Finding the proportionality constant :
y = k/x16 = k/(1/2)k = 8Finding y when x = 17 :
y = 8/(17)y = 8/17The value of y is 8/17 when x = 17.
Please help!!!!
A triangular patch of grass in a park is bordered by walking paths. The longest path bordering the patch of grass measures 135 feet. The smallest path bordering the patch of grass measures 60 feet. The smallest angle formed by the paths measures 26°. What is the measure of the largest angle of the triangular patch of grass? Round your answer to the nearest degree. Show all your work.
The measure of the largest angle of the triangular patch of grass is 81 degrees
Application of sine ruleIn order to determine the measure of the largest angle, we will use the expression below;
[tex]\frac{60}{sin26^0} =\frac{135}{sinx^0}[/tex]
Cross multiply
135sin26 = 60sinx
sinx = 135sin26/60
sinx = 59.18/60
sinx = 0.986
x = 80.5 degrees
Hence the measure of the largest angle of the triangular patch of grass is 81 degrees
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if l and m are parallel,which pair of angles are supplementary?
Answer:
Option (1)
Step-by-step explanation:
Angles 2 and 5 are supplementary by the same-side interior angles theorem.
Using your answer from the previous question, state the value of 't' if Josephine is going to run a dis-
tance of 15 miles at a rate of 5 miles per hour.
Previous answer t=d/r
Using the relation between velocity, distance and time, it is found that t = 3 hours.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence:
[tex]v = \frac{d}{t}[/tex]
For this problem, the parameters are given as follows:
d = 15 miles, v = 5 mph
Hence the time in hours is found as follows:
[tex]v = \frac{d}{t}[/tex]
[tex]5 = \frac{15}{t}[/tex]
5t = 15
t = 15/5
t = 3 hours.
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find the surface area of the pyramid
Answer:
145
Step-by-step explanation:
mutiply each 6 and 7 twice and add 7x7 from the bottom
Which of the following is a secant on the circle below?
A. SU
B. RT
C. SU
D. UT
The secant of circle is SU and RT.
What is Secant of the Circle?A straight line that intersects a circle in two points is called a secant line.
From the given diagram,
The line which intersects the circle at two points or an extended chord is SU and RT.
Hence, secant is SU and RT.
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Which inequality defines the shaded region graphed below?
Answer:
Every ordered pair within this region will satisfy the inequality y ≥ x. Incorrect. The boundary line here is y = x, and the correct region is shaded, but remember that a dotted line is used for < and >. The inequality you are graphing is y ≥ x, so the boundary line should be solid.
Describe the correlation in terms of strength (weak or strong) and direction positive or negative).
The description of the correlation in terms of strength (weak or strong) and direction positive or negative) is as explained below.
How to Interpret Correlation Problems?
A correlation coefficient, is expressed as r and it indicates a measure of the direction and strength of a relationship between two variables.
Now, in terms of strength, Correlation strength ranges from -1 to +1. Thus, The closer the correlation is to 0, the weaker it is while the closer it is to ±1, the stronger it is.
Now, in terms of direction;
A correlation of +1 indicates a perfect positive correlation which tells us that both variables move in the same direction together. A correlation of –1 indicates a perfect negative correlation, which tells us that as one variable goes up, the other goes down.A zero correlation suggests that the correlation statistic does not indicate a relationship between the two variables.Read more about Correlation at; https://brainly.com/question/4219149
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what is the value when 18times of the difference of 15 and 12 divided by 6
Donte simplified the expression below. 4 (1 3 i) minus (8 minus 5 i). 4 3 i minus 8 5 i. negative 4 8 i. what mistake did donte make? he did not apply the distributive property correctly for 4(1 3i). he did not distribute the subtraction sign correctly for 8 – 5i. he added the real number and coefficient of i in 4(1 3i). he added the two complex numbers instead of subtracted.
Donte did a mistake that 'he did not apply the distributive property correctly for 4(1 3i)' option (A) is correct.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have an expression:
= 4(1 + 3i) – (8 – 5i)
= 4 + 12i - 8 + 5i
He did not distribute the subtraction sign correctly for 8 – 5i.
= -4 + 17i
Thus, Donte did a mistake in that 'he did not apply the distributive property correctly for 4(1 3i)' option (A) is correct.
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Answer:
(A) is correct.
Step-by-step explanation:
Gerald is constructing a line parallel to line l through point P. He begins by drawing line m through points P and Q. He then draws a circle centered at Q, which intersects line l at point N and line m at point S. Keeping the compass measure, he draws a congruent circle centered at point P, which intersects line m at point T.
Which next step will create point R, such that when a line is drawn through points P and R, the line will be parallel to line l?
Lines m and n intersect at point Q. A circle is drawn around point Q and forms point S on line m and forms point N on line l. Point P is also on line m. A circle is drawn around point P and forms point T on line m.
Use the compass to construct a circle centered at Q through point P.
Using the compass measure between points S and N, draw an arc to the right of line m, centered at T, intersecting the edge of circle P.
Using the compass measure between points S and N, draw an arc above line l, centered at N, intersecting the edge of circle Q.
Use the compass to construct a circle centered at P through point Q.
Mark this and return
Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope. The correct option is C.
How are parallel straight lines related?Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.
Since the given parallel line has equation y = 2x + 2 , thus its slope is 2 and thus, the slope of the needed line is 2 too.
The next step that Gerald should take is Using the compass measure between points S and N, draw an arc to the right of line m, centered at T, intersecting the edge of circle P.
Hence, the correct option is C.
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A school show had ticket sales of $1345 the first night and $935 the second night. 180 student tickets were sold and 110 adult tickets were sold on the first night. 100 student tickets were sold and 90 adult tickets were sold. find the price of a student ticket
Using a system of equations, it is found that the price of a student ticket is of $3.49.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The variables are given as follows:
Variable x: Price of a student ticket.Variable y: Price of an adult ticket.Considering the revenues and the number of tickets sold, the equations are given as follows:
180x + 110y = 1345.100x + 90y = 935.From the second equation:
90y = 935 - 100x
y = (935 - 100x)/90
y = 10.39 - 1.11x
Replacing in the first equation:
180x + 110y = 1345.
180x + 110(10.39 - 1.11x) = 1345
57.9x = 202.1.
x = 202.1/57.9
x = 3.49.
The price of a student ticket is of $3.49.
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Which graph represent f of x equals square root of the quantity x plus 2 end quantity minus 3? The graph shows a curve with an end point at 2 comma 3 that increasing to the right The graph shows a curve with an end point at 3 comma 2 that increasing to the right The graph shows a curve with an end point at negative 3 comma negative 2 that increasing to the right The graph shows a curve with an end point at negative 2 comma negative 3 that increasing to the right
The graph of the function:
[tex]f(x) = \sqrt{x + 2} - 3[/tex]
Is the last graph (bottom graph of the second image).
Which graph represents the given function?
Here we have the function:
[tex]f(x) = \sqrt{x + 2} - 3[/tex]
Remember that the argument of a square root must be zero or larger, then the minimum of the domain is the value of x such that:
x + 2 = 0
x = -2
Then the function starts at:
[tex]f(-2) = \sqrt{-2 + 2} - 3 = -3[/tex]
Then the graph should start at (-3, 2).
We can also identify another point by evaluating in x = 2.
[tex]f(2) = \sqrt{2 + 2} - 3 =2 - 3 = -1[/tex]
So the function also passes through (2, - 1).
Notice that the only graph that contains these two points is the last graph (the bottom graph on the second image), so that is the correct option.
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Answer:
D
Step-by-step explanation:
did the test got it right
What is the scale factor of a drawing if the scale is 1 inch equals 4 feet
Answer:
the scale factor of a drawing=1:4
Which of the following appear in the diagram below?
Answer:
Step-by-step explanation:
Comment
The one you can pick out that is true is D. The others you have to be careful with. C is a line and it has two arrowheads in the symbol above the two letters which makes it correct as well. A is not correctly marked, so it is not there the way it is marked. One would think ZX is a ray the way it is marked.
Answer: C and D
A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are approximately 2.2 pounds in 1 kilogram. Assuming the weight loss happened at a constant rate, about how many pounds did the group lose each day?
Answer:8.8 pounds a day
Step-by-step explanation:
7 days in a week
28/7=4 kg a day
2.2*4=8.8
8.8 pounds
URGENT!
Select the correct reason for each statement.
Step-by-step explanation:
if you have any doubts or queries regarding the answer please feel free to ask
Who wants to solve a question
70 packages can be filled from a jar that contains 7/8pounds of the leaves
Ratio and proportionsFractions are written as a ratio of two integers. If each bad contains 1/80 pound peppermint leaves, then;
1/80pounds = 1 package
To determine the total package for 7/8 pounds of leaves
7/8 pounds = x
Take the ratios
1/80 * 8/7 = 1/x
8/560 = 1/x
x = 560/8
x = 70
70 packages can be filled from a jar that contains 7/8pounds of the leaves
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Which table of ordered pairs represents a proportional relationship?
Answer:
The second table
Step-by-step explanation:
A proportional relationship is a relationship in which the ratio of two variables is equivalent.
2:10, 4:20, and 6:30 are all equivalent ratios that can all be simplified and written as 1:5, thus the second table is the correct answer
A carton of one dozen eggs costs $1.92. What is the unit price of each egg?
Answer:
$0.16
Step-by-step explanation:
unit price = price of carton / number of eggs
unit price = $1.92/12
unit price = $0.16
Jaime adds equations A and B to solve this system of equations. Why is this method
generally valid for solving a system of equations?
The elimination method is valid for the system of equation because the y term cancels.
How to solve a system of equation using elimination method?The system of equation can be solved using elimination methods.
Therefore,
x - 2y = 3
3x + 2y = 17
Hence,
x + 3x = 4x
-2y + 2y = 0
3 + 17 = 20
Therefore,
4x = 20
The y term cancels. Therefore, we can solve for x and later solve for y.
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Answer:
Adding a quantity like x – 2y to one side of an equation and another quantity like 3 to the other side maintains the equality if the two quantities are equal.
Jackson took 8 fewer pictures on Saturday than he did on Friday. If he took 11 pictures on Friday, how many pictures did he take on Saturday?
Friday =11
Saturday =?
But, we know that the pictures he took on Saturday are eight times fewer than those he took on Friday.
Saturday = 11-8
= 3
∴ He took 3 pictures on Saturday.
Hope this helps >3
2x²-5x-12=0 (simplify solution set)
Answer:
x = 4 or x = -3/2
Step-by-step explanation:
To simplify and solve this, let's use the quadratic formula.
So the format of a quadratic equation is supposed look like this:
[tex]ax^2+bx+c=0[/tex]
Let's find a, b, c:
a is the coefficient of x^2b is the coefficient of xc is the constant termNow let's solve the equation.
Let's solve your equation step-by-step.
2x^2−5x−12=0
For this equation: a=2, b=-5, c=-12
2x^2+−5x+−12=0
Step 1: Use quadratic formula with a=2, b=-5, c=-12.
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{-(-5)\pm\sqrt{(-5)^2-4(2)(-12)} }{2(2)}[/tex]
[tex]x=\frac{5\pm\sqrt{121} }{4}[/tex]
[tex]x=4[/tex] or [tex]x=\frac{-3}{2}[/tex]
Answer:
x = 4 or x = -3/2
From the top of a cliff 90 m high, the angle of depression of a boat on the sea is 26.2°. Calculate how far the boat is
a from the foot of the cliff,
b from the top of the cliff.
Answer:
a) 182.90 m
b) 203.85 m
Step-by-step explanation:
The relations between trig functions and measures in a right triangle are summarized in the mnemonic SOH CAH TOA. Here, we are given an angle and the side opposite, and we are asked to find the adjacent side and the hypotenuse.
__
a)The foot of the cliff to the boat is the adjacent side of the angle in our model. So, we can use the relation ...
Tan = Opposite/Adjacent
Solving for the adjacent side, we have ...
BF = (90 m)/tan(26.2°) ≈ 182.90 m
The boat is about 182.90 meters from the foot of the cliff.
__
b)The top of the cliff to the boat is the hypotenuse of the triangle we're using to model the situation. This means the applicable relation is ...
Sin = Opposite/Hypotenuse
BC = (90 m)/sin(26.2°) ≈ 203.85 m
The boat is about 203.85 meters from the top of the cliff.
An amusement park prices tickets at $55 and sells an average if 500 tickets daily. The management finds, over multiple increases in ticket pricing that a $2 increase in the price of a ticket leads to an average of 20 fewer tickets being sold in a day.
Management uses the combined function P to model the daily earning of the amusement part, where x is the number of $2 increases in the price of a ticket.
P(x) = -40x^2- 100x + 27,500
Use the given Information to complete the sentences.
The constant of the polynomial expression represents the
___ in the price of a ticket.
The binomial (500 - 20x) is a factor of the polynomial expression and represents the ___ in the price of a ticket.
The complete sentence is as follows:
The constant of the polynomial expression represents the daily earnings of the amusement park before any $2 increase in the price of a ticket.
The binomial (500 - 20x) is a factor of the polynomial expression and represents the number of tickets sold after x increases of $2 in the price of a ticket.
Given, An amusement park prices tickets at $55 and sells an average of 500 tickets daily. The management finds, over multiple increases in ticket pricing that a $2 increase in the price of a ticket leads to an average of 20 fewer tickets being sold in a day.
Management uses the combined function P to model the daily earning of the amusement part, where x is the number of $2 increases in the price of a ticket.
[tex]P(x) = -40x^2- 100x + 27,500[/tex].
What is the combined function?In mathematics, function composition is an operation ∘ that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.
We need to use the given information to complete the sentences.
The complete sentence is as follows:
The constant of the polynomial expression represents the daily earnings of the amusement park before any $2 increase in the price of a ticket.
The binomial (500 - 20x) is a factor of the polynomial expression and represents the number of tickets sold after x increases of $2 in the price of a ticket.
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The constant of the polynomial expression represents the daily earning of the amusement park before any $2 increase in the price of a ticket, and (500 - 20x) represents the number of tickets sold after x increases by $2.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
An amusement park prices tickets at $55 and sells an average if 500 tickets daily.
The function P(x) represents the daily earning of the amusement part, where x is the number of $2 increases in the price of a ticket.
Plug x = 0
P(0) = 27500
The above value is the constant of the polynomial function.
The constant of the polynomial expression represents the daily earning of the amusement park before any $2 increases in the price of a ticket.
As the x is the number of $2 increases in the price of a ticket.
Then,
= (500 - 20x) is the binomial that represents the number of tickets sold after x increases by $2
Thus, the constant of the polynomial expression represents the daily earning of the amusement park before any $2 increase in the price of a ticket, and (500 - 20x) represents the number of tickets sold after x increases by $2.
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What is the value of x?
(See attached image for details.)
Enter your answer in the box.
x = ...°
Answer:
x = 55°
Step-by-step explanation:
Hello!
The sum of angles in a triangle is 180°.
To solve for x, we have to subtract the given angles from 180°.
Solve for x180° = ∠1 + ∠2 + ∠x180° = 75° + 50° + x°180° - 75° - 50° = x°55° = x°The value of x is 55°.
Angle sum property of a triangle
Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.∠A + ∠B + ∠C = 180°
∠A = ?∠B = 75°∠C = 50°We need to find the value of ∠A
According to the angle sum property of a triangle
⇢∠A + ∠B + ∠C = 180°
⇢∠A + 75° + 50° = 180°
⇢∠A + 125° = 180°
⇢∠A = 180° - 125°
⇢∠A = 55°
What is the solution (a+b) to this system of linear equations
3a+6b=45
2a-2b=12
The value of the equation a + b is 12
How to determine the solution?The system of equations is given as:
3a + 6b = 45
2a - 2b = 12
Multiply the second equation by 1.5
3a - 3b = 18
Subtract this equation from the first equation to eliminate a
9b = 27
Divide by 9
b = 3
Substitute b = 3 in 2a - 2b = 12
2a - 2*3 = 12
Divide through by 2
a - 3 = 6
Add 3 to both sides
a = 9
So, we have:
a + b = 9 + 3
Evaluate
a + b = 12
Hence, the value of the equation a + b is 12
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Which expression represents the product of negative three-fourths x and –8x? negative 35 over 4 x 6x negative 35 over 4 x squared 6x2
The expression that represents the product of negative three-fourths x and –8x is 6x^2
How to determine the equivalent expression?The statement is given as:
the product of negative three-fourths x and –8x
Rewrite properly as:
-3x/4 * -8x
Divide 4 and 8 by 4
-3x * -2x
Multiply -3 and -2
6x * x
Multiply x and x
6x^2
Hence, the expression that represents the product of negative three-fourths x and –8x is 6x^2
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Answer:
answer is 6x2 or D
Step-by-step explanation:
sin2pheta/sinpheta + 1+cos2pheta/cospheta =
4sinpheta
4cospheta
2cospheta
2sinpheta
Answer:
4cos(θ)
{4cospheta}
Answer:
4cos(θ)
{4cospheta}
Step-by-step explanation:
[note, brainly doesn't allow pheta to be entered as a symbol when writing an equation, so I had to write it out, my apologies]
[tex]\frac{\sin \left(2pheta \right)}{\sin \left(pheta\right)}+\frac{1+\cos \left(2pheta\right)}{\cos \left(pheta\right)}\\[/tex]
[tex]\frac{1+\cos \left(2pheta\right)}{\cos \left(pheta\right)}\ = 2\cos \left(pheta\right)[/tex]
[tex]\frac{\sin \left(2pheta \right)}{\sin \left(pheta\right)}=2\cos \left(pheta\right)[/tex]
2cos(θ) + 2cos(θ) = 4cos(θ)
so, 4cos(θ) is your answer
(4cospheta)
hope this helps!! :)
A bakery has a sale on cookies. If a customer buys a dozen cookies for $15, each additional single cookie is $0.75. What is an equation that shows how the total cost depends on the number of single cookies purchased? (Assume that the order starts with a dozen cookies.) How much would a dozen cookies plus six single cookies cost?
Answer:
T = 15 + 0.75c
T = $19.5
Step-by-step explanation:
Assume that T stands for total cost and c stands for number of single cookies purchased, the equation would be:
T = 15 + 0.75c
Therefore, a dozen cookies plus six single cookies would cost:
T = 15 + 0.75(6)
T = 15 + 4.5
T = $19.5
A solid right pyramid has a square base with an edge
length of x cm and a height of y cm.
X
Which expression represents the volume of the
pyramid?
O1/3 xy cm³
O1/3 x²y cm³
O1/2 xy² cm³
O1/2 x²y cm³
The correct answer is option D which is the volume of the square pyramid will be [tex]V = \dfrac{1}{2}x^2y\ cm^3[/tex].
What is a square pyramid?A solid made up of a square base and four triangles connected side by side and meet at the same edge is called a square pyramid.
Given that:-
The side of the square base is x cmThe height of the pyramid is y cm.The volume of the pyramid will be calculated as:-
Volume = [tex]\dfrac{1}{2}[/tex] x Length of square pyramid x Height
Volume = [tex]\dfrac{1}{2}[/tex] x (x)² x y
Volume = [tex]\dfrac{1}{2}[/tex] x²y
Therefore the correct answer is option D which is the volume of the square pyramid will be [tex]V = \dfrac{1}{2}x^2y\ cm^3[/tex].
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