Answer:
[tex]y+5=-\frac{3}{4}(x-8)[/tex]
Step-by-step explanation:
[tex]4x-3y=15 \\ \\ 3y-4x=-15 \\ \\ 3y=4x-15 \\ \\ y=\frac{4}{3}x-5[/tex]
The slope of the given line is [tex]4/3[/tex]. So, the slope of the line that we need to find is [tex]-3/4[/tex].
Using point-slope form, the equation is [tex]y+5=-\frac{3}{4}(x-8)[/tex].
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.
write an algebraic expression for 2 times the difference of x and y
Answer: x - y *2
Step-by-step explanation:
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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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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11. The area of a circle is πr2 where r is the length of the radius. Thus, one could take the measure of the central angle in degrees and ____________ _________. Then, multiply that result by πr2.
The measure of the central angle θ in degrees and then multiply by 1/(2π). Then that result by πr²
What is the area of the sector?We will use the following points to find the area of the sector;
First of all, the angle that is formed in a full rotation is 2π.
The area of a circle is given by the formula; A = πr²
The central angle is given by the angle symbol θ. Thus, we have to multiply the area of the circle by a factor θ/2π
Thus, the area of a sector is given by the formula;
A = (θ/2π) * πr²
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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:
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.
Mariano tosses a quarter into a wishing well. The top of the well is represented by 0 feet. The location of the quarter after the fall is represented by -22 feet. How far did the quarter fall?
The quarter fall a distance of 22 feet
How to determine how far did the quarter fall?From the question, we have the following parameters that can be used in our computation:
Top of the well = 0 feet
Location of the quarter after the fall = -22 feet.
The distance fell by the quarter is then calculated as
Distance = Top of the well - Location of the quarter after the fall
Substitute the known values in the above equation, so, we have the following representation
Distance = 0 + 22
Evaluate
Distance = 22
Hence, the distance is 22 feet
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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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9 pints equals how many quarts equals how many pints or how many quarts?
Answer:
there are 4.5 pints in a quart
Step-by-step explanation:
There are 2 pints in a quart so just divide 9 by 2 and you get 4.5
Answer: 9 pints = 4.5 quarts
Step-by-step explanation:
1 pint = 0.5
9 pints = 0.5 x 9 = 4.5
If jane walks north for 3 miles, turns $45^\circ$ to the right, and then walks another 4 miles, how many miles will jane be from her starting point? give your answer as a decimal rounded to the nearest hundredth. (you may use a calculator to compute the approximation.) if you are having trouble with this question, read problem 4.10 in the textbook.
Jane will have traveled a average of 7 miles, so she will be 5 miles away from her starting point. This can be approximated to 5.00 miles, which can be rounded to the nearest hundredth.
1. Jane has walked north for 3 miles.
2. Jane has turned 45 degrees to the right.
3. Jane has walked 4 miles after turning 45 degrees to the right.
4. Jane is now 5 miles away from her starting point. This can be approximated to 5.00 miles, which can be rounded to the nearest hundredth.
Jane has walked 3 miles north and then turned 45 degrees to the right and walked 4 more miles. This means that she has traveled a total of 7 miles from her starting point. To calculate the exact distance, we use trigonometry. We can approximate the distance to 5.00 miles, which can then be rounded to the nearest hundredth. This means that Jane is 5 miles away from her starting point.
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what is the inverse of the function f(x) = 3(x+5)^2-4 such as x < -5
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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What’s the correct answer answer asap for brainlist
Answer: Simile since as is used.
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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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.
Three bells ring at an interval of 9 minutes, 15 minutes and 21 minutes. The bells will next ring together at 11.00pm. Find the time the bells had last rang together?
The lowest coMmon denominator of 9, 15, and 21 is 315 (3•3•5•7). These 3 bells ring together every 315 minutes after 5:45 pm.
45 min • 1/60 hr/min = 0.75 hr
5:45 = 5 + 0.75 hr = 5.75 hr
5:45 pm to 10:00 am next day in minutes is:
available time = (12 - 5.75 + 10) hr • 60 min/hr
available time = 16.25 • 60 = 975 min
So as much as 975 min are available for the synchronized or periodic ringings.
Number of simultaneous ringings in 975 min:
975/315 = 3.1
3•315 = 945 min
975 - 945 = 30 mins after 3rd ringing after 5:45 pm.
315 min = 315•1/60 hr/min = 5.25 hr. 5.25 hr between simultaneous rings.
The next 3 ringings after 5:45 pm (5.75 hr) are at 5.75 + 5.25 hr = 11:00 pm, and then 11.0 pm + 1 = 12 am + 4.25 = 4.25 am (4:15 am), and then 4.25 + 5:25 hr = 9:30 am. There are 30 minutes left to 10:00 am (975 mins after 5:45 pm), so a 4th ringing does not have enough time.
ANSWER: Including 5:45 pm, the bells ring together at 11:00 pm, 4:25 am, and 9:30 am — a total of 4 times
Joan is selling handmade bead necklaces
at a local art fair. She paid $230 to
reserve her booth. The cost of supplies
for each necklace averages $2. So, her
cost, y, for x necklaces is represented by
y = $230 + 2x. If she sells her necklaces
for $12, her revenue, y, is represented
by y = 12x.
The solution of this system is the break-
even point, the point beyond which she
starts making a profit.
Answer:
After Joan sells 23 necklaces, she will start to make a profit.
Step-by-step explanation:
y=230+2x
y=12x
substitute y in the first equation for 12x
12x=230+2x
subtract 2x from both sides
10x=230
divide 10 from both sides
x=23
True or False: Two pounds of apples costs more than
$3.50.
True: Two pounds of apples costs more than $3.50.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Andrew Buys 8 pounds of apples for $11.60.
To find the unit rate of apples:
Use division operation,
unit rate = Total cost of apples / total weight of apples
= 11.60 / 8
= $1.45
That means, the unit rate is $1.45 per pound of an apple
So, 2 pound of apples costs 1.45 x 2 = $2.9
Therefore, 2 pound of apples costs less than $3.50.
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The complete question:
Andrew Buys 8 pounds of apples for $11.60. He wants to know and use the unit rate of the cost per pound. Tell whether the statement is True or False.
Two pounds of apples costs less than $3.50.
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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15 postcards and 10 envelopes cost 1 dollar and 70 cents. an envelope is 2 cents more expensive than a postcard. whats the price of the postcard and the envelope?
The unit cost of postcard and envelope are given as 6 and 8 cents respectively.
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
Suppose the cost of postcard be $x.
Then, the cost of envelope is x + 0.02.
As per the question, the following question can be written for the cost as,
15x + 10(x + 0.02) = 1.70
⇒ 25x = 1.50
⇒ x = 0.06
Thus, the cost of envelope is 0.06 + 0.02 = $0.08.
Which is equivalent to 8 cents.
Hence, the cost of each postcard and the envelope are obtained as 6 and 8 cents respectively.
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Is a rational number is always an integer? Explain
Answer: A rational number is not always an integer, but an integer is ALWAYS an rational number
Step-by-step explanation:
-> A rational number is a number that can be expressed as the ratio of two integers. For example, 1/2, 3/4, and 5/6 are all rational numbers.
However, a rational number is not always an integer. An integer is a whole number, whereas a rational number can be a fraction with a non-zero denominator.
-> For example, 1/2 is a rational number, but it is not an integer because it is a fraction with a non-zero denominator. On the other hand, 1 is a rational number and an integer because it can be expressed as the ratio of two integers (1/1).
So in summary, a rational number is not always an integer, but all integers are rational numbers.
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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A butterfly starts at 20m and changes -16m? What is the final elevation
Answer: = 4 m
There is a negative sign before number 16. It means the butterfly moved in a backward direction. =4 m, from the Initial position
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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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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25 % A. B. C. 12 Task #3: Which question best describes the diagram above? Answer the question. 120 is 25% of what? 25% of 120 is what? 6 is what percent of 120? 120 is what percent of 25? D. OP
(A) 120 is 25% of 500.
(B) 25% of 120 is 30.
(C) 6 is 5 percent of 120
(D) 120 is 500 percent of 25
What is percentage?Percentage is a part of the whole number. It is denoted by % sign.
1 %= 1/100.
(A)
Let 120 is 25 % x,
125 = (25/100) x
x = 500
(B)
Let 25% of 120 is x,
(25/100) x 120 = x
x = 30
(C)
Let 6 is x percent of 120.
6= (x/100) 120
x = 5
(D)
Let 125 is x percent of 25.
125 = 25 (x/100)
x = 500
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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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what property is (8•x•2)=(x•8•2)
