Answer:
Rs.2700
Step-by-step explanation:
14% profit means 100% +14% more=114% profit
then to make into decimal 114% divided by 100 to give 1.14
then divide 2850 by 1.14 to find original selling price of bicycle
which will be Rs.2,500
next, a 8% profit means 100%+8% which equals 108% and then make into decimal which is 1.08
then multiply the original selling price (Rs.2,500) by 1.08 to give your final selling price after the 8% profit of ...
Rs.2,700
In the example what is 3/4 over 1/3 the unit rate for
Step-by-step explanation:
the unit rate for 60 miles per hour is 60 miles/hour.
write an algebraic expression for 2 times the difference of x and y
Answer: x - y *2
Step-by-step explanation:
what property is (8•x•2)=(x•8•2)
Previous 5
2023 F
5
Graphing Polynomial Functions: Mastery Test
Select the correct answer.
Identify the end behavior and the zeros of function h.
h(z) = -³ 92² + 4x + 96
Based on these key features, which statement is true about the graph representing function h?
The graph is positive on the intervals (-8, -4) and (3, 0o).
The graph is negative on the intervals (-oo, -8) and (-4, 3).
O C. The graph is positive on the intervals (-00, -8) and (-4, 3).
OD. The graph is negative on the intervals (-3, 4) and (8,00).
OA.
OB.
Reset
Next
According to the end behavior of the function h(z) = 5x³-9x²+4x+96, the graph is positive on the intervals (-∞, -8) and (-4, 3).
What is a polynomial function?
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.
The given polynomial function is -
h(z) = 5x³-9x²+4x+96
The end behavior of a function f(x) describes the behavior of the function as x approaches +∞, and as x approaches -∞.
Domain of function h(z) = -∞<x<∞
The end behavior of the function h(z) is -
lim x→∞, (5x³-9x²+4x+96) = ∞
as x→∞, h(z)→∞
lim x→-∞, (5x³-9x²+4x+96) = -∞
as x→-∞, h(z)→-∞
Therefore, the graph is positive on the intervals (-∞, -8) and (-4, 3).
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Complete and show the following.
a ABCD is a rhombus and AC} is one of its diagonals.
Without assuming parallel sides, explain why Δs ABC and ADC are congruent.
b Deduce from a that ABCD is a parallelogram.
The evaluation of the rhombus ABCD and are as follows;
a. The sides of the Δs ABC and ADC are all congruent, therefore, ΔABC ≅ ΔADC by SSS
b. The opposite sides and opposite angles of ABCD are congruent, the adjacent angles are supplementary, therefore, ABCD is a parallelogram by its properties which defines a parallelogram
What is a rhombus?A rhombus is a quadrilateral that has four sides which are congruent and the opposite sides are parallel, therefore a rhombus is a special form of a parallelogram.
a. The specified details in the question are;
AB ≅ BC
AB ≅ AD
AB ≅ CD
Therefore; BC ≅ AD ≅ CD, by transitive property of congruency
AB = BC, AB = AD, AB = CD, BC = AD = CD, by definition of congruency
AC is congruent to AC by reflexive property of congruency, therefore;
ΔABC ≅ ΔADC by Side-Side-Side, SSS, congruency rule
b. ∠D ≅ ∠B by Corresponding Parts of Congruent Triangles are Congruent, CPCTC
∠DAC ≅ ∠DCA by base angles of an isosceles triangle, ΔADC
∠BAC ≅ ∠BCA by base angles of an isosceles triangle, ΔABC
∠DAC ≅ ∠BAC by CPCTC
∠DAC = ∠BAC by definition of congruency
∠DCA ≅ ∠BCA by CPCTC
∠DCA = ∠BCA, definition of congruency
∠DAB = ∠DAC + ∠BAC (Angle addition postulate)
∠DCB = ∠DCA + ∠BCA (Angle addition postulate)
∠DAC + ∠BAC = ∠DCA + ∠BCA substitution property
∠DAB = ∠DCB by substitution property
∠DAB ≅ ∠DCB definition of congruency
The opposite angles of the quadrilateral ABCD are congruent,
The opposite sides are congruent
∠D + ∠DCA + ∠DAC = 180° (angle sum property of a triangle)
∠D + ∠ADC + ∠BCA = 180° (substitution property)
Similarly;
∠B + ∠BAC + ∠DAC = 180°
Adjacent angles of the quadrilateral ABCD are supplementary, therefore;
Quadrilateral ABCD is a parallelogram, by the properties of a parallelogram
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Which is the graph of y = 3^√x+1-2?
The graph of the function y = ∛(x +1 ) - 2 is represented by the graph represented by option 1.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.
The graph of the function y = ∛(x +1 ) - 2 is attached with the answer below,
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What’s the correct answer answer asap for brainlist
Answer: Simile since as is used.
Factor f(x) = x² – 3x³ - 12x² + 54x - 40 with real coefficients given that 3-i is a zero of f(x).
f(x) = x² – 3x³ - 12x² +54x - 40 =
(x - 3 + i)(x² - 3x - 10) This means that 3 - i is a zero of f(x). This is because when f(3 - i) is evaluated, the result is 0. The factorization of f(x) shows that 3 - i is a zero of the function.
What is factorization?Factorization is the process of breaking a number or expression into its prime factors. This is done by expressing the number as a product of its prime factors. Factorization is a key concept in mathematics, particularly in algebra and number theory. Factorization can be used to simplify expressions and equations, and it is often used to solve problems involving divisibility and prime numbers. Factorization can also be used to find the greatest common divisor, least common multiple, and other properties of numbers.
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You have 99 cats and 77 dogs and 10998 horses what is the ratio of dogs to cats?
The ratio of dogs to cats is 7 to 9
How to determine the ratio of dogs to cats?From the question, we have the following parameters that can be used in our computation:
You have 99 cats and 77 dogs and 10998 horses
The ratio is represented as
Ratio = Dogs : Cats
Substitute the known values in the above equation, so, we have the following representation
Dogs : Cats = 77 : 99
Divide by 11
Dogs : Cats = 7 : 9
Hence, the ratio is 7 to 9
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what is 3.2 times 3.2 to the second power to the fourth power to all
The value of 3.2 times 3.2 to the second power to the fourth power to all is [tex](3.2)^{12}[/tex].
What is exponent?The amount of times a number has been multiplied by itself is shown by its exponent.
3.2 to the second power is represented as [tex](3.2)^2[/tex].
3.2 times 3.2 to the second power, thus, is represented as:
[tex](3.2) (3.2)^2[/tex]
Since, the base is similar, the powers can be added:
[tex](3.2)^{1+2}\\\\(3.2)^3[/tex]
Now, the fourth power to all is represented as:
[tex]((3.2)^3))^4\\[/tex]
Using the rule of exponents [tex]((a^m))^n = a^{mn}[/tex] we have:
[tex](3.2)^{3*4}\\\\(3.2)^{12}[/tex]
Hence, the value of 3.2 times 3.2 to the second power to the fourth power to all is [tex](3.2)^{12}[/tex].
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25. What must be the value of y below so that the line passing through the points (4,4) and (-3, y) has a slope of -2 ?
A. 18
B. 10
C. 2
D. -6
Answer:
A. 18
Step-by-step explanation:
............... .....k
which point represents 2 1/3 -5/6 and -3 1/2 on the number line
Answer:
Provided at image
Step-by-step explanation:
Green dot = -3.5
Red dot = -5/6
Orange dot = 2.3
Since there are 5 lines between every 1 number, you can divide 100/6 to see the distance between the lines (16.6666) and plug in the points.
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equation have the same solution as 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p
How to determine the equations that have the same solution?Given: 2.3p – 10.1 = 6.5p – 4 – 0.01p.
Using this given property, let's write the equation
We can subtract like terms (6.5p– 0.01p = 6.49p) to get:
2.3p – 10.1 = 6.5p – 0.01p – 4
2.3p – 10.1 = 6.49p – 4
Also, we can multiply both sides of the algebraic equation by 100:
(2.3p – 10.1) x 100 = (6.5p – 4 – 0.01p) x 100
230p – 1010 = 650p – 400 – p
Therefore, the equations have the same solution as 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p. The 2nd and 3rd options are the answers
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Ken has 1.71 meters of string in 52.3 seconds. He cut the string into 0.19 meters lengths .
How many peices does he have?
4 step plan
The number of string pieces which Ken has after he cuts the string into 0.19 meter lengths is; 9.
How many 0.19 length string pieces does Ken have?It follows from the task content that initially, Ken has 1.71 meters of string. However, he cuts the string into 0.19 meters strings.
It is however required that the number of string pieces he has after cutting the 1.71 meter string into 0.19 meters lengths be determined.
On this note; the number of 0.19 string lengths he has can be evaluated by estimating the quotient as follows;
= 1.71 / 0.19
= 9.
On this note, Ken would have 9 pieces of the 0.19 meters strings.
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(Score for Question 2:
of 6 points)
2. One-half of the fudge at the fudge shop on Monday morning contain nuts. Helena works at the fudge shop
and prepares 10 pounds of fudge containing walnuts to fulfill a special order Monday afternoon. With this
additional amount of fudge, there are at least 24 pounds of fudge containing nuts at the fudge shop on
Monday.
(a) Write an inequality that represents the scenario. Begin by defining your variable.
(b) Solve the inequality. Show your work.
(c) Fudge is packaged into 1-pound boxes. What is the fewest number of boxes of fudge at the fudge
shop Monday moming? Show your work.
Answer:
a) The inequality that represents the scenario is 10 + x ≥ 24.
b) The solution of the inequality is x ≥ 14.
c) The fewest number of boxes of fudge at the fudge shop Monday morning is 14.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
a) Let x denote the amount of fudge at the shop.
Helena prepares 10 pounds of fudge containing nuts.
The Inequality can be
10 + x ≥ 24
b) The inequality can be solved as
10 + x ≥ 24
x ≥ 24 -10
x ≥ 14
c) The fewest number of boxes would be almost 14 boxes.
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Need help ASAP due tomorrow!
Answer:
Step-by-step explanation:
m∠O = 118 because opposite angles of a parallelogram are equal
LNO forms a triangle and the sum of the interior angles of a triangle is 180.
To find m∠NLO:
22 + 118 + m∠NLO = 180
m∠NLO = 180 - 22 - 118 = 40
PLS HELP QUICK!!!!!!!!! 100 points.
The following is a list of movie tickets sold each day for 10 days. 7, 18, 23, 41, 34, 12, 48, 65, 57, 52 Which of the following intervals are appropriate to use when creating a histogram of the data?
A 0 – 9, 10 – 19, 20 – 29, 30 – 39, 40 – 50
B 0 – 14, 15 – 29, 30 – 44, 45 – 59, 60 – 74
C 0 – 15, 15 – 20, 20 – 35, 35 – 60, 60 – 75
D 0 – 20, 20 – 40, 40 – 60, 60 – 80
The interval that is the most appropriate for creating the histogram is: 0 – 9, 10 – 19, 20 – 29, 30 – 39, 40 – 50. Option A
How to find the best interval for the histogramIn order to get the best interval, we would have to check the distance that lies in the data from what the question has told us.
The tickets are sold each day for ten days. Hence we would have to look for the interval that lies between 10 days.
From the options we have here, option A is seen to lie between the distance of 10 days. 0 - 9 is 10 days e.t.c
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Answer:
0 – 14, 15 – 29, 30 – 44, 45 – 59, 60 – 74
Step-by-step explanation:
what is the inverse of the function f(x) = 3(x+5)^2-4 such as x < -5
C Dax packs cans into boxes.
He fits eight rows of five
cans into the bottom of
each box, and a second
layer of cans on top. How
many cans are in each
box?
The number of cans in each box is 80.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of rows in each layer = 8
Number of cans in each row = 5
Number of layers = 2
The total number of cans.
= Cans x Rows x Layer
= 5 x 8 x 2
= 40 x 2
= 80
Thus,
There are 80 cans in each box
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Mr. Paxon can pack 960 toy pachyderms in an eight hour shift.
A. How many toy pachyderms can Mr. Paxon pack per hour?
B. At that rate, how long will it take to pack 660 pachyderms?
The number of toy pachyderms that Mr. Paxon can pack per hour will be 120 per hour. And the number of hours to pack 660 pachyderms will be 5.5 hours.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
Mr. Paxon can pack 960 toy pachyderms in an eight-hour shift.
The number of toy pachyderms that Mr. Paxon can pack per hour will be given as,
Rate = 960 / 8
Rate = 120 per hour
At that rate, the number of hours to pack 660 pachyderms will be given as,
⇒ 660 / 120
⇒ 5.5 hours
The number of toy pachyderms that Mr. Paxon can pack per hour will be 120 per hour. And the number of hours to pack 660 pachyderms will be 5.5 hours.
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Let f be the function given by f(x)=x(x−4)(x+2) on the closed interval [−7,7]. Of the following intervals, on which can the Mean Value Theorem be applied to f ?
I.[−1,3] because f is continuous on [−1,3] and differentiable on (−1,3).
II.[5,7] because f is continuous on [5,7] and differentiable on (5,7).
III.[1,5] because f is continuous on [1,5] and differentiable on (1,5).
mean value theorem can be applied for option 1 and 2.
According to the Mean Value Theorem, if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then f'(c) must equal the function's average rate of change over [a, b] at some point c on the interval (a, b).
f(x) = x/{(x-4)(x-2)} on [-7,7]
f'(x) = [{(x-4)(x+2)*1} - {x(x-4)*1} - {x(x+2)}]/ {(x-4)^2 (x+2)^2}
or, f'(x) = [{(x-4)(x+2)} - {x(x-4)} - {x(x+2)}]/{(x-4)^2 (x+2)^2}
Now, if the value of X becomes 4, the entire function would be undefined.
So for option 1, set [-1,3] f is continuous on [-1,3] and differentiable on (-1,3).
For option 2, [5,7] because f is continuous on [5,7] and differentiable on (5,7).
But for option 3, since the 4 is an element of set [1,5] it would be an incorrect statement.
so mean value theorem can be applied for option 1 and 2.
note: all '−' used in the given question has been considered as - sign while solving the question.
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The Mean Value Theorem can be applied to f on intervals I, II, and III.
The Mean Value Theorem can be applied to a continuous and differentiable function on a closed interval. Therefore, to determine on which of the intervals the Mean Value Theorem can be applied to f, we must first check if f is continuous and differentiable on those intervals.
For interval I, f is continuous on [-1,3] and differentiable on (-1,3).
For interval II, f is continuous on [5,7] and differentiable on (5,7).
For interval III, f is continuous on [1,5] and differentiable on (1,5).
Therefore, the Mean Value Theorem can be applied to f on intervals I, II, and III.
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It takes 4 oz. of cherry syrup, 4 oz. of grenadine, and 1
quart of white soda to make a batch of Shirley Temples.
To make them for a party, how much white soda would
you need to buy if you had a quart of cherry syrup and a
quart of grenadine?
Answer:
8 quarts of white soda
Jayden has $7.69. His coach will give him $3.21 every mile he runs If he run 18 miles how much will he have
ASAP!!! HURRY!!
Answer:
Jayden will earn $3.21 x 18 = $<<3.21*18=57.78>>57.78 from running 18 miles.
So he will have $7.69 + $57.78 = $<<7.69+57.78=65.47>>65.47 in total.
Step-by-step explanation:
Graph the line that represents a proportional relationship between y and x where the unit rate of change of y with respect to x is 0.4. In other words, a change of 1 unit in x corresponds to a change of 0.4 units in y.
The graph of the line y = 0.4x is attached below.
What is unit rate?There is independent quantity, and a quantity which depends on it (dependent quantity). When independent quantity moves by a unit measurement (single unit increment), the increment in dependent quantity is called rate of increment of dependent quantity per unit increment in independent quantity.
We are given that the line that represents a proportional relationship between y and x where the unit rate of change of y with respect to x is 0.4.
The graph of the line with the slope m and the y-intercept , has the form as;
y = mx + c
In this case the rate of change is 0.4 ; therefore we have the equation
y = 0.4x
The graph of the line is attached.
Here we have set b = 0 by default.
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The bearing of P from Q is 040°.
The bearing of R from Q is 124°.
QR = QP.
Work out the bearing of R from P.
The bearing of R from P is 172°.
What are bearing(angles)?The horizontal angle between an object's direction and either north or another object is known as a bearing or azimuth in navigation. You can specify the angle value in a number of different angular units, including degrees, mils, and grad.
The angle between the magnetic north and the absolute bearing
The angle between the craft's forward motion and the relative bearing.
Given The bearing of P from Q is 040°.
The bearing of R from Q is 124°.
QR = QP.
Bearing angles are 180 degrees different than forward-bearing angles. This difficulty can be resolved by combining these relations with the standard angle sum relation for triangles.
Angle PQR will be the difference in the bearings from Q to P and Q to R:
∠PQR = 124° -40° = 84°
Triangle PQR is isosceles, so the base angle at P will be ...
∠QPR = (180° - 84°)/2 = 48°
The bearing from P to R will be 48° less than the bearing from P to Q. The bearing from P to Q is 180° more than the bearing from Q to P.
PR bearing = PQ bearing - ∠QPR
= PQ bearing - 48°
= (40° +180°) - 48° = 172°
Hence, The bearing of R from P is 172°.
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What is the solution to the system of equations x-y=-1 and x-3y=-13?
why did you choose this answer?
Answer:
(5,6)
Step-by-step explanation:
x -y = -1
x - 3y = -13 ⇒ multiply through by -1 ⇒ -x + 3y = 13 Add this to the first equation
-x + 3y = 13
x - y = -1
2y = 12 Divide both sides by 2
y = 6
To find y substitute 6 for y in the equation x - y = -1
x - 6 = -1 Add 6 to both sides
x = 5
(5,6)
Mrs. Olson and Mrs. Alcorn went shopping together for spring break. Mrs. Olson bought six shirts and four pairs of shorts that cost her 106.80. Mrs. Alcorn bought 3 shirts and 3 pairs of shorts that cost her 68.85. How much does one shirt cost.
Answer:
One shirt costs $7.50.
One pair of shorts cost $15.45
Step-by-step explanation:
Approximate fx(1,3) using the contour diagram of f(x,y) shown below.
fₓ (1,3) ≈
Considering the contour diagram, fₓ (1, 3) is traced to be 10
What are contour maps?A contour line for a function of two variables, more generally speaking, a curve that connects places where the function has the same specific value.
A topographic map, for example, which displays valleys, hills, and the steepness or gentleness of slopes, is an example of a map with contour lines.
The elevation difference between successive contour lines is known as the contour interval in a contour map.
Using the map provided point (1, 3) is traced to the contour line that has the mark of 10
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When a number is subtracted from 24 and the difference is divided by that number, the result is 3. What is the value of the number?
Answer:
6
Step-by-step explanation:
[tex]\frac{24-x}{x}=3 \\ \\ 24-x=3x \\ \\ 24=4x \\ x=6[/tex]
Answer:
5.25
Step-by-step explanation:
Let the number be x. The equation is:
24 - x / x = 3
We can rearrange this equation to solve for x:
24 - x = 3x
21 = 4x
x = 21/4
x = 5.25
So the value of the number is 5.25.
how can be the period of function sinx + cosx = 2π besides that period of Sinx= 2π also cosx = 2π
The period of function sinx + cosx = 2π besides that period of Sinx= 2π also cosx = 2π.
What is Least common multiple?The Least common multiple of two or more numbers are the smallest number that is multiple of two or more numbers.
Here, The period of function sin x + cos x = 2π
And, The period of Sin x= 2π and cos x = 2π
Now, We know that;
If period of Sin x= 2π and cos x = 2π
Then, The period of function sin x + cos x = LCM {2π , 2π }
= 2π
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Answer:
The period of a function is the smallest positive number 'p' such that f(x+p) = f(x) for all x in the domain of f.
To find the period of the function sinx + cosx, we can use the fact that sin(x+π/4) = sinx*cos(π/4) + cosx*sin(π/4) = (sqrt(2)/2)*sinx + (sqrt(2)/2)*cosx. Therefore, sinx + cosx = sqrt(2)*sin(x+π/4).
Now, we know that the period of sin(x+π/4) is 2π since sin(x+π/4) = sin((x+π/4)+2kπ) for all integers k. Therefore, the period of sinx + cosx is also 2π/sqrt(2), which simplifies to π*sqrt(2).
To answer your question, the period of sinx and cosx are both 2π because they are fundamental trigonometric functions with a repeating pattern every 2π radians. However, when we add them together as in sinx + cosx, their pattern changes and becomes more complex.
