Select the correct answer from the drop-down menu.
A new park is adding two new walking paths, as indicated by and , which are measured in meters. The park resembles an isosceles trapezoid.
Figure shows a trapezium ABCD. AC and BD are diagonals. The length of BD is 14x plus 4, and AC is 11x plus 31.
Determine the length of each path.
A.
The length of each path is
130
meters.
B.
The length of each path is
140
meters.
C.
The length of each path is
120
meters.
D.
The length of each path is
150
meters.
Answers
A.The length of each path is 130 meters.
Given:
The park resembles an isosceles trapezoid.
Figure shows a trapezium . AC and BD are diagonals. The length of BD is 14x plus 4, and AC is 11x plus 31.
we know that:
Diagonals are equal in isosceles trapezoid.
14x + 4 = 11x + 31
14x - 11x = 31 - 4
3x = 27
divide by 3 on both sides
3x/3 = 27/3
x = 9
Diagonal length = 14x + 4.
= 14*9 + 4
= 126 + 4
= 130 meters.
Therefore The length of each path is 130 meters.
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Related Questions
A coin is tossed and a die is rolled. What is the probability of tossing a tail and then rolling a number greater than 5?
A. 5/6
b. 2/3
c. 1/12
d. 1/6
Answers
Answer:
the number greater than 5 is only 6 in the case of a coin.
Step-by-step explanation:
in a coin numbers greater than 5 is only 6
probability= No of required outcome/ No of possible outcome.
P.B= 1/6
in a coin there is head or tail
P.B of getting tail
P.B= Tail/Head + Tail
P.B= 1/2
The coin of course, has two sides, heads and tails. Assume we are talking about a six-sided die. Let's look at the individual probabilities.
There are only two sides to the coin, tails being one of them, so:
p(tails) = 1/2
The die goes from 1 to 6. We need to see the numbers that fit the inequality:
p(5 < x ≤ 6)
There is only one integer that is greater than five and less than or equal to six, and that is six. If there is only one number out of six, then:
p(>5) = 1/6
When dealing with probabilities, to determine the probability of two things happening, multiply both probabilities.
1/2 x 1/6 = 1/12
Give two ordered pairs on the line with equation x = 7
Answers
(7,0); (7,−5) ;(7,3); (7,10);. (7,y)
Step-by-step explanation:
Answer:
The equation x = 7 forms a vertical line which we refer to as undefined. So any points with a x value of 7 will pass through the line.
Step-by-step explanation:
For example, points like (7, 0) (7, 1) (7, 2) are all points that the line x = 7 passes through.
A point is made up of 2 values. An x-value and and a y-value. You simply plug in 7 for the x and any value for y.
Points that are on the line x = 7 include:
(7, 0)
(7, 1)
(7, 2)
(7, 4)
(7, 5)
(7, 6)
X
0
123
4
f(x)
36
54
81
121.5
182.25
کے
Using the given table, what are the y-values of the table?
Answers
Using the given table, the y-values are 36, 54, 81, 121.5, and 182.25.
We are given a table. Mathematical tables are collections of numbers that represent the outcome of a computation with varied arguments. The table has two columns and five rows. The first column shows the x-values. The second column shows the f(x) values. We know that y = f(x). So, the second column shows the y-values. The y-value is the vertical value in a pair of coordinates. It denotes how high or low the point is. In an ordered pair of coordinates, the y-coordinate is always written second (x, y). The five rows show the data points with corresponding x-values and y-values.
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Which letter(s) on the diagram below represents a radius of the circle?
Answers
Answer: AB
Step-by-step explanation:
Radius of a circle is defined as the distance from the center of a circle to its perimeter (the edge). Line AB is the only choice that meets this definition. CE is the diameter of the circle.
Answer:
AB
Step-by-step explanation:
radius goes in half the circle
At a carnival game, it cost Noah $12 to toss 30 rings. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
Answers
The table complete table that shows equivalent ratios is:
Toss Dollars
5 2
30 12
45 18
See image in the attachment that shows the points on a coordinate plane.
What are Equivalent Ratios?The ratios that give the same value when we compare them together are regarded as equivalent ratios.
For example, 2:3 is an equivalent ratio to 4:6, because 4/6 can be simplified as 2/3.
If it cost $12 to toss 30 rings, the ratio of dollars to number of toss would be: 12:30 = 2:5.
Let x = number of toss
Let y = amount in dollars
The equation that models the equivalent ratios can be written as y = 2/5x.
Therefore, when we have 2 dollars (y = 2):
2 = 2/5(x)
10 = 2x
10/2 = x
x = 5 toss
When we have 45 tosses (x = 45):
y = 2/5(45)
y = 18 dollars
The table of equivalent ratios would be:
Toss Dollars
5 2
30 12
45 18
The points, (5, 2), (30, 12), and (45, 18) are shown on the coordinate axes in the diagram below, where y = dollars, and x = toss.
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Find the value of z and z + 45.
angles:
(z+45)
55
78
Z
74
Answers
z = 144°
z + 45 = 189°
Explanation:
Angles in a five-sided polygon sum up to 540°.
z° + z° + 45° + 55° + 74° + 78° = 540°
Simplify:
2z° + 252° = 540°
2z° = 288°
Solve for z°:
z° = 288° / 2 = 144°
Hence, z° = 144°; z° + 45° = 189°
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Animal-like protists, which are heterotrophs and have the ability to move. Plant-like protists, which are autotrophs that photosynthesize.
Answers
Answer:
so the answer would be a protozoa
Step-by-step explanation:
.
There are 17 counters in a bag. The table shows the number of counters of each colour. Colour Number of Counters Red 7 What fraction of the counters are blue? Blue 2 Yellow 5 Green 3
Answers
Answer: 2/17 or 2 over 17
Step-by-step explanation:
Fill in the gaps in the equation below by
completing the square.
x² - 6x-1=(x −
|) ² − |
Answers
Answer:
(x -3)² -10
Step-by-step explanation:
You want the vertex form of x² -6x -1, found by completing the square.
Completing the squareThe square of a binomial is ...
(x -a)² = x² -2ax +a²
The constant in this perfect square trinomial is the square of half the coefficient of the linear term: a² = (-2a/2)²
ApplicationTo complete the square for the given quadratic, the perfect square trinomial must have a constant of (-6/2)² = 9. We can add and subtract 9 to rearrange the quadratic to the desired form.
x² -6x -1
= (x² -6x +9) -1 -9 . . . . . . . +9 -9 was added
= (x -3)² -10
For the polynomial below, -1 is a zero.
f(x)=x^3+5x^2+6x+2
Express f(x) as a product of linear factors.
Answers
The product of linear factors for f(x) is given as (x + 1)(x² + 4x + 2) for -1 as a zero of the polynomial x³ + 5x² + 6x + 2.
What is the factor theorem?The factor theorem states that;
f(x) is divisible by x - a if and only if f(a) = 0
f(x) is divisible by x + a if and only if f(-a) = 0
in both cases, a and -a are the zeros of the polynomials.
From the question, given that -1 is a zero of
f(x) = x³ + 5x² + 6x + 2, then it is divisible by x + 1 and f(-1) = 0.
Dividing x³ + 5x² + 6x + 2 by x + 1 using the long division will result to another factor x² + 4x + 2 with a remainder of zero. (complete long division is attached as a photo!)
Therefore we can then conclude that (x + 1)(x² + 4x - 2) is the product of linear factors for f(x) = x³ + 5x² + 6x + 2 and -1 as a zero.
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For each ordered pair, determine whether it is a solution to the system of equations.
Answers
Answer:
no, no, yes, yes
Step-by-step explanation:
You want to know which of the ordered pairs are solutions to the given system of equations: 6x -3y = 9, y = 2x -3.
GraphThe attached graph shows that the two equations describe the same line. The given points are plotted on the same graph. The ones on the line are solutions.
(4, -5) . . . not a solution
(-1, 8) . . . not a solution
(7, 11) is a solution
(0, -3) is a solution
The diameter of the circle is 10 centimeters and the measure of is 72º. Find the length of.
Round your calculations to the nearest tenth. Complete your work in the space provided.
Answers
The arc length of the segment it 6.28 meters
How to calculate the arc length using?From the question, we have the following parameters:
Central angle, x = 72 degrees
Diameter, d = 10 centimeters
The radius of the circle can be calculated using
r = d/2
So, we have
r = 10/2
Evaluate
r = 5 cm
The exact arc length using the central angle measure is calculated as:
Arc length = x/360 * 2πr
Substitute the known values in the above equation
Arc length = 72/360 * 2π * 5
Evaluate
Arc length = 6.28
Hence, the exact arc length using the central angle measure is 6.28 meters
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Possible question
The diameter of the circle is 10 centimeters and the measure of is 72º. Find the length of arc
Round your calculations to the nearest tenth. Complete your work in the space provided.
Q2) Megan, a sales representative at a jewelry store,
receives a 1.50% commission for the first $12,000 in
sales she makes, 3.50% for the next $25,000, and
6.00% thereafter. If she was paid $2,000.00 in
commissions last month, calculate the amount of sales
she made.
Answers
She made sales of =$61,200.00
WHAT is compound intrest?Compound interest is, to put it simply, interest that is earned on interest. Compound interest is interest that is earned on both the initial principal and interest that builds up over time in a savings account.Over time, you will earn more interest if an account has a greater interest rate and compounding occurs more frequently. Compound interest is calculated as follows:Initial balance = 1 + (interest rate / period's worth of compoundings).acc to our question-
Step-by-step explanation:
1.5% = 0.015 , 4% = 0.04 , 5% = 0.05
16,000 × 0.015 = $240.00
$25,000 × 0.04 = $1,000.00
$2,250.00 - ($240.00 + $1,000.00) = $1,010.00
$1,010.00 ÷ 0.05 = $20,200.00
$20,200.00 + $25,000.00 + $16,000.00 = $61,200.00
hence,She made sales of =$61,200.00
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Calculate the average speed if a car travels 213 km in 2 hours and 30 minutes
Answers
Answer:
average speed of car is 48 km/hr.Answer:
85.2 km/h
Step-by-step explanation:
you are looking for the average speed of a car=rate of the car
distance =213km
time=2 hours 30 minutes also 2 1/2h or 2.5h
distance =rate×time
213km=rate×2.5h
(transpose)
213km÷2.5h=rate
85.2km/h=rate
hope this helps!!!
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Rotation of a Point
What is the image of the point (-7, 9) after a rotation of 270° counterclockwise
about the origin?
(00)
Answers
The highlighted point is (9, -7) . A shape or item is said to be rotated when it is spun around a central point (center) without being moved in any other direction. Size and shape are unaffected by rotation. Basic Transformations in Geometry.
What does it mean to rotate around a point?A shape or item is said to be rotated when it is spun around a central point (center) without being moved in any other direction. Size and shape are unaffected by rotation. Basic Transformations in Geometry.
If the picture is the point (-7, -9)
Detailed explanation:
When the point (x, y) rotates 90 degrees counterclockwise with respect to the origin, its image is (-y, x)
When the point (x, y) rotates 180 degrees counterclockwise around the origin, its image is (-x, -y)
The picture of the point (x, y) if it were rotated 270 degrees counterclockwise with respect to the origin is (y, -x)
The highlighted point is (9, -7)
∴ x = 9 and y = -7
The provided point is turned 270 degrees counterclockwise with respect to the origin.
Utilizing the third rule listed above
The illustration of the point is (y, -x)
That is to say, alter the x-sign coordinate's before switching them.
∵ x = 9 and y = -7
The illustration if the point is (-7,-9).
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Reflect across the y-axis.
H(1,-3)→H
Z(1,2)→ Z
W(4,1)→ w
Answers
Reflection across the y-axis is H(-1,-3), Z(-1,2) W(-4,1).
When point M (h,k) is reflected along the y-axis, the image M' with coordinates of forms in the second quadrant (-h, k).
Thus, we get the conclusion that when a point is mirrored along the y-axis, the y-coordinate stays constant but the x-coordinate changes to the negative.
H(1,-3) → H(-1,-3)
Z(1,2) → Z(-1,2)
W(4,1) → W(-4,1)
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efetue as adições 3/4 + 1/2
Answers
Fraction form : 3/4 + 1/2
= 3/4 + 1x2/2x2
= 3/4 +2/4
= 3+2/4
= 5/4 = 1 1/4
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answers
The statement that is true about the quadratic function is (b) the graph of the function is a parabola.
How to determine the true statements?The quadratic function is given as
f(x) = x2 – 5x + 12
Rewrite as
f(x) = x² – 5x + 12
All quadratic functions are parabola
This means that option (b) is true
Set x = -10 to calculate f(-10)
So, we have
f(-10) = (-10)² – 5(-10) + 12
Evaluate
f(-10) = 162
This means that option (a) is false
Set x = 20 to calculate f(20)
So, we have
f(20) = (20)² – 5(20) + 12
Evaluate
f(20) = 312
This means that option (d) is false
Set x = 0 to calculate f(0)
So, we have
f(0) = (0)² – 5(2) + 12
Evaluate
f(0) = 12
This means that option (e) is false
The leading coefficient in f(x) = x² – 5x + 12 is positive
Graphs with positive leading coefficient opens up
This means that option (c) is false
Hence, the true statement about the quadratic function is (b)
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PLS ANSWER THIS QUESTION
FAST
WILL MARK BRAINLIEST
Answers
Angle x= 45
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.Vertex: The intersection of two lines or sides at an angle is called a vertex. In the diagram, O is the vertex.Arms: The angle's two sides linked at a single end. The arms of an angle are OA and OB.Initial Side: A straight line from which an angle is drawn, sometimes referred to as the reference line. The reference line is OB.The side that the angle measurement is done up to is known as the terminal side. OA is the terminal side in the diagram that is shown below.acc to the question-
N + M = 90X + X= 902X=90X=45Hence, Angle x= 45
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The graph of the absolute value parent function, f(x) = |x), is stretched
horizontally by a factor of 3 to create the graph of g(x). What function is g(x)?
OA. g(x)= x+3|
OB. g(x) = 31x1
C. g(x) = 13x1
OD. g(x)= |||
Answers
Answer:
OB. g(x) = 31x1
C. g(x) = 13x1
Step-by-step explanation:
The table shows a proportional relationship between x and y.
x 3.6 12.2 2.1
y 14.4 48.8 8.4
Which of the following correctly describes the graph of the relationship?
OA line that goes through (3.6, 14.4) and (48.8, 12.2)
OA line that goes through (14.4, 3.6) and (12.2, 48.8)
OA line that goes through (0, 0) and (3.6, 14.4)
OA line that goes through (0, 0) and (14.4, 3.6)
Answers
The correct answer which define proportional relationship between x and y is OA line that goes through (0, 0) and (3.6, 14.4)
What does proportionality mean to you?
Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.
As we can see that in the given question [tex]\frac{x}{y} =\frac{1}{4}[/tex]
and there is only one option which fits this ratio is third one
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Answer:
to simplify the dude aboves' answer its C
Step-by-step explanation:
A line that goes through (0, 0) and (3.6, 14.4)
Which expression is equivalent to
-2 + 4/5h -1
Answers
Answer:
1/2=0.5
Step-by-step explanation:
-2+4/5°-1=1/2
What is the price of a jacket that originally costs $125 but has a 25%
discount?
Answers
Answer:
$93.75
Step-by-step explanation:
$125 × 0.75 = $93.75
PLEASE MARK AS BRAINLIEST!!!Answer:
$93.75
Step-by-step explanation:
125x0.25
31.25
125-31.25
$93.75
Hopes this helps
f: x → 15/x - 5 What number must be excluded from the domain of f?
Answers
Answer:
x = 5
Step-by-step explanation:
You want to know what number must be excluded from the domain of f(x) = 15/(x -5).
DomainThe domain of a function is the set of numbers for which it is defined. The function f(x) = 15/(x-5) will be undefined when the denominator is zero:
x -5 = 0
That will be the case when x = 5.
The domain of f must exclude x=5.
How do work out 349 divided by 60
Answers
Answer:
5 with a remainder of 49
Step-by-step explanation:
A harbour seal dives 35 metres below the ocean's surface. Then it dives down an additional 12 metres Determine the seal's new position relative to the surface of the ocean?
Answers
The seal's new position relative to the surface of the ocean is 47 meters below.
How to calculate the value?It is important to note that that question has to do with elevation which is the change in position with regards to the sea or ocean level.
In this case, the harbour seal dives 35 metres below the ocean's surface and then it dives down an additional 12 metres
The new position will be;
= -35 - 12
= -47
This implies that it's 47 meters below the ocean surface.
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A trust company offers 3-year compund interest GIC earning annual interest of 5.50% compounded monthly or 5.70% compounded semi-annually. Which rate should an investor choose?
Answers
As per the given interest rate and types of annual interest , investor should choose compounded monthly as it gives interest more frequently .
As given in the question,
Time period to calculate the compound interest = 3years
Interest rate compounded monthly = 5.50%
Each month interest output is 5.64079
Rate of interest compounded semi- annually = 5.70%
Each month interest output is 5.78123
Compounded monthly gives interest every month and semi-annually gives twice a year.
Monthly is more frequent compare to semi-annually.
Investor should choose monthly.
Therefore, as per the given interest rate and types of annual interest , investor should choose compounded monthly as it is more frequent .
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From an elevation of 10.7 meters below the surface of the ocean a penguin can dive at a rate of 146 meters per minute what is the penguin's depth (d) after 4 minutes (m)
The function rule is: BLANK
After 4 minutes the penguin's depth is: BLANK
Answers
The penguin's depth after 4 minutes is d = 10.7 + 146m
what is rate?A rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate. The word "per" can be further replaced by the symbol "/" in problems.
if the penguin moves with a speed of 146 meters per minute, then its distance after m minutes is = 146 x m
Since it moved from an elevation 10.7 below the sea surface, its total distance(d) would be = 10.7 + 146m
substitute m = 4 minutes,
we have
d = 10.7 + 146(4)
d = 594.7metres
In conclusion, the function rule is 10.7 + 146m and the distance d covered after 4 minutes is 594.7 meters
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What is the solution to the equation 3m-4-3/2m+8=0?
Om = -24
Om = -12
Om = -6
O m = -4
Answers
Answer:
[tex]m=-8/3[/tex], the options are wrong
Step-by-step explanation:
[tex]3m-4-\frac{3}{2}m+8=0 \\ \\ 6m-8-3m+16=0 \\ \\ 3m+8=0 \\ \\ m=-\frac{8}{3}[/tex]
The question is incorrect.
How do I solve this ?
Answers
See attachment, this took me a while so please say thanks and rate <3