Answer: brainly.... D. f(x) = 1.06x; $169.60
sales tax = 6% or 6/100.
assuming tax is added onto the item:
total cost function f(x) = price + tax
however, assuming the cost price = sales price - tax, then:
f(x) = sales price - tax
This is not really a business or accounting forum, its a maths forum, so you need to be clearer about business or accounting terms such as total cost, selling price, selling cost.
Step-by-step explanation: brainly
if y= the item after tax
y=x+(x*6%) or y=x+6%
and then for the answer you would go:
y=160+6% or 160+(160*6%)= $169.60
Answer: f(x)=1.06x; $169.60
Step-by-step explanation: pearson
A car travels at a constant speed of 60 miles per hour. The distance, d, the car travels in miles is a function of time, t, in hours given by d(t)
The equation of distance traveled by the car is d(t) = 60 · t, for t ≥ 0.
What is the equation of the distance travelled by a car?In accordance with the statement, car travels in a straight line at constant speed. The distance traveled (d), in miles, is equal to the product of the speed (v), in miles per hour, and time (t), in hours:
d(t) = v · t (1)
If we know that v = 60 mi/h, then the equation of distance traveled by the car is d(t) = 60 · t, for t ≥ 0.
RemarkThe statement is incomplete and complete form cannot be found. Then, we decided to complete the statement by asking for the equation that describes the distance of the car.
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Write the equation of the transformed graphs of each trigonometric function
The equations of the transformed graphs are [tex]y = \tan(\frac{\pi}{4}x) + 3[/tex] and [tex]y = -\frac34\sin(2x)[/tex]
How to transform the functions?The tangent function
The parent function is:
y = Atan(Bx) + k
It has a period of 4.
So, we have:
[tex]\frac{\pi}{B} = 4[/tex]
Make B the subject
[tex]B = \frac{\pi}{4}[/tex]
It is shifted vertically up by 3 units.
So, we have:
k = 3
Substitute these values in y = Atan(Bx) + k and remove A
[tex]y = \tan(\frac{\pi}{4}x) + 3[/tex]
Hence, the equation of the transformed graph is [tex]y = \tan(\frac{\pi}{4}x) + 3[/tex]
The sine function
The parent function is:
y = Asin(Bx) + k
It has a period of [tex]\pi[/tex]
So, we have:
[tex]\frac{2\pi}{B} = \pi[/tex]
Make B the subject
B = 2
It has an amplitude of 3/4
So, we have:
A = 3/4
It is flipped across the x-axis
So, we have:
A = -3/4
Substitute these values in y = Asin(Bx) + k and remove k
[tex]y = -\frac34\sin(2x)[/tex]
Hence, the equation of the transformed graph is [tex]y = -\frac34\sin(2x)[/tex]
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Expand the following using the Binomial Theorem and Pascal’s Triangle. Show your work
2. (x-4)^4
3. (2x+3)^5
4. (2x-3y)^4
Answer:
2
Step-by-step explanation:
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 18, 3, 0, 3, 6, 3.
Using only the values given in the table for the function f(x) = –x3 + 4x + 3, what is the largest interval of x-values where the function is increasing?
(
,
)
The largest interval of x-values where the function is increasing is (-1, 1)
How to determine the largest increasing interval?The table of values is added as an attachment
From the table, the function f(x) decreases from x = -3 to x = -1 and x = 1 and x = 2
So, we make use of the intervals
x = -1, 0 and 1
From the table,
From x = -1 to 0, the change is 3
From x = 0 to 1, the change is 3
From x = -1 to 1, the change is 6
Using the above highlights, the largest increasing interval is (-1, 1)
Hence, the largest interval of x-values where the function is increasing is (-1, 1)
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The following is a 3-step proof. Complete the proof.
Given: 1 = 2
AP = BP
1) [tex]\angle 1=\angle 2[/tex], [tex]AP=BP[/tex] (given)
2) [tex]\angle APD=\angle BPC[/tex] (vertical angles are equal)
3) [tex]\triangle ABD \cong \triangle BAC[/tex] (ASA)
What is the equation of the line through the origin and (-2,3)?
Step-by-step explanation:
[tex]algenbraic[/tex]
14. Kathy lives directly east of the park. The football field is directly south of the park. The library (1 point) sits on the line formed between Kathy's home and the football field at the exact point where an altitude to the right triangle formed by her home, the park, and the football field could be drawn. The library is 9 miles from her home. The football field is 12 miles from the library.
Park
Home
9 miles
Library
12 miles
Football field
a. How far is the library from the park?
b. How far is the park from the football field?
6.√3 miles; 6.7 miles
6.7 miles: 6.3 miles
√33 miles. √21 miles
√21 miles, √33 miles
Answer:
(a) 6√3, 6√7
Step-by-step explanation:
The right triangles shown are all similar, so corresponding sides are proportional. This gives rise to three "geometric mean" relations between the various lengths.
Geometric mean relationsUsing P, F, L, and H to represent the points marked Park, Football field, Library, and Home, the relations are ...
PF/FH = FL/PF ⇒ PF = √(FH·FL)
PL/FL = HL/PL ⇒ PL = √(FL·HL)
PH/HL = HF/PH ⇒ PH = √(HL·HF)
Application(a) The distance from the park to the library is ...
PL = √(FL·HL) = √(12·9) = 6√3 . . . miles
(b) The distance from the football field to the park is ...
PF = √(FH·FL) = √(21·12) = 6√7 . . . miles
What is the domain of the function shown on the graph?
Answer:
domain {x:x≥-2}or in interval notation [-2,∞)
what is the volume of a sphere with a radius of 6 inches
Answer:
288pi in^3 , which is 904.78 in^3 to nearest hundredth.
Step-by-step explanation:
V = 4/3 pi r^3
= 4/3 pi * 6*3
= 288pi in^3
= 904.7786842 in^3
Jason deposited $18 000 in a bank that offers an interest rate of 5% per annum compounded
daily.
He kept the money in the bank for 20 days, before withdrawing an amount, H.
Given that, the balance in the bank after another 20 days is $16 093.41, find H.
Answer:
$1995.97.
Step-by-step explanation:
Amount in bank after 20 days =
18000(1 + 0.05/365)^20
= $18049.38
So H = 18049.38 - 16093.41
= $1995.97.
4. If a = 1+ 1/b where b>1, find the value of a ?
Answer: a is more than 1 but less than 2
Step-by-step explanation:
b > 1
0 < [tex]\frac{1}{b}[/tex] < 1
0 + 1 < 1 + [tex]\frac{1}{b}[/tex] < 1 + 1
1 < 1 + [tex]\frac{1}{b}[/tex] < 2
So 1 < a < 2
help....
delta math questions...
The length of BD is √182
How to solve for x?The given parameters are:
AD = 7
DC = 26
BD = x
The side lengths are represented by the following ratio:
7 : x = x : 26
Express as fraction
7/x = x/26
Cross multiply
x^2 = 182
Take the square roots
x = √182
Hence, the length of BD is √182
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Answer:
The length of BD is √182
hope this helps :)
6 out of 24 as a percentage
Answer:
25%
Step-by-step explanation:
When you simple 6 out of 24 you get a quarter.
A quarter us equivalent to 25%
Find the area of the shaded region.
Answer:
18π cm² ≈ 56.5 cm²
Step-by-step explanation:
The area of the sector can be found using an appropriate area formula.
Sector areaWhen the sector central angle is given in radians, the formula for the area of that sector is ...
A = 1/2r²θ . . . . . . where θ is the central angle, and r is the radius
When the angle is in degrees, the formula will include a factor to convert it to radians:
A = 1/2r²θ(π/180) . . . . where angle θ is in degrees
A = (πθ/360)r² . . . . simplified slightly
The figure shows r=9 cm, and θ=80°. Using these values in the formula gives an area of ...
A = π(80/360)(9 cm)² = 18π cm² ≈ 56.5 cm²
On a coordinate plane, quadrilateral D G A R is shown. Point G is at (negative 8, 3), point A is (4, 8), point R is at (10, 0), and point (negative 2, negative 5).
A grid map marks the plot of Harold’s garden in meters. The coordinates of the quadrilateral-shaped property are G(–8, 3), A(4, 8), R(10, 0), and D(–2, –5). He wants to build a short fence around the garden.
The perimeter of his garden is
meters.
The perimeter of the garden is 46 units.
How to calculate the perimeter?To calculate for the perimeter of the garden, we have to solve for the measures of each of the sides of the four-sided polygon. That is calculated by getting the distances between consecutive points.
The equation for the distance is:
d = sqrt ((x₂ - x₁)² + (y₂ - y₁)²)
Distance from G and A,
d = sqrt ((4 - -8)² + (8 - 3)²)
d = 13
Distance from A to R,
d = sqrt ((10 - 4)² + (0 - 8)²)
d = 10
Distance from R to D,
d = sqrt ((-2 - 10)² + (-5 - 0)²
d = 13
Distance from D to G,
d = sqrt ((-8 --2)² + (-5 -3)²)
d = 10
Summing up all the four calculated distances will give us an answer of 46.
Thus, the perimeter of the garden is 46 units.
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Answer: 46 meters.
Step-by-step explanation: I just did it on edge 2023. Hope this helps!
Circle C is shown. 2 secants intersect at a point outside of the circle to form angle 1. The first arc formed is 36 degrees, and the second arc formed is 106 degrees.
In the diagram of circle C, what is the measure of ∠1?
17°
35°
70°
71°
The measure of the ∠1 is 35 degrees.
How to determine the angleit is important to know that the measure of an angle with its vertex outside the circle is half the difference of the intercepted arcs.
Also, the angle subtended by the arc at the center of the circle is the angle of the arc
From the diagram, we have
m ∠ of external angle = half of the difference of arc angles
The arc angles are
106°36°m ∠ of external angle = ∠ 1
Let's substitute the angles
∠1 = [tex]\frac{106 - 36}{2}[/tex]
∠ 1 = [tex]\frac{70}{2}[/tex]
∠ 1 = 35°
We can see that the external angle 1 measures 35 degrees.
Note that the complete image is added.
Thus, the measure of the ∠1 is 35 degrees.
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Simplify the expression
The solution to the expression [tex]\frac{x^2+7x+12}{x-3} .\frac{x^2-6x+9}{2x^2-18}[/tex] gives (x + 4)/2
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
[tex]\frac{x^2+7x+12}{x-3} .\frac{x^2-6x+9}{2x^2-18} \\\\=\frac{(x +3)(x +4)}{x-3} .\frac{(x-3)(x-3)}{2(x+3)(x-3)} =\frac{x+4}{2}[/tex]
The solution to the expression [tex]\frac{x^2+7x+12}{x-3} .\frac{x^2-6x+9}{2x^2-18}[/tex] gives (x + 4)/2
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i will mark brainlyist
The following are the distances (in miles) to the nearest airport for 12 families. 6, 7, 8, 8, 16, 19, 23, 24, 26, 27, 34, 35 Notice that the numbers are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
Using it's definitions, the five-number summary and the interquartile range for the data-set is given as follows:
Minimum: 6Lower quartile: 8Median: 21.Upper quartile: 27Maximum: 35Interquartile range: 19What are the median and the quartiles of a data-set? How to find the interquartile range using it?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference of the third quartile and the first quartile.This data-set has 12 elements, which is an even number, hence the median is the mean of the 6th and 7th elements, as follows:
Me = (19 + 23)/2 = 21.
The minimum is the lowest value in the data-set, which is of 6, while the maximum is of 35, which is the largest value in the data-set.
The first quartile is the median of the first half, composed by 6, 7, 8, 8, 16, which is the third element of 8.
The third quartile is the median of the second half, composed by 23, 24, 26, 27, 34, 35, which is of 27. Hence the interquartile range is of 27 - 8 = 19.
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A deck of 52 cards contains an equal amount of hearts, diamonds, clubs, and spades. If one card is picked at random from the deck, the probability that it is a club is:
a)1/52
b)1/13
c) 1/10
d) 1/4
Answer: B) 1/13
Step-by-step explanation:
There are 52 cards. So, there are 52/4 = 13 cards of each amount of hearts, diamonds, clubs and spades. In this case, we're looking for the probability of picking a club. Since there are 13 club cards and we want to know the probability of picking ONE, our answer is b) 1/13.
Considering the definition of probability, the correct answer is option d): if one card is picked at random from the deck, the probability that it is a club is 1/4.
Definition of probabilityThe higher or lower possibility that a particular event will occur is known as the probability. This is, the probability establishes a relationship between quantity of favorable events and the total quantity of possible events.
The ratio of favorable situations (the number of cases in which event A may or may not occur) to all possible cases is used to calculate the the probability of any event A. This is called Laplace's Law:
probability= number of favorable cases÷ total number of possible cases
Probability that the picked card is a clubIn this case, you know:
Total number of cards = 52 (number of possible cases)The deck of cards contains an equal amount of hearts, diamonds, clubs, and spades.Total number of cards that are clubs= 52÷4= 13 (number of favorable cases)Replacing in the definition of probability:
probability= 13÷ 52
Solving:
porbability= 1/4
Finally, if one card is picked at random from the deck, the probability that it is a club is 1/4.
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The sum of a number and its reciprocal is 122/11. Find the
number.
O -11
09
O 11
Answer:
11
Step-by-step explanation:
if the some of a number is an restrocal is 122 upon 11 find the integers value of x let the number bees two values of x i e 11 and 1 upon 11 are possible hence required in future value of x is 11
See picture to answer!
Using the law of cosines, it is found that the length of side AB is of AB = 13.
What is the law of cosines?The law of cosines states that we can find the angle C of a triangle as follows:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
in which:
c is the length of the side opposite to angle C.a and b are the lengths of the other sides.For this problem, the parameters are:
C = 120, a = 8, b = 7.
Hence:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
[tex]c^2 = 8^2 + 7^2 - 2(8)(7)\cos{120^\circ}[/tex]
[tex]c^2 = 169[/tex]
[tex]c = \sqrt{169}[/tex]
c = 13.
Hence AB = 13.
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Determine the equation of the parabola graphed below. Note: be sure to consider the negative sign already present in the template equation when entering your answer. A parabola is plotted, concave up, with vertex located at coordinates negative one and negative two.
The equation of the parabola graphed is given as follows:
y = a(x + 1)² - 4.
What is parabola and examples?
A parabola is nothing but a U-shaped plane curve. Any point on the parabola is equidistant from a fixed point called the focus and a fixed straight line known as the directrix. Terms related to Parabola.The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
Considering the vertex given, we have that h = -1, k = -4, hence the equation is:
y = a(x + 1)² - 4
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The product of two powers is 11^8 and their quotient is 11². What are the two powers? Explain.
Answer:
The powers are 3 and 5.
Step-by-step explanation:
When you multiply 2 exponential functions you add the powers and when you divide these functions you subtract the powers, so we have:
11^a * 11^b = 11^(a+b)
11^a/ 11^b = 11^(a-b)
So, from the information given:
a + b = 8
a - b = 2 Adding:-
2a = 10
a = 5.
and substituting in the second equation
5 - b = 2
b = 3.
What is the equation of the line described below written in slope-iWhat is the equation of the line described below written in slope-intercept form?
the line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0
The equation of a line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0 is y = -1/2x + 1
Equation of a lineA line is the shortest distance between two points. The equation of a line in point-slope form and perpendicular to a line is given as;
y - y1 = -1/m(x-x1)
where
m is the slope
(x1, y1) is the intercept
Given the following
Point = (4, -1)
Line: 2x-y - 7 = 0
Determine the slope
-y = -2x + 7
y= 2x - 7
Slope = 2
Substitute
y+1 = -1/2(x -4)
Write in slope-intercept form
2(y + 1) = -(x - 4)
2y+2 = -x + 4
2y = -x + 2
y = -1/2 + 1
Hence the equation of a line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0 is y = -1/2x + 1
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Answer:
y = - (1/2) x + 1
Some band members have raised much more money than other. which measure can be used to show this?explain.
A ratio measure can be used to show this.
What is a ratio measure?A ratio in mathematics describes how many times one number contains another.The highest (most sophisticated) level of measurement that a variable can have is referred to as a ratio measure.A 3 to 5 ratio (3:5) A 3:5 ratio can be written as 3:5, 3/5, or 3/5. Furthermore, 3 and 5 can represent any number or measurement, including pupils, fruit, weights, heights, speed, and so on. A 3 to 5 ratio simply means that for every three of something, there are five of something else, for a total of eight.Therefore, a ratio measure can be used to show the given situation.
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Which logarithmic equation correctly rewrites this exponential equation? 8x = 64
The logarithmic equation of 8^x = 64 is [tex]x = \log_8(64)[/tex]
How to determine the logarithmic equation?The exponential equation is given as:
8^x = 64
Take the logarithm of both sides
xlog(8) = log(64)
Divide both sides by log(8)
x = log(64)/log(8)
Apply the change of base rule
[tex]x = \log_8(64)[/tex]
Hence, the logarithmic equation of 8^x = 64 is [tex]x = \log_8(64)[/tex]
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Can someone help me out on this problem and show work please !!
Given the area of the rectangular community garden, the length and width of the garden are 30ft and 10ft respectively.
What is the length and width of the garden?A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.
Area of a rectangle is expressed as;
A = length × Width
Given the data in the question;
Area of the rectangular community garden A = 300ft²Let width w = xLength = three times width = 3xWe substitute the values into the equation
A = length × breadth
300 = 3x × x
300 = 3x²
Divide both sides by 3
x² = 100
Take the square root of both sides
x = ±√100
x = 10, -10
Since, dimension of a rectangle cannot be Negative.
x = 10
Hence;
Width w = x = 10ft
Length = 3Width = 3x = 3( 10 ) = 30ft
Given the area of the rectangular community garden, the length and width of the garden are 30ft and 10ft respectively.
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3. The slope of a line shows the___
for that line. This means it tells us how far ____ the line moves each time you move over one unit on the x-axis.
for that line.
The slope of a line shows the distance of that line. This means it tells us how far the line moves each time you move over one unit on the x-axis for that line.
What is the slope of a line?The slope of a line can be defined a number that describes the direction and steepness of the line.
It is also known as gradient
It is denoted by the letter 'm'
Thus, the slope of a line shows the distance of that line. This means it tells us how far the line moves each time you move over one unit on the x-axis for that line.
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Which expression represents the product of ³ + 2x - 1 and 4 -³ +3?
I7-214-3
1¹+2x+2
1¹2-1⁹ +²+2x³ +6x-3
27-26 +225-3x² + 4x³ + 6x - 3
Don
The expression that gives the product of the polynomials x³ + 2x + 1 and 4x³ + 3 is:
[tex](x^3 + 2x + 1)(4x^3 + 3) = x^6 + 2x^4 + 7x^3 + 6x + 3[/tex]
How do we multiply polynomials?We multiply them applying the distributive property, multiplying all the terms and then combining the like terms.
In this problem, the factors are given as follows:
x³ + 2x + 1,4x³ + 3.Hence the multiplication will be given by:
[tex](x^3 + 2x + 1)(4x^3 + 3) = x^6 + 2x^4 + 7x^3 + 6x + 3[/tex]
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Pls help with b
The diameters of two circular pulleys are 6cm and 12 cm, and their centres
are 10cm apart.
a. Angle a = 72.54 degrees
b. Hence find, in centimetres correct to one decimal place, the length of a
taut belt around the two pulleys
The length of a taut belt around the two pulleys is 79.3 cm.
Length around the pulley
The length of a taut belt around the two pulleys is calculated as follows;
Shapes formed within the two circles of the pulley.
From top to bottom, a rectangle, a right triangle and a trapezium.
Length of the rectangleThe height of the right triangle is equal to length of the rectangle
base of the right triangle = radius of big circle - radius of small circle
base of the right triangle = (0.5 x 12 cm) - (0.5 x 6 cm) = 3 cm
tan α = height/base
tan (72.54) = h/3
h = 3 tan(72.54)
h = 9.54 cm
Length of trapezium at bottomThe length of the trapezium at bottom is equal to length of rectangle at top, L = h = 9.54 cm
Angles and length of belt in each circlePortion of belt in contact with circumference of small circle is subtended by an angle = 2 × 72.54 = 145.08°
Length of belt in contact with circumference of smaller circle
= 2πr (θ/360)
= (2 x 6 cm)π x (145.08/360)
= 15.19 cm
Portion of belt in contact with circumference of big circle is subtended by an angle = 360 - 145.08° = 214.92⁰
Length of belt in contact with circumference of smaller circle
= 2πr (θ/360)
= (2 x 12 cm)π x (214.92 / 360)
= 45.01 cm
Length of a taut belt around the two pulleys= 9.54 cm + 9.54 cm + 15.19 cm + 45.01 cm
= 79.28 cm
= 79.3 cm
Thus, the length of a taut belt around the two pulleys is 79.3 cm.
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