The function f(17) represent your friend paid for 17 rides and had $42.75 left over.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
Let f(x) represent the amount that the rider has left over after x rides.
f(x) = -1.25x + 64
f(17) = -1.25(17) + 64 = 42.75
f(17) = $42.75
f(17) represent the money left
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Yosef drops a basketball from his bedroom window, which is 3m off the ground. After each bounce,
the basketball comes back to 75% of its previous height. If it keeps on bouncing forever, what
vertical distance, to the nearest metre, will it travel?
After the sixteenth bounce, the basketball would be nearest which is 0.01 meters.
Height after dropping from a height = 3m
Bounce up rate = 75%
Height in first bounce = 2.25m (3 x 0.75)
Height in second bounce = 1.68m (2.25 x 0.75)
Height in third bounce = 1.26m (1.68 x 0.75)
Height in fourth bounce = 0.70m (0.94 x 0.75)
Height in fifth bounce = 0.525m (0.70 x 0.75)
Height in sixth bounce = 0.39m (0.52 x 0.75)
Height in seventh bounce = 0.29m (0.39 x 0.75)
Height in eighth bounce = 0.21m (0.29 x 0.75)
Height in ninth bounce = 0.15m (0.21 x 0.75)
Height in tenth bounce = 0.11m (0.15 x 0.75)
Height in eleventh bounce = 0.08m (0.11 x 0.75)
Height in twelfth bounce = 0.06m (0.08 x 0.75)
Height in thirteenth bounce = 0.04m (0.06 x 0.75)
Height in fourteenth bounce = 0.03m (0.04 x 0.75)
Height in fifteenth bounce = 0.02m (0.03 x 0.75)
Height in sixteenth bounce = 0.01m (0.02 x 0.75)... so on
After the sixteenth bounce, the basketball would be nearest.
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Please answer the two questions in the photo ( will mark brainliest if correct )
Find the zeros of the function. Answer in exact form. Do not round. m(x) = -x^2 - 27
Zeroes of the equation are i3√3 and -i3√3.
What are the zeroes of the polynomial?A value (a number) at which the polynomial evaluates to zero is referred to as the "zero of a polynomial." For instance, the zeros of the polynomial x²-3x+2 are 1 and 2. A polynomial's zeros are frequently referred to as its "roots." Every polynomial has a unique multiset of zeros, which is an unordered list. The coefficients of a zero polynomial, which is a constant polynomial, are all equal to 0. The value of the variable that brings a polynomial to zero is referred to as its zero. As a result, any real integer is the zero of the zero polynomial.
Given Data
(x) = -x² - 27
To find zeroes,
m(x) = 0
0 = -x² - 27
x² = -27
As we know,
i² = -1
x² = i²(27)
x² = i (±3√3)
x = i3√3
x = -i3√3
Zeroes of the equation are i3√3 and -i3√3.
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what is 2.6 to the lower bound
Lower bound of 2.6 is 2.5
What is lower bound?An element of K that is greater than or equal to each element of S is referred to as an upper bound or majorant in mathematics, notably in order theory. To determine a rounded number's upper and lower bounds: Determine the place value of the claimed level of accuracy. By two, multiply this place value. Find the upper bound by adding this amount to the provided value, and the lower bound by deducting this amount from the given value.
Given Data
2.6 to the lower bound
Bound of 2.6 is 2.5 to 2.7
Lower bound of 2.6 is 2.
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Question 6: A rideshare company charges a flat fee of $3.50 and $1.25 for each mile. Write an inequality to determine how many miles Jessica can travel if she has $45 to spend.
$1.25x + $3.50 ≥ $45
$1.25 + $3.50x ≥ $45
$1.25x + $3.50 ≤ $45
$1.25 + $3.50x ≤ $45
Answer: $1.25x + $3.50 ≤ $45
Step-by-step explanation:
The total cost for a given number of miles is the initial cost number of miles multiplied by the cost per mile.
So, the expression for the cost is 1.25x+3.50.
Since she has $45 to spend, Jessica can spend no more than this, so the inequality is that in Option 3.
Which method and additional information would prove ΔONP and ΔMNL similar by the AA similarity postulate?
The method and additional information would prove ΔONP and ΔMNL similar by the AA similarity postulate is A. Use a rigid transformation to prove ∠NOP ≅ ∠NML.
What is the postulate about?The AA Similarity Postulate states that two angles in one triangle must be congruent with two angles in another triangle for the two triangles to be comparable. The AA Similarity Postulate is a shortcut for demonstrating the similarity of two triangles.
In this case, B is incorrect because angles NOP and ONP are not corresponding angles
Also, options (c) and (d) are incorrect, because they prove the similarities by lines segments.
In conclusion, the correct option is A.
The complete question is written below.
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Complete question
Which method and additional information would prove ΔONP and ΔMNL similar by the AA similarity postulate?
A. Use a rigid transformation to prove ∠NOP ≅ ∠NML.
B. Use a rigid transformation to prove ∠NOP ≅ ∠ONP.
C. Use rigid and nonrigid transformations to prove segment LN over segment ON = segment PN over segment MN.
D. Use rigid and nonrigid transformations to prove segment LM over segment ON = segment PN over segment MN
After a tax of 22%, a car sells for $9800.
What was its original price?
Before a tax of 22 %, the product has an original price of $ 8032.79.
How to determine the original price of a product
In this problem we find the case of a product that is sold including a given tax, that is, the price of the product before taxes. The original price can be found by means of the following equation, which is in terms of resulting price and tax rate:
C = C' / (1 + r / 100)
Where:
C - Original price, in monetary unit.C' - Resulting price, in monetary unit.r - Tax rate, in percentage.If we know that C' = $ 9800, r = 22 %, then the original price of the product is:
C = 9800 / (1 + 22 / 100)
C = 9800 / (122 / 100)
C = 9800 / 1.22
C = $ 8032.79
Therefore, the original price of the product, that is, the price before a tax of 22 %, is equal to $ 8032.79.
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3 ÷ 4 on number line
Take a look at the picture below to see how 3/4 looks when represented on a number line.
This is further explained below.
What is a number line?Generally, A image of a graded straight line is what is known as a number line, and its purpose is to provide a visual representation of the actual numbers.
It is generally accepted that a real number may be assigned to each point on a number line and that each real number can be assigned to a point.
In conclusion, consider the image below for the number line representation of 3/4
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You roll a fair 6-sided die twice. Find the probability of getting the same number.
The probability of getting the same number is 1/6.
The ratio of good outcomes to all possible outcomes of an event is known as the probability.
utilizing two ethical six-sided dice.
The likelihood that the dice will produce the same number must be determined.
36 total outcomes were obtained.
The positive results are (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6).
6 good outcomes total.
Therefore, the likelihood of an event is equal to the ratio of good outcomes to all possible outcomes.
Changing the values
Event probability is 6/36, or 1/6.
As a result, there is a 1/6 chance that both dice will reveal the same number.
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Describe each transformation of the parent function y + |x|. Then, graph each function.
33. y = |x| - 4
35. y = -|x + 4| + 3
PLEASE HELP
The correct transformation include
Transformation 1: Shifted down by 4 unitsTransformation 2: Shifted left by 4 units, reflected across the x-axis and shifted up by 3 unitsHow to determine the transformation of the graph?The equation of the function is given as
y = |x|
The transformed functions are given as
y = |x| - 4
y = -|x + 4| + 3
The transformation 1
Here, we have
y = |x|
y = |x| - 4
This can be represented as
y = f(x) - 4
The description of the above transformation is:
The function y = |x| is shifted down by 4 units
The transformation 2
Here, we have
y = |x|
y = -|x + 4| + 3
This can be represented as
y = -f(x + 4) + 3
The description of the above transformation is as follows
The function y = |x| is shifted left by 4 unitsThe function is then reflected across the x-axisThe function y = |x| is shifted up by 3 unitsNext, we graph the functions where the blue line represents y = |x|, the green line represents y = |x| -4 and the orange line represents y = -|x + 4| + 3
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If an exercise ball has a weight on 150N calculate its weight in pounds.
Answer: 33.7lbs
Step-by-step explanation: One N equals 0.225lb so you do that times 150
Hope this helped!!!!
What is the slope of the line?
Answer:
-2
Step-by-step explanation:
find two points on the line. You go down 2 units and 1 unit to the right.
What is the solution to the following equation?
6(2x - 6) + 2(13 - x) = 10
a
9
b
5
c
3
d
2
Hey there!
6(2x - 6) + 2(13 - x) = 10
6(2x) + 6(-6) + 2(13) + 2(-x) = 10
12x - 36 + 26 - 2x = 10
10x - 10 = 10
ADD 10 to BOTH SIDES
10x - 10 + 10 = 10 + 10
SIMPLIFY IT
10x = 10 + 10
10x = 20
DIVIDE 10 to BOTH SIDES
10x/10 = 20/10
SIMPLIFY IT
x = 20/10
x = 2
Therefore, your answer should be:
Option D. x = 2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
A basketball team wants to see if its fans like its new uniforms. Which description represents a population?
children who root for the team
season ticket holders
employees who work for the basketball team
fans of the basketball team
Answer:
Step-by-step explanation:
On a clearance rack, t-shirts cost $10 and shorts cost $13. You have $25 to spend. Write an equation that models the possible combinations of t-shirts t, and shorts, s, you can buy.
The equation that models the situation is 10t + 13s = 25
How to model equation?T-shirts cost $10 and shorts cost $13.
The shorts cost $13.
The total amount to be spend is $25.
let
t = number of T-shirt
s = number of shorts
The equation that models the possible combinations of T-shirt t, and shorts s, is as follows:
An equation is a mathematical statement that shows that two mathematical expressions are equal.
Hence,
10t + 13s = 25
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What are the slope and the Y-Intercept of the linear function y=5X-2
slope = 5 or 5 rise over 1 run.
y-intercept = (0,-2)
use multiplication to show how how many twenty fourths equal 3/6
Answer:
10 times
Step-by-step explanation:
To figure this out, the first thing we will do is to find the LCM (Least Common Multiple). We will do this by making a list of the denominators that we have right now. Right now we have [tex]\frac{20}{4}[/tex] and [tex]\frac{3}{6}[/tex]. We will use 4 and 6 to make a list to find our multiple that is in both lists. (That comes up first)
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42...
Now, we just realized that we have 24 that are in common with both 4 and 6. Now we will multiply both the numerator and denominator by the same number to have the denominator equal 24.
[tex]\frac{20}{4} * \frac{6}{6}[/tex] = [tex]\frac{120}{24}[/tex] & [tex]\frac{3}{6} * \frac{4}{4}[/tex] = [tex]\frac{12}{24}[/tex]
Now that we have [tex]\frac{120}{24}[/tex] and [tex]\frac{12}{24}[/tex]. We will read the question again about how many [tex]\frac{3}{6}[/tex] equal to [tex]\frac{20}{4}[/tex]. Since we have our fractions, we will add [tex]\frac{12}{24}[/tex] multiple times until we get [tex]\frac{120}{24}[/tex].
[tex]\frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} = \frac{120}{24}[/tex]
Therefore, [tex]\frac{3}{6}[/tex] equals to [tex]\frac{20}{4}[/tex] 10 times.
A and B are complementary angles. If mA = (x - 22)° and
m/B=(x-16)°, then find the measure of A.
Answer:
Complementary angles have a sum of 90°.
(x - 22) + (x - 16) = 90
2x - 38 = 90
2x = 128
x = 64
Substitute x into angle A
A = 64 - 22 = 42°
Diane's living room is 12 feet wide and 20 feet long. She wants to
put a border around the top of the room. The cost of the border is
$1.19 per foot. How much will it cost to buy enough of the border
to go around the room?
The most appropriate choice for perimeter of rectangle will be given by
It costs $76.16 to buy enough of the border to go around the room.
What is perimeter of a rectangle?
The total length of the outline of a rectangle is called perimeter of rectangle.
If the length of a rectangle is l units and breadth of a rectangle is b units, then perimeter of rectangle will be given by
[tex]2 \times (l+b)[/tex] units
Here,
Length of room = 20 feet
Width of room = 12 feet
Perimeter of room = [tex]2 \times (20 + 12)[/tex]
= [tex]2 \times 32[/tex]
= [tex]64[/tex] feet
cost of 1 foot of border = $1.19
cost of 64 foot of border = $[tex]1.19 \times 64[/tex]
= $[tex]76.16[/tex]
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Use the figure to find the measure of the angle (#1-15)
Answer:
1. 82 2. 82 3. 82 4. 98 5. 123 6. 122 7. 119 8. 60 9. 60 10. 125 11. 35 12. 105
What fraction of an hour is 24 minutes?
Give your answer in its simplest form
Answer:
Step-by-step explanation:
I hour = 60 minutes
So x hours = 24 minutes
to find x-->
Using the ratio method,
[tex]\frac{1}{60}[/tex] = [tex]\frac{x}{24}[/tex]
where x is the unknown number of hours we have to find.
After solving it, we get 60 * (x) = 24
we get x= 24/60
x= 0.4 hours
Hence, 24 mins is 4/10 of an hour.
In the simplest form--> x= 2/5
the 2 boxes are cubiods work out how many of the smaller boxes you would need to completely fill the larger one.
From calculations, we can see that the number of smaller boxes to completely fill the larger one are; 250 boxes
How to find the volume of the cuboid?The volume of a cuboid is given by the formula;
Volume = Length * Width * Height
Looking at the given dimensions of the larger box in the cuboid image attached, we can calculate the volume as;
Volume = 50 * 30 * 20
Volume = 30000 cm³
The length , width and height of smaller box are 10 cm, 3 cm and 4 cm respectively. Thus, the volume of smaller box is;
volume = 10 * 3 * 4
volume = 120 cm³
Thus, the number of smaller boxes to completely fill the larger one are;
n = 30000/120
n = 250 boxes
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What is the input value for which f(x) = -3?
The diagram shows a prism. The cross section of the prisim is a right-angled triangle. The base of the triangle has length 5cm. The prisim has length 25cm. The prisim has volume 750. Work out the height of the prisim.
The height of the triangular prism is calculated as: 12 cm.
How to Find the Height of a Right-Triangular Prism?The volume of a right-triangular prism = 1/2(base of triangular face)(height of triangular face)(length of the triangular prism).
Given the following:
Base length of the triangular face = 5 cmVolume of the right-triangular prism = 750 cubic cmLength of the right-triangular prism = 25 cmHeight of the right-triangular prism (height of the triangular face) = hPlug in all the values into the volume formula for the triangular prism:
750 = 1/2(5)(h)(25)
750 = (1 × 5 × h × 25)/2
750 = (125h)/2
Multiply both sides by 2
750 × 2 = (125h)/2 × 2 [multiplication property of equality]
1,500 = 125h
Divide both sides by 125
1,500/125 = 125h/125 [division property of equality]
12 = h
h = 12 cm
Thus, the height of the prism that has a base of the triangle measuring 5cm, a prism length of 25 cm., and a volume of 750 cubic cm is determined as 12 cm.
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Three fifths of the T-shirts in a T-shirt shop are blue. Five eights of those T-shirts are on sale. one third of the blue T-shirts are on sale are size medium. what fraction of the shops T-shirts are blue T-shirts that are on sale and are size medium
Answer:
The fraction of the shop’s T-shirts are blue T-shirts that are on sale and are size medium is 1/ 8
Step-by-step explanation:
What’s the answer pls
The length of the side marked x is 10.2 cm.
What is the missing side?We know that it is possible to solve the right angle triangle by the use of the Pythagoras theorem. Also, we could make use of the trigonometric ratios when we have to solve the right angled triangle.
The task here id to find the angle that has been marked x in the image that was shown above.
We are going to use the trigonometric ratios here;
Given that;
Cos θ = adjacent/ hypotenuse
θ = 40 degrees
Adjacent = x
Hypotenuse = 13.4 cm
adjacent = cos 40 * 13.4 cm
adjacent = 10.2 cm
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what is the answer to 2 4/5 x 4 1/16
Answer:
91/8
Step-by-step explanation:
[tex]2\frac{4}{5} *4\frac{1}{6}[/tex]
→ Convert to improper fraction
14/5 × 65/16
→ Simplify
7 × 13/8 = 91/8
Multiplying Rational Numbers- 5/8 (-2/15)
The product of the rational numbers - 5/8 and - 2/15 will be 1 / 20.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction is referred to as the PEMDAS rule. To answer the problem properly and accurately, this rule is applied.
The rational numbers are given below.
- 5/8 and - 2/15
Then the product of the rational numbers - 5/8 and - 2/15 will be given by the multiplication of the rational numbers - 5/8 and - 2/15.
⇒ - 5/8 × - 2/15
⇒ 5/8 × 2/15
⇒ 1/20
The product of the rational numbers - 5/8 and - 2/15 will be 1 / 20.
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Work out the missing numbers:
a) (-4) x __ = 320
b) __ x 3 = 180
c) __ / (-7) = (-14)
d) __ / (-9) = 6
please help i’m so confused
A particular jury consists of 7 jurors. Each juror has a 0. 2 chance of making the wrong decision, independently of the others. If the jury reaches a decision by majority rule, what is the probability that it will reach a wrong decision?.
The probability that the jury will make a wrong decision when it reaches a decision by majority rule is 0.033
To solve this, the number of jury that makes the wrong decision can be modeled as a binomial random with parameters n=7 and p=0.2. This jury as a whole will make wrong decision if 4, 5, 6, or 7 make the wrong decision.
We denote these events with A, B, C, D for 4, 5, 6, 7 respectively. The probability of this union is the sum of probabilities, so
P(Jury Error) = P(A)+P(B)+P(C)+P(D)
= [tex]\left({{7} \atop {4}} \right.)(0.2)^{4} *0.8^{3} +(\left \({7} \atop {5}} \right)(0.2)^{5} *0.8^{2} +(\left{7} \atop {6}} \right.)(0.2)^{6} *0.8^{1} +(\left{7} \atop {7}} \right.)(0.2)^{7} *0.8^{0}[/tex]
=0.033
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