2 + BD^2 = AD^2
Substituting the values, we get:
12^2 + BD^2 = (1.5 + 9)^2
Simplifying, we get:
BD^2 = 56.25
Taking the square root of both sides, we get:
BD = 7.5
Hence, the length of AB is 12 and the length of BD is 7.5.
MARK AS BRAINLIEST!!!
Please help thank you
Answers
Answer:
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
A house was valued at $299,000 . Over several years, the value decreased by, 9% giving the house a new value.
(a) Fill in the blank to write the new value in terms of the old value.
Write your answer as a decimal.
(b) Use your answer in part (a) to determine the new value.
Answers
A) - The NEW VALUE in terms of the old value is 0.91 times the old value.
B) - The NEW VALUE of the HOUSE is: 299,000 * 0.91 = $272,090
Step-by-step explanation:Make A Plan:
A) - Calculate the Percentage of the Value Remaining After the Decrease
B) - Calculate the NEW VALUE of the house
SOLVE THE PROBLEM:
A) - The PERCENTAGE of the VALUE REMAINING AFTER the DECREASE
100% - 9% = 91%
As A DECIMAL:0.91
B) - Calculate the NEW VALUE of the house:
NEW VALUE = OLD VALUE * REMAINING PERCENTAGE
NEW VALUE = 299,000 * 0.91
Draw the conclusion:
A) - The NEW VALUE in terms of the old value is 0.91 times the old value.
B) - The NEW VALUE of the HOUSE is: 299,000 * 0.91 = $272,090
I hope it helps!
Write an equation for the line through the point (x0,y0) with a slope of M in point slope form. Enter X0 and Y0 as y0. Use X and Y for variables names. Your equation should be of the form y=….
Answers
The equation of the line in point slope form is y = M(x - x₀) + y₀ .
The Point slope form of the line passing through the point (x₁,y₁) with slope m is given by the formula
(y - y₁) = m(x - x₁)
In the question ,
it is given that
the required line passes through the points (x₀ , y₀)
and the slope is M .
So, the point slope form equation of the line will be
( y - y₀) = M(x - x₀)
y - y₀ = M(x - x₀)
y = M(x - x₀) + y₀
Therefore , the equation of the line in point slope form is y = M(x - x₀) + y₀ .
The given question is incomplete , the complete question is
Write an equation for the line through the point (x₀,y₀) with a slope of M in point slope form. Your equation should be in the form of y = ... ?
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A ball is thrown vertically upwards from 'O' with a speed of 15m/s.Find the greatest height reached.
Answers
The greatest height reached will be 11.47m.
As it is obvious the motion is in a straight liner and the acceleration due to gravity is constant, sop we can use our equations of motions to find the height reached by the ball.
The initial velocity U of the ball is 15 m/s, when it was thrown vertically upwards,
The final velocity of the ball will be zero, because the ball will come to rest at the highest point of its motion.
the acceleration on the balls is same as the acceleration due to gravity g because the motion is under the influence of earth.
Let say the ball reaches the height H,
Applying the equation,
V² - U² = 2gH
-(15)² = 2 x (-9.8) x H
-225 = 2 x (-9.8) x H
we took the value of acceleration due to gravity as negative because the motion is against the gravity,
H = 11.47 meters.
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A number m is equal to twice the sum of two numbers n and p.
Answers
Answer:
oh
Step-by-step explanation:
Libbie can buy a package of 50 disks for $14.50. What would be the cost of one disks
Answers
Answer:
0.29
Step-by-step explanation:
\(14.50 \div 50 =0.29\)
Answer:
0.29
Step-by-step explanation:
14.50 divided by 50 = 0.29
(use standard algorithm)
If 50 disks cost 14.50, 1 disk would cost 0.29 if we divide them up.
Therefore, 0.29 would be your answer.
Hope this helps! Good Luck!
-kiniwih426
describe the polynomial expression 3x^2 + 2
Answers
Answer:
3×^2+2
The product of three times a number is multiplied with the same product and added with 2.
The phone company Splint has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 380 minutes, the monthly cost will be $173. If the customer uses 570 minutes, the monthly cost will be $249.
A) Find an equation in the form
y
=
m
x
+
b
,
where
x
is the number of monthly minutes used and
y
is the total monthly cost of the Splint plan.
Answer:
y
=
B) Use your equation to find the total monthly cost if 942 minutes are used.
Answer: If 942 minutes are used, the total cost will be
dollars.
Answers
The solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.
What is an equation?The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.
Part A:
Given:
customer uses 380 minutes, the monthly cost will be $173.customer uses 570 minutes, the monthly cost will be $249.To find an equation,
Where x is number of monthly minutes.
and y is total monthly of splint plan.
So, equation is:
\(\rightarrow \text{y} =\text{mx} +\text{b}\)
For the first case:
\(\rightarrow\bold{173 = 380x + b}\)
Second case:
\(\rightarrow\bold{249= 570x + b}\)
Solve for x:
\(\rightarrow{173 - 380\text{x}=249- 570\text{x}\)
\(\rightarrow{-207=-321\)
\(\rightarrow \text{x} =\dfrac{321}{207}\)
\(\rightarrow \text{x} =\dfrac{107}{69}\)
\(\rightarrow \text{x} \thickapprox1.55\)
For value of b
\(\rightarrow 173 = 380(1.55) + \text{b}\)
\(\rightarrow 173 - 589 = \text{b}\)
\(\rightarrow -416 = \text{b}\)
Part B:
\(\rightarrow \text{y} = 942(1.55) - 416\)
\(\rightarrow \text{y} = 1460.1 - 416\)
\(\rightarrow \text{y} \thickapprox1044\)
Therefore, the solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.
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Casey and Lance run laps to train for basketball. Casey runs 2 laps in the time it takes for Lance to run 9 laps.
If Casey runs 16 laps, how many laps does Lance run in the same amount of time?
Answers
Answer:
72 laps
Step-by-step explanation:
2/16=8
8x9=72
Given: SAO=30, SO ⊥ AO, SO=10. Find: V
look at link correct answer get brainliest
Answers
Answer:
1000π
Step-by-step explanation:
π(r^2*h/3)=volume of cone
π(10√3^2*10/3)
10√3 is from using 30 60 90 Triangle to find AO
Need this answered as soon as possible please!! Flo is designing a rectangular billboard using a scale drawing. the billboard is 6 m long. Flo draws a rectangle 12 cm long. The area of Flo's rectangle is 72 cm squared. What is the area of the billboard in square meters?
Answers
Multiply.
(2x+6)²
NEED ANSWER ASAPP
Answers
Answer:
4x² + 24x + 36
Step-by-step explanation:
(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36
What is the measure of angle C?
Hint: Angle C and the 67° angle are a linear pair or supplementary angles.
Answers
Answer:
113
Step-by-step explanation:
supplementray means 180-67=113
113
The diagonal line is a straight line which means when another straight line passes through it, both sides will add up to 180
9= 3 3_4- 2 7_8- b
B?
Answers
Answer:
Step-by-step explanation:
9 - 3¾ - 2⅞ = 3⅜
He gave his grandmother 3⅜ pounds of apples.
93,83,65,59,88,76,86,93,48,73,54,79
What is the percentage of these test scores that are less than 88?
Answers
If the graph passes the horizontal-line test, then the function is one-to-one. Functions that are one-to-one have inverses that are also functions. Therefore, the inverse is a function. Compare your response to the sample response above. What did you include in your explanation? a reference to the horizontal-line test a statement that the function is one-to-one the conclusion that the inverse is a function
Answers
Based on the sample response given, the statements included in the explanation on the horizontal line test are:
a reference to the horizontal-line test.a statement that the function is one-to-one. inverse is a function.What is the horizontal-line test?The horizontal line test is used to not only find out if a graph has an inverse function, but also if that inverse is also a function itself.
To pass the horizontal line test, the function has to be one-to-one which means that a horizontal line can intersect the graphed function at one point in all places. If this happens, then there is an inverse and the inverse itself is a function.
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What is the meaning of "A formula without free variables"?
Answers
A formula without free variables is a formula that does not contain any variables that are not quantified.
What is a formula without free variables ?Sentences are commonly referred to as formulas devoid of any unrestricted variables. These statements hold a truth value independent of the variable values, hence the reason.
Open formulas are frequently referred to as formulas with free variables. These are not actually declarations; instead, they are arrangements that can transform into declarations by allotting definite values to the independent variables.
Formulas without free variables are often easier to work with than formulas with free variables.
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Help !!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
34/149
Step-by-step explanation:
Suppose a one-year subscription to a magazine costs $12.99 and a three-year subscription costs $25.98. The cost and length of a subscription are related. Write a slope-intercept equation to model the cost of a subscription for any period of time.
Answers
Answer:
\(y = 6.495x + 6.495\)
Step-by-step explanation:
Represent years with x and cost with y.
So, we have:
\((x_1,y_1)=(1,12.99)\)
\((x_2,y_2)=(3,25.98)\)
Required
Determine the slope intercept equation
First, we calculate the slope (m)
\(m = \frac{y_2 - y_1}{x_2 - x_1}\)
\(m = \frac{25.98 - 12.99}{3 - 1}\)
\(m = \frac{12.99}{2}\)
\(m = 6.495\)
The equation is then calculated as:
\(y - y_1 = m(x - x_1)\)
Where
\(m = 6.495\)
\((x_1,y_1)=(1,12.99)\)
\(y - 12.99 = 6.495(x - 1)\)
\(y - 12.99 = 6.495x - 6.495\)
Make y the subject
\(y = 6.495x - 6.495 + 12.99\)
\(y = 6.495x + 6.495\)
five times three fourths
Answers
Answer:
3.75
Step-by-step explanation:
HELP!!!
What is m∠EFG?
Answers
The measurement of angle EFG is 42.
The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. A circle can be divided into sectors by using the central angle. An excellent illustration of a central angle is a pizza slice. A pie chart is made up of several sectors and is useful for representing various amounts.
A straightforward illustration of a sector with a center angle of 180o is a protractor. The angle created by a circle's arc at its center is another way to describe the term "central angle."
We have a circle with center H and the central angle is 84 degrees
The central angle of the circle is double of circumference angle.
Then the measurement of angle EFG is 42.
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Factor the expression and then evaluate without a calculator: 3·(m−4)−n·(m−4), if m=5, and n=4 : The factored expression is ___, the numerical value of it is ___.
Answers
Answer:
-1
Step-by-step explanation:
equation:
3(5-4)-4(5-4)
3*5-3*4 -4*5-4*-4
15-12-20+16
3-4
-1
Chad used a number line to show the distance from the library to his house and the distance from the library to Kelli's house. How much farther is Chad's house than Kelli's house from the library? A number line from 0 to 1 is divided into 8 equal parts. Library is at 0, Kelli's House is at four-eighths, and Chad's House is at seven-eighths on the number line.
Answers
Chad's house is 3/8 units farther away than Kelly's house.
How to use the number line?By reading the number line, we can see that:
Library = 0Kelli's House = 4/8Chad's House = 7/8.These fractions are the positions of each location. We want to find how much farther is Chad's house than Kelli's house from the library, this is given by:
(Chad's house position - library position) - (Kelli's house position - library position)
Writting the fractions, we get:
(7/8 - 0) - (4/8 - 0) = 3/8
So Chad's house is 3/8 units farther away than Kelly's house.
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Answer: 3/8
Step-by-step explanation: 7/8 -4/8 equals 3/8
What is 85% of £60?? I NEED HELPPP
Answers
Answer:
51 euros
Step-by-step explanation:
Hopefully this helps
Answer:
51 pounds
Step-by-step explanation:
What kind of graph is characterized by presenting values as coordinate points without any connecting element? a. bar graph b. line graph c. scatter plot d. histogram
Answers
Answer:
Option C, Scatter Plot. Hope this helps!
Step-by-step explanation:
Answer:
The answer is C on edge 2020.
Step-by-step explanation:
