In the diagram shown,
ABCE is a trapezium,
AD is parallel to BC,
DE = 4cm,
Area of ABCE = 60cm^2,
Area of ABCD = 48cm^2,
Work out the values of f and g.
You must show all your working.
Answers
The values of f and g are;
f = 6
f = 6g = 8
We are given the trapezium ABCE where;
AD is parallel to BC
DE = 4 cm
Area of ABCE = 60 cm²
Area of ABCD = 48 cm²
f and g are sides of the rectangle ABCD. Thus;
fg = 48 - - - (eq 1)
Also,for the trapezium ABCE;
½(g + g + 4)f = 60
(2g + 4)f = 120 - - - (eq 2)
From eq 1, f = 48/g
Thus;
(2g + 4) × (48/g) = 120
96 + 192/g = 120
192/g = 120 - 96
192/g = 24
g = 192/24
g = 8
Thus;
8f = 48
f = 48/8
f = 6
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Related Questions
Plz help me it’s emergency
Answers
Answer:
idk
Step-by-step explanation:
1/4 can also be written as .25
1 divided by 4 is .25
114 times .25 = answer
154 times .25 = answer
For f(x)=4x+1 and g(x)=x^2-5 , find (fg) (x) .
A.4x^3+x^2-20x-5
B.4x^3+x^2-5x-5
C.4x^3+x^2-4x-6
D.4x^2-19
Answers
Answer:
the answer is B.
4x^3+x^2-5x-5
Step-by-step explanation:
multiply: (sqrt10 +2 sqrt8)(sqrt10-2 sqrt8)
Answers
Answer:
(√10 +2√8)(√10 -2√8)=
(10 -8√5 + 8√5 -32)
10+0-32
10-32
= -22
Hope this helps.
Answer:
The other person is right, A. -22
Step-by-step explanation:
Which of the following terms correctly describe the object below?
Check all that apply.
Answers
Answer:
Pyramid
Step-by-step explanation:
Because a pyramid has a polygon as its base
Answer:
The correct answers are A. polyhedron. and C. pyramid
Step-by-step explanation:
will mark bianleast plz asap
What is the mode of the data set?
Line plot titled Books Read with 0 - 3 dots, 1 - 2 dots, 2 - 7 dots, 3- 6 dots, 4 - 4 dots, 5 - 2 dots, 6 - 1 dot.
Six books
Two books
Four books
Three books
Answers
Answer:
2 books
Step-by-step explanation:
The mode is the one that is most frequent, and reading 2 books during the summer is the most frequent thing to do in this diagram as it has been performed the most times.
Hope this helps!
treviglaslibrary
8. Lilly paid $19.16 for a 1kg apple basket. This amount includes a tax of 3%. What was the cost of the apple before tax?
Answers
Answer:
$18.59
Step-by-step explanation:
19.16=100%
0.1916=1%
97(0.1916)
18.59
Answer:
$18.5852
Step-by-step explanation:
help me please <3 thank youu
Answers
Answer:
7,2,3
D
Step-by-step explanation:
Which of the following represents a 1.00 M (M = mol/dm3) aqueous solution of glucose (C6H12O6)?
A. 180 g glucose per 1000 cm3 solution
B. 10.0 g glucose per 10.0 cm3 water
C. 90.0 g glucose per 500 cm3 water
D. 0.100 g glucose per cm3 solution
Answers
Answer:
Option C. 90.0 g glucose per 500 cm3 water
Step-by-step explanation:
1.00 M (mol/dm3) aqueous solution of glucose (C6H12O6) means that 1 mole of glucose is dissolved in 1dm³ (1000cm³) of water.
The concentration of a substance is defined as the mole of solute per unit volume of solvent (water) in dm³.
Option A is wrong since it state: 180g of C6H12O6 per 1000cm³ of solution. Concentration is always expressed as per 1000cm³ or dm³ of water.
For option B:
We shall determine the number of mole of C6H12O6, followed by the concentration.
This is illustrated below:
Molar mass of C6H12O6 = (12x6) + (12x1) + (16x6) = 180g/mol
Mass of C6H12O6 = 10g
Mole = Mass /Molar Mass
Mole of C6H12O6 = 10/180 = 0.056 mole.
Volume of water = 10cm³ = 10/1000 = 0.01dm³
Concentration = mole /Volume
Concentration = 0.056/0.01 = 5.6mol/dm³
Option B is wrong
For option C:
We shall determine the number of mole of C6H12O6, followed by the concentration.
This is illustrated below:
Molar mass of C6H12O6 = 180g/mol
Mass of C6H12O6 = 90g
Mole = Mass /Molar Mass
Mole of C6H12O6 = 90/180 = 0.5mole
Volume of water = 10cm³ = 500/1000 = 0.5dm³
Concentration = mole /Volume
Concentration = 0.5/0.5 = 1mol/dm³
Option C is correct.
For option D is wrong as well as it states 0.1g of C6H12O6 per cm³ of solution. Concentration is always per 1000cm³ or dm³ of water.
From the above illustrations, option C is the correct answer.
IS THIS A FUNCTION OR NOT HELP PLEASEEEEEE! The table compares the amount of homework Khaled gave to his class, and the number of students who completed them, for several different occasions. Can the number of students who completed their homework be represented as a function of the homework's size? Homework (# of questions) Complete (# of students) 5 55 30 3030 8 88 24 2424 6 66 26 2626 10 1010 20 2020 4 44 32 3232 7 77 25 2525 6 66 26 2626 8 88 24 2424 Choose 1 answer:
Answers
Answer: The answer is Yes.
Step-by-step explanation:
Can not represent as a function. since some output have more than one input
What is sample space?The sample space S of a random experiment is defined as the set of all possible outcomes of an experiment. In a random experiment, the outcomes, also known as sample points, are mutually
No, because various numbers of students complete different sizes of homework, the number of students who finish their homework cannot be expressed as a function of the size of the assignment.
Khaled, for instance, was assigned a size 8 assignment twice, and on each occasion, a different amount of pupils finished it (24 and 21). There should only be one output for each input in a function, yet in this situation, some inputs have more than one output.
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Complete question:
The table compares the amount of homework Khaled gave to his class, and the number of students who completed them, on several different occasions. Can the number of students who completed their homework be represented as a function of the homework's size?
Homework Complete
5 30
8 24
6 26
10 20
4 32
7 25
6 26
8 24
On a soccer team 40% of the goal are scored by a star player on the team.If 70 goals were scored all season, how many are scored by the rest of the team? Plz help me
Answers
Answer:
42
Step-by-step explanation:
During the season, 40% of the goals are scored the by the star player. This means that 60% of the goals are scored by everyone else.
100% - 40% = 60%
To find how many goals are scored by the rest of the team, convert the percentage to a decimal. You then have to multiply the decimal by the total goals scored.
60% = 0.6
70 × 0.6 = 42
The rest of the team scored 42 goals.
Answer:
42
Step-by-step explanation:
40% of 70=28
70-28=42
A survey was held to find the time taken by students to reach school from their homes. Each student was asked to choose from 10, 20, 30, 40, or 50 minutes. What is the mode for the data set?
A. 30 min.
B. 10 min.
C. 20 min.
D. 40 min.
only thoughts answer's if u give a bad one no brainly
Answers
Answer:
there is no mode
Step-by-step explanation:
because there is no doubles
The required, mode of the given data set is not defined. None of the options are correct.
What is the mode?In statistics, the mode is the value that appears most frequently in a data set. It is the most common observation or measurement in the data set. The mode is one of the measures of central tendency, along with the mean and median.
The mode is the value that appears most frequently in a data set. Since the given data set only has values of 10, 20, 30, 40, and 50, we can simply count which value appears most frequently. From the given options, the is no mode in the data, since it appears no value in the data set appears twice in the data set.
Therefore, None of the options are correct.
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Classify the following triangle based on its shape.
A. Right
B. Isosceles
C. Equilateral
D. Scalene
Please answer this
Answers
Answer:
A
Step-by-step explanation
the square in the corner
The shape of the given triangle is right angle.
The square in the corner
We have given that,
A. Right
B. Isosceles
C. Equilateral
D. Scalene
We have to determine the shape of the given triangle.
What is the right angle?
A right angle is an angle of exactly 90 degrees or \pi /2 radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles.
The shape of the given triangle is right angle.
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In a bag there are 3 red marbles, 2 yellow marbles, and 1 blue marble. What is the likelihood of a yellow marble being selected on the first draw?
Answers
Answer:
1/3
Step-by-step explanation:
there's 6 total marbles and 2 are yellow so this can be expressed as 2/6 which can be simplified to 1/3.
hope it helps!
Answer:
1/3
Step-by-step explanation:
The total number of marbles
3 red marbles, 2 yellow marbles, and 1 blue marble = 6 marbles
P( yellow) = yellow / total
= 2/6
= 1/3
A small toy rocket is launched from a 20-foot pad. The height (h, in feet) of the rocket t seconds after
taking off is given by the formula h = – 2t^2– 6t + 20. How long will it take the rocket to hit the
ground?
Answers
Answer:
t = 2 sec
Step-by-step explanation:
h = – 2t²– 6t + 20
When the rocket hits the ground. h = 0 ft.
– 2t²– 6t + 20 = 0 /: (-2)
t² + 3t - 10 = 0
(t + 5)(t - 2)=0
t = - 5, t = 2
Time can be only positive.
Find the quotient of 1 5/6÷ 2 1/8 Give your answer as a fraction in its simplest form.
Answers
Answer:
1 5/6 = 11/6
2 1/8 = 17/8
11/6 ÷ 17/8
11/6 × 8/17
= 44/51
Hope this helps.
Answer:2.67 or 4/2
Step-by-step explanation: it just is
Graph the inequality.
3x + 4y <4
In the box below, describe the graph.
Answers
Answer:
y < 1 - (3x)/4
Step-by-step explanation:
Graph the inequality by finding the boundary line, then shading the appropriate area.
y < 1 − 3 x /4
the graph is partially shaded. the shade crosses through (0,1) and (1,0). I hope you can figure that out :)
what is the equation of a line that passes through the points -2 -2 and has a slope of four
Answers
Answer:
y = 4x + 6
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 4, thus
y = 4x + c ← is the partial equation
To find c substitute (- 2, - 2) into the partial equation
- 2 = - 8 + c ⇒ c = - 2 + 8 = 6
y = 4x + 6 ← equation of line
Which of the following represents 45 = 5 × 9?
A.
45 is 3 times as many as 15
B.
9 is 5 times as many as 45
C.
5 is 9 times as many as 45
D.
45 is 9 times as many as 5
Answers
Answer:
D 45 is 9 times as many as 5
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
45 is 9 times as many as 5 is the answer because when you turn the equation 45=5*9 into words, it has three numbers 9, 5 and 45. 45 is the product of 9 and 5 and 9 and 5 are the numbers that must be multiplied to give the product 45.
A building 50 feet high casts a shadow 68 feet long. Find the measure of the angle of elevation of the sun. Round answer to nearest while degree
Answers
Answer:
36 °
Step-by-step explanation:
In this case a rectangular triangle is formed so we can use the trigonometric functions to calculate the angle, they give us the value of the two legs, therefore we can apply the tangent function.
Tan A ° = opposite / adjacent
replacing:
Tan A ° = 50/68
Tan A ° = 0.735
A ° = arc tan (0.735)
A ° = 36.32
Which means that the angle of inclination is 36°
Here is a picture of a Ferris wheel. It has a diameter of 80 meters.
About how far does a rider travel in one complete rotation around the Ferris wheel? Round your answer to the nearest whole number. Use 3.14 for π.
Enter your answer in the box below.
_____ meters
Answers
Answer:
251.2 m
Step-by-step explanation:
Circumference = 2 x π x r
C = 2 x 3.14 x 40
C = 251.2
Circumference of a circle
The path or the boundary that encircles any shape is defined by its circumference. In other words, the perimeter is another name for the circumference, which makes it easier to determine how long a shape's outline is. The circle's perimeter is measured in this way. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it.
We take radius of the circle and pi to calculate the circumference of circle.
The formula of circumference of circle is 2πr.
R is radius of the circle and π is mathemetical constant which value approx 3.14
In the question it is given that the diameter of a wheel is 80m. So, radius is half of diameter, 40m.
So, the circumference = 2πr
= 2 × 3.14 × 40 = 251.2m
Rider has to travel 251.2m to cover one complete rotation.
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pls help help me need help!! thank you!!
Answers
Answer: 55 feet of rope
Step-by-step explanation:
The absolute value of -30 is the distance 30 is away from 0, so |-30| = 30. And |25| = 25.
|-30| + |25| = 30 + 25 = 55
1. Water is filling a bathtub at a rate of 7 gallons per minute. Complete the table of equivalent
ratios for the first 5 minutes of the bathtub filling up.
Answers
Answer:
amount of water: 7, 14, 21, 28, 35
time : 1,2,3,4,5
Determine whether (2, - 1) and (-4, 2) satisfy the inequality 2x – 3y > 4.
O (2, -1) satisfies the inequality, but (- 4, 2) does not.
Both (2, -1) and (-4, 2) satisfy the inequality.
(-4,2) satisfies the inequality, but (2, - 1) does not.
Neither (2, - 1) nor (- 4,2) satisfies the inequality.
Answers
Answer:
Both
Step-by-step explanation:
The correct option is (2, -1) satisfies the inequality, but (- 4, 2) does not.
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:
(2, - 1) and (-4, 2) and inequality 2x – 3y > 4
Now, (2, -1)
2(2) - 3(-1)
4 + 3
7>4
and, take (-4, 2)
2(-4) - 3(2)
= -8 -6
= -14 < 4
Hence, (2, -1) satisfies the inequality, but (- 4, 2) does not.
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Solve for : 3 2 + −10 = 0. PLEASE HELP
Answers
Answer:
Step-by-step explanation:
32+(-10)
32-10
22 is not equal to 0
so its false
Answer: no solution
Step-by-step explanation:
Remove parentheses.
32+-10=0
Simplify 32+-10 to 32-10
32-10=0
Simplify 32-10 to 22
22=0
Since 22=0 is false, there is no solution.
An electrician charges $15 per hour and spends $30 a day on gasoline. At the
end of the day, he is left with $105. Represent his earnings for one day using
a mathematical statement if he works for "x" hours in a day.
Answers
directly with the number of tickets suppose seven tickets cost 126 how much would 12 tickets cost
Answers
Explanation: first you have to do 126/7 to find out how much each individual ticket costs. That would be 18 dollars per ticket. Then you do 18*12 and you get $216.
Answer:
$216
Step-by-step explanation:
126 ÷ 7 = $18
18 × 12 = $216
I’m really confused the question is on shapes
Answers
Answer:The polygon has 18 sides.
Step-by-step explanation;since it is a straight line, we get 8x since they said that each interior angle is 8 times the exterior angleso it is 8x =x which is the exterior angle +180 degrees since it is a sraight line.
n:
Answer:
A) Each Interior Angle = 180 degrees - (360 / number sides)
B) Each Exterior Angle = 360 / number of sides
A) = 8 * B)
8 * 360 / # sides = 180 - (360 / #sides)
We'll call # sides as "n".
2,880 / n = [ 180 - (360 / n)]
2,880 = n * [ 180 -(360 / n)]
3,240 = 180n
180n = 3,240
n = 18 sides.
The polygon has 18 sides which is an octadecagon.
Step-by-step explanation:
Which of the following is equal to the rational expression when x ≠ -6 ?
Answers
Answer:
X-6
Step-by-step explanation:
Just did this one
A cylinder has a volume of 24 cubic feet. Which of the following could have the same radius and height as the cylinder? A A cone with a volume of 32 cubic feet B A sphere with a volume of 18 cubic feet C A cone with a volume of 72 cubic feet D A cone with a volume of 8 cubic feet
Answers
Answer:
A. a cone with a volume of 32 cubic feet
Step-by-step explanation:
The question is attached
perimeter
Answers
Answer:
62 cm
Step-by-step explanation:
48/4 = 12 so 1 side = 12
the base of the triangle therefore must also be 12 so 38 - 12 = 26
26 + 36 = 62
(2 sides of triangle + 3 sides of square)
