Plot the points A(−2, − 2), B(4, −2), ( 8, 3) and D(−3, 3 ) on the Cartesian plane. Join them in order and identify the figure so formed. Join AC and BD. Also write the coordinates of the points of intersection of both the diagonals with the X-axis as well as the Y-axis.
Answers
Answer:
The shape formed is trapezium
Step-by-step explanation:
Diagonal BD point of intersection with the y-axis = (0, 9) ,
Point of intersection of diagonal BD with the x-axis = (1.2, 0)
Diagonal AC point of intersection with the y-axis = (2, 0),
Point of intersection of diagonal AC with the x-axis = (0, 1)
Length of segment DC = 10.99 ≈ 11
Length of segment AB = 6.04
Length of segment DA = 5.13
Length of segment CA = 6.38
The perimeter of the formed trapezium = 11 + 5.13 + 6.38 + 6.04 = 28.55
The area of the trapezium = 1/2*(sum of parallel sides)*distance between the parallel sides
The parallel sides are DC and AB
The area of the trapezium = 1/2*(6.04+11)*5 = 42.6 unit.
Related Questions
what is the slope of y =2x-1
Answers
Answer:
The slope m = 2Step-by-step explanation:
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept
We have the equation:
y = 2x - 1 → m = 2, b = -1
Answer:
The slope of this equation is 2.
Step-by-step explanation:
In a y=mx+b equation, the slope is 'm,' so whatever number is before x in an equation like this is the slope.
So y=mx+b -> y=2x+b -> 2=m, b=-1
Dora can plant 150 flowers in the same time it takes charlie to plant 120 flowers. Also Dora can plant 18 flowers more per day than charlie. How many flowers can Charlie plant per day?
Answers
Answer:
Number of flowers planted planted by Charlie per day = 72
Step-by-step explanation:
Given:
Dora can plant 150 flowers and Charlie plants 120 flowers in same time.
Dora can plant 18 flowers more per day than that of Charlie.
To find:
Flowers that can be planted by Charlie per day = ?
Solution:
Let the time taken by Dora to plant 150 flowers = T days
So, T will be the time taken by Charlie to plant 120 flowers.
Number of flowers planted by Dora per day = Total Number of flowers planted by Dora divided by number of days
Number of flowers planted by Dora per day = [tex]\frac{150}{T}[/tex]
Similarly, Number of flowers planted by Charlie per day = Total Number of flowers planted by Charlie divided by number of days
Number of flowers planted by Charlie per day = [tex]\frac{120}{T}[/tex]
As per condition given:
[tex]\dfrac{150}{T} = \dfrac{120}{T} +18[/tex]
Solving the above equation by taking LCM:
[tex]\Rightarrow \dfrac{150}{T} = \dfrac{120 +18T}{T}\\\Rightarrow 150=120+18T\\\Rightarrow 18T = 30\\\Rightarrow T = \dfrac{30}{18}\\\Rightarrow T = \dfrac{5}{3}\ days[/tex]
Number of flowers planted by Charlie per day = [tex]\frac{120}{T}[/tex] = [tex]\frac{120\times 3}{5} = 72[/tex]
So, answer is:
Number of flowers planted planted by Charlie per day = 72
what is the slope of a line parallel to the line whose equation is 3x-3y=-45
Answers
y = x + 15
This means the slope of a line parallel to the given line is 1.
Answer:
The slope is 1Step-by-step explanation:
To find the slope first write the equation in the form
y = mx + c
where m is the slope
c is the y intercept
3x - 3y = -45
3y = 3x + 45
Divide both sides by 3
y = 3/3x + 45/3
y = x + 15
From the equation the slope = 1
Parallel lines have equal slope
So
The line parallel to the above line is also
1
Hope this helps you
Please help! I need help with this question!
Answers
Explanation:
The vertical angles at C are congruent with each other, so we have the necessary conditions to invoke the SAS congruence postulate:
∆BCA ≅ ∆ECD
BA ≅ ED by CPCTC (corresponding parts of congruent triangles are congruent)
How to do this question plzzz
Answers
Hi king,
Let's split it into two prisms.
1st prisim volume:[tex]V_{1}=5cm*10cm*3cm\\V_{1} =150cm^{3}[/tex]
2nd prisim volume:[tex]V_{2}=5cm*10cm*(9cm-5cm)\\V_{2}=5cm*10cm*4cm\\V_{2} =200cm^{3}[/tex]
The prism in the picture:
[tex]V_{final}=150cm^{3} +200cm^{3} \\V_{final}=350cm^{3}[/tex]
Have a good day.
In Central City, Elm Street and Maple Street are parallel to one another. Oak Street crosses both Elm Street and Maple Street as shown.
Choose True Or False for each statement
Answers
Answer:rut
Step-by-step explanation:
Three years after a company was founded, its assets were $11,283,500. Ten years after being founded, its assets had grown to $21,794,600. During that period of time, at what rate did the company's assets grow per year?
Answers
Answer:
$1,051,110Step-by-step explanation:
Given
Step one:
Company's initial asset value = $11,283,500
Company's final asset value = $21,794,600
Step two
we can calculate the company's asset appreciation after 10 years as
$21,794,600- $11,283,500= $10,511,100
Step three
Hence, the growth rate of the company's asset value per year can be expressed as = $10,511,100/10= $1,051,110
write the recurring decimal 0,101010101... . as a fraction in its simplest form.
Answers
Answer:
[tex]\frac{10}{99}[/tex]
Step-by-step explanation:
Answer:
[tex]\frac{10}{99}[/tex]
Step-by-step explanation:
We require to create 2 equations with the repeating decimal after the decimal point.
let x = 0.10101.... → (1)
Multiply both sides by 100
100x = 10.10101.... → (2)
Subtracting (1) from (2) eliminates the repeating decimal, thus
99x = 10 ( divide both sides by 99 )
x = [tex]\frac{10}{99}[/tex]
Unit test Problem Becky tried to evaluate an expression step by step. \quad\begin{aligned} &\dfrac{4}{5} +7 -\dfrac{5}{4}\\\\ \\ =&\dfrac{4}{5} -\dfrac{5}{4}+7&\green{\text{Step } 1} \\\\ \\ \\ =&0+7&\blue{\text{Step } 2}\\\\ \\ \\ =&7&\purple{\text{Step } 3} \\\\ \\ \\ \end{aligned} = = = 5 4 +7− 4 5 5 4 − 4 5 +7 0+7 7 Step 1 Step 2 Step 3 Find Becky's mistake.
Answers
Answer:
Becky's mistake was that she said [tex]\frac{4}{5} - \frac{5}{4} = 0[/tex], while it's actually equal to [tex]-\frac{9}{4}[/tex].
Step-by-step explanation:
[tex]\quad\begin{aligned} &\dfrac{4}{5} +7 -\dfrac{5}{4}\\\\ \\ =&\dfrac{4}{5} -\dfrac{5}{4}+7&\green{\text{Step } 1} \\\\ \\ \\ =&0+7&\blue{\text{Step } 2}\\\\ \\ \\ =&7&\purple{\text{Step } 3} \\\\ \\ \\ \end{aligned}[/tex]
Step 1 looks fine as she just rearranged the equation, keeping the negatives and positives right.
Step 2 is where she said that [tex]\frac{4}{5} - \frac{5}{4} = 0[/tex]. This would only be true if we were multiplying one of the numbers by 0. So Step 2 was wrong.
Step 3 is right, as 0+7 = 7.
Hope this helped!
Answer:
step 2 is wrong
Step-by-step explanation:
If the measure of ∠1 is 50°, what is the measure of ∠8?
Answers
Hey there! :)
Answer:
Measure of ∠8 is 130°.
Step-by-step explanation:
We can solve for ∠8 in multiple steps:
∠1 = 50°
∠5 = 50° due to corresponding angles being equivalent
180° - m∠5 = m∠8 due to supplementary angles
180° - 50° = m∠8 = 130°
Therefore, the measure of ∠8 is 130°.
Answer: The measure of angle 8 is 130 degrees.
Step-by-step explanation:
Angle 8 and angle 4 has the same measures. The same way angle 1 and angle 5 also have the same measures.So we know that angle 1 is 50 degrees so angle 5 is also 50 degrees. Angle 5 and 8 lies on a straight line.And straight lines have a measure of 180 degrees.So we know that angle 5 is 50 degrees so what angle measure will 50 degrees add up to get 180 degrees.
Use the equation
50 + x =180 solve for x
-50 -50
x = 130
This means angle 8 is 130 degrees .
A company uses two vans to transport
workers from a free parking lot to the
workplace between 7:00 and 9:00 a.m.
One van has 9 more seats than the other.
The smaller van makes two trips every
morning while the larger one makes only
one trip. The two vans can transport 69
people, maximum. Let x be the seats in the small van and y the
seats in the large van. How many seats does the
larger van have?
Answers
Answer:
x=20 seats, y=29 seats
Step-by-step explanation:
y-x=9 y=9+x
2x+y=69 solve by substitution
2x+9+x=69
3x=69-9 3x=60
x=60/3=20 (small van)
y=9+x
y=29 (large van)
Answer : 20 in small , 29 in big as big van has 9 small van
what is −67b+6≤9b+43 solve for b
Answers
Answer:
−67b + 6 ≤ 9b + 43
Group like terms
That's
- 67b - 9b ≤ 43 - 6
Simplify
- 76b ≤ 37
Divide both sides by - 76
b ≥ - 37/76Hope this helps you
ASAP! I need help, and please do not send nonsense answers. BRAINLIEST will be given to the person who gets it correct with full solutions.
Answers
Answer:
C. all whole numbers
Step-by-step explanation:
Well Roberts can’t have a negative income and due to the number of violins being whole numbers, it is impossible to have 2.273 violins.
Hence, the annual income can only be whole numbers
Answer:
c
Step-by-step explanation:
Calculate the area of triangle RST. a = 38.
Answers
Answer:
722 √(3) square units
Step-by-step explanation:
Mathematically, the area of a triangle is 1/2 * b * h
But in this question, we have the base which is a while the height is absent
We can use trigonometric ratios since we are given the angle to find the value of the height.
Since we are dealing with the opposite and the adjacent, the correct trigonometric identity to use is the tangent
Mathematically;
Tan 60 = h/a
where h represents the height which we want to calculate
h = a tan 60
But tan 60 = √(3)
So h = a √(3)
Now the area of the triangle will be;
A = 1/2 * a * a √(3)
But a has a value of 38 units.
Substituting this value, we have ;
A = 1/2 * 38 * 38 √(3)
A = 19 * 38√(3)
A = 722 √(3) square units
ax = bx + 1. How is the value of x related to the difference of a and b?
Answers
Answer:
x = 1/(a-b)
Step-by-step explanation:
The given equation is ax = bx + 1
Collecting like terms:
ax - bx = 1
Factorizing x out of the equation:
x(a - b) = 1
Dividing both sides by (a - b):
[tex]\frac{x(a - b)}{(a - b)} = \frac{1}{a - b} \\x = \frac{1}{a - b}[/tex]
Therefore, x is related to the difference of a and be by the equation
x = 1/(a-b) where a - b is the difference of a and b
Answer:
x = 1/(a-b)
Step-by-step explanation:
Eric has a bag of 100 marbles. The bag contains 27 red marbles and 42 green marbles, and the rest are blue
marbles.
Eric is interested in the following events.
A: drawing a blue marble
B drawing a red marble
if Eric randomly draws two marbles, without replacing the first one, what is P(AB)?
Enter your answer as a fraction in simplest form. For example. If your answer is which reduces to enter it like
this: 3/4
Answers
Answer:
P(AB) = 837/9100
Step-by-step explanation:
The given parameters are;
The number of marbles in the bag = 100 marbles
The number of red marbles = 27
The number of green marbles = 42
The number of blue marbles = 100 - 27 - 42 = 31
The probability, A of drawing a blue marble = 31/100
The probability,B of drawing a red marble after a blue marble has been taken without replacement = 27/91
The probability P(AB) = 31/100× 27/91 = 837/9100
The probability that Eric randomly draws two marbles without replacing the first one where the first one is a blue marble and the second marble is a red marble is 837/9100.
Identify the two tables which represent quadratic relationships
Answers
Answer:
Option (4) and Option (5)
Step-by-step explanation:
By calculating the second difference, if the second difference in a table is equal, table will represent the quadratic relationship.
In the given option, we analyze that table given in Option (4) will represent the quadratic relationship.
x y Ist difference [tex](y_2-y_1)[/tex] IInd difference
0 4 - -
1 -4 -4 - (4) = -8 -
2 -4 -4 - (-4) = 0 0 - (-8) = 8
3 4 4 - (-4) = 8 8 - 0 = 8
Second difference of the terms in y are the same as 8.
Therefore, table of Option (4) represents the quadratic relationship.
Similarly, in Option (5) we will calculate the second difference of y terms.
x y Ist difference IInd difference
0 -4 - -
1 -8 -8 - (-4) = -4 -
2 -10 -10 - (-8) = -2 -2 - (-4) = 2
3 -10 -10 - (-10) = 0 0 - (-2) = 2
Here the second difference is same as 2.
Therefore, table of Option (5) will represent the quadratic relationship.
Answer:
Option 5 is wrong
Step-by-step explanation:
The function f(x) = 2x − 1 is transformed to function g through a horizontal shift of 7 units left. What is the equation of function g?
Answers
Greetings from Brasil...
If we have a translation for left/right, we have to use the expression:
F(X ± C)
if F(X + C), so the function shifted C units to the left
if F(X - C), so the function shifted C units to the right
Bringing to our problem
G(X) = F(X + C)
F(X) = 2X - 1
G(X) = F(X + 7) = 2.(X + 7) - 1
G(X) = F(X + 7) = 2X + 14 - 1
G(X) = F(X + 7) = 2X + 13
G(X) = 2X + 13convert 5.6cm squared into mm squared
Answers
convert 5.6 cm = 56 mm squared
Answer: 560 mm²
Step-by-step explanation:
Note that 1 cm = 10 mm
Given: 5.6 cm²
= 5.6 cm· cm
[tex]=5.6\ cm \cdot cm\times \dfrac{10\ mm}{1\ cm}\times \dfrac{10\ mm}{1\ cm}\quad[/tex]
[tex]=560\ mm\cdot mm\\[/tex]
[tex]=\large\boxed{560\ mm^2}[/tex]
Which two of the following numbers round to 752.3 if we're rounding to the nearest tenth? Choose 2 answers: a 752.32 b 752.27 c 752.36
Answers
A, B is the answer..................
Answer:
its A and C
Step-by-step explanation:
Just because...........
do side lengths 8,7 and 15 create a triangle ?
Answers
Answer:
Yes
Step-by-step explanation:
To make a triangle the 2 smaller sides must join together to become greater than or equal to the biggest side.
8+7=15
Therefore,
side lengths 8, 7, and 15 do create a triangle.
Hope this helps
Answer:
No, this can cannot create a triangle because to create a triangle you need two sides greater than one of the side and since 8+7=15 and 15 cannot be equal to 15 and it had to be more than 15 or so.
Possible ways to create triangle
a+b>c
a+c>b
b+c>a
Step-by-step explanation:
Use the property of equality to solve this equation 4.5x=18
Answers
Answer:
x = 4
Step-by-step explanation:
Given
4.5x = 18 ( divide both sides by 4.5 )
x = 4
Answer:
x=4
Step-by-step explanation:
to isolate x, we need to divide both sides by 4.5, and 18/4.5 is equal to 4, so x=4.
Solve the inequality. 6(b – 4) > 30 b > 34 b > 5 b 9
Answers
Answer:
b > 9
Step-by-step explanation:
6(b – 4) > 30
Divide each side by 6
6/6(b – 4) > 30/6
b-4 > 5
Add 4 to each side
b-4+4 > 5+4
b > 9
Answer:
[tex]\boxed{b > 9}[/tex]
Step-by-step explanation:
[tex]6(b-4) > 30[/tex]
Resolving Parenthesis
6b - 24 > 30
Adding 24 to both sides
6b > 30+24
6b > 54
Dividing both sides by 6
b > 9
solve for e.
0.75(8 + e) = 2 - 1.25e
Answers
Answer:
e = -2
Step-by-step explanation:
Well to solve for e in the following equation,
.75(8 + e) = 2 - 1.25e
We need to distribute and use the communicative property to find e.
6 + .75e = 2 - 1.25e
-2 to both sides
4 + .75e = -1.25e
-.75 to both sides
4 = -2e
-2 to both sides
e = -2
Thus,
e is -2.
Hope this helps :)
can someone please helppp
Answers
Answer:
D
Step-by-step explanation:
The range is the values of y the graph covers
The minimum value of y is - 9 and the maximum value is 5, thus
- 9 ≤ y ≤ 5 is the range → D
Answer:
[tex]\boxed{-9\leq y\leq 5}[/tex]
Step-by-step explanation:
The range is the set of possible y values, which are shown on the y-axis.
The minimum value of y on the graph is -9.
The maximum value of y on the graph is 5.
The set of possible output values (y) are equal to or greater than -9 and less than or equal to 5.
Emma opens a savings account with $100. She saves $60 per month. The equation T(n) = 60n + 100 can be used to represent this problem, where T(n) is Emma's total savings in dollars and n, represents the number of months. Question 1 (2 points) Which term in the equation is fixed? What does the fixed term represent in the context of the problem?
Answers
Answer:
The fixed term is the y-intercept. In this case the y-intercept would be 100.
Step-by-step explanation:
This is because the 100 dollars cannot be changed. You can always change the amount you save per month and the amount of months you save.
Juan uses 0.1 pound of flour to make a batch of cookies. Exactly how many batches of cookies can he make with 3.75 pounds of flour?
Answers
Answer:
37.5
Step-by-step explanation:
0.1 pound for one batch of cookies
3.75 pound for x batches of cookies
3.75/0.1=x
he can make 37.5 batches of cookies
geometric sequence 1 on mymaths
Answers
Answer:
start with 97 and multiply each term by 0.5
3.03 cells
Step-by-step explanation:
1. The colony begins with 97 cells. The cells split into two which is the same as multiplying by 0.5.
2. Multiply 97 by 0.5 5 times for 5 minutes.
97 · 0.5 · 0.5 · 0.5 · 0.5 · 0.5 = 3.03
Solve x4 – 17x2 + 16 = 0. Let u = .
Answers
To solve the equation, we need to let u = x²
What is a quadratic equation?A quadratic equation is an algebraic expression that takes the power of the second degree.
From the given parameter:
x⁴ - 17x² + 16 = 0For us to be able to solve the given equation, we need to reduce the equation to a quadratic form.
This can be achieved by making an assumption that:
u = x²So, we will replace x² with u in the given equation.
By doing so, we have:
u² - 17u + 16 = 0Learn more about quadratic equations here:
https://brainly.com/question/1214333
Answer: Solve x4 – 17x2 + 16 = 0.Let u = xX 17x²✔ x²X -17x².
let u = x^2
Step-by-step explanation: just did it
What true bearing is WSW equivalent to?
Answers
Answer:
S 67.50° W
Step-by-step explanation: