Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match the rectangles formed by the sets of points to their corresponding areas.
A(-9, 8), B(-5,5), C(1, 13), D(-3, 16)
50 square units
E(30, 20), F(39, 29), G(49, 19), H(40, 10)
300 square units
I(-6, 2), J(2, 2), K(2, -8), L(-6, -8)
100 square units
M(5,5), N(11,5), O(11,-5), P(5,-5)
80 square units
Q(10, 0), R(15,5), S(25,-5), T(20,-10)
U(0,5), V(15, 20), W(25, 10), X(10,-5)
Answers
Answer:
A(-9, 8), B(-5, 5), C(1, 13), D(-3, 16) → 50 square units
I(-6, 2), J(2, 2), K(2, -8), L(-6, -8) → 80 square units
Q(10, 0), R(15, 5), S(25, -5), T(20, -10) → 100 square units
U(0, 5), V(15, 20), W(25, 10), X(10, -5) → 300 square units
Step-by-step explanation:
The area of a rectangle, given the coordinates of the vertices is found as follows;
1) The vertices of the rectangle ABCD are; A(-9, 8), B(-5, 5), C(1, 13), and D(-3, 16)
The length of side AB = √((-9 - (-5))² + (8 - 5)²) = 5
The length of side BC = √((1 - (-5))² + (13 - 5)²) = 10
The length of side CD = √((1 - (-3))² + (13 - 16)²) = 5
The length of side DA = √(((-9) - (-3))² + (8 - 16)²) = 10
The area of rectangle ABCD = 5 × 10 = 50 square units
2) The vertices of the rectangle EFGH are; E(30, 20), F(39, 29), G(49, 19), and H(40, 10)
The length of side EF= √((39 - 30)² + (29 - 20)²) = 9·√2
The length of side FG = √((39 - 49)² + (29 - 19)²) = 10·√2
The length of side GH = √((40 - 49)² + (10 - 19)²) = 9·√2
The length of side HE = √((40 - 30)² + (10 - 20)²) = 10·√2
The area of rectangle EFGH = 9·√2 × 10·√2 = 180 square units
3) The vertices of the rectangle IJKL are; I(-6, 2), J(2, 2), K(2, -8), and L(-6, -8)
The length of side IJ= √((-6 - 2)² + (2 - 2)²) = 8
The length of side JK= √((2 - 2)² + ((-8) - 2)²) = 10
The area of rectangle IJKL = IJ × JK
∴ The area of rectangle IJKL = 8 × 10 = 80 square units
4) The vertices of the rectangle MNOP are; M(5, 5), N(11, 5), O(11, -5), and P(5, -5)
The length of side MN = √((5 - 11)² + (5 - 5)²) = 6
The length of side NO = √((11 - 11)² + ((-5) - 5)²) = 10
The area of rectangle MNOP = 6 × 10 = 60 square units
5) The vertices of the rectangle QRST are; Q(10, 0), R(15, 5), S(25, -5), and T(20, -10)
The length of side QR = √((10 - 15)² + (0 - 5)²) = 5·√2
The length of side RS = √((25 - 15)² + ((-5) - 5)²) = 10·√2
The area of rectangle QRST = 5·√2 × 10·√2 = 100 square units
6) The vertices of the rectangle UVWX are; U(0, 5), V(15, 20), W(25, 10), and X(10, -5)
The length of side UV = √((0 - 15)² + (5 - 20)²) = 15·√2
The length of side VW = √((25 - 15)² + (10 - 20)²) = 10·√2
The area of rectangle UVWX = 15·√2 × 10·√2 = 300 square units
Answer:
A(-9, 8), B(-5, 5), C(1, 13), D(-3, 16)—
(50 square units)
I(-6, 2), J(2, 2), K(2, -8), L(-6, -8)—
(80 square units)
Q(10, 0), R(15, 5), S(25, -5), T(20, -10)—(100 square units)
U(0, 5), V(15, 20), W(25, 10), X(10, -5)—(300 square units)
Step-by-step explanation:
got it right on test, hope I helped
Related Questions
What is the equation of the line that passes through the given point and is perpendicular to the given line?
Point: (1,1)
Line: y=15x+45
Answers
Answer:
y= -1/15x + 16/15
Step-by-step explanation:
When two lines are perpendicular to each other that means their slopes are the negative reciprocals of each other.
So that means if a line has has a slope of 6, a line perpendicular to that line will have a slope of -1/6.
(a reciprocal is when the fraction is flipped over)
In this case, the negative reciprocal of 15 would be -1/15. So the slope of the line that is perpendicular would be -1/15.
The equation we would have so far for that line would be: y=-1/15x+b
Now we have to find the 'b' or the y intercept, which we can get by plugging in the point that was given (1,1), which is on that line.
Which gives us 1=-1/15(1)+b.
1=-1/15+b
1+1/15=b
Then you solve for b and get b= 16/15.
The equation of the line that is perpendicular to the given line is y= -1/15x + 16/15.
The equation of the line that passes through the point (1, 1) and is perpendicular to y = 15x + 45 is
y = 15x - 14.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Let the equation of a line is y = mx + c.
The line is perpendicular to y = 15x + 45.
y = 15x + 45 is in the form of y = mx + c
This means,
Slope = 15
m = 15
The line passes through the point (1, 1) = (x, y).
This means,
y = mx + c
1 = 15 x 1 + c
1 = 15 + c
c = 1 - 15
c = -14
The equation of the line is y = 15x - 14.
Thus,
The equation of the line that passes through the point (1, 1) and is perpendicular to y = 15x + 45 is
y = 15x - 14.
Learn more about equation of a line here:
https://brainly.com/question/23087740
#SPJ2
Ali sold some cakes at a cake sale.
The cakes are chocolate, lemon or vanilla flavoured.
The cakes are either large or small.
complete the two way table
Answers
Answer:
vanilla small= 14
lemon large= 25
Step-by-step explanation:
total= 120
120÷3= 40
each of flavoured cake have 40
lemon= 40 - 26= 14
vanilla= 40- 15= 25
50 points and brainless
1. In a board game, you must roll two 6-sided number cubes. You can only start the game if you roll a 3 on at least one of the number cubes.
(a) Make a list of all the different possible outcomes when two number cubes are rolled.
(b) What fraction of the possible outcomes is favorable?
(c) Suppose you rolled the two number cubes 100 times, would you expect at least one 3 more or less than 34 times? Explain. Answer:
Answers
Answer:
The answer for (a) is
1, 1 2, 2 3, 3 4, 4 5, 5 6, 6
1, 2 2, 3 3, 4 4, 5 5, 6
1, 3 2, 4 3, 5 4, 6
1, 4 2, 5 3, 6
1, 5 2, 6
1, 6
The answer for (b) is 6/21 or 0.285714286
The answer for (c) is Less than. {its in the explanation}
===================================================================
Explanation:
(a)- Its not really hard, it just takes a bit of time.
(b)- The total number of possibilities is 21. Favorable outcomes would have a 3 as one of the dice, and only 6 of the 21 outcomes has a 3. (they are in bold)
There are only 21 possible outcomes because the prompt says "Make a list of all the different possible outcomes." For example: I have 3, 4 as an outcome, but not 4, 3 because that would be the same outcome.
(c)- Less than, because the possibility of getting an outcome with at least one 3 is only 0.285714286. If you multiply that by 100, thats only 28.5714286, or 29, still less than 34.
Please help ASAP and if u can show work
Answers
Angle 1=x
Angle 2=y
x+y=180(linear pair)
y=180-x___(1)
(3/2)x=y
(one angle is 1and half the measure of the other)
3x=2y
substitude (1)
3x=2(180-x)
3x=(360-2x)
5x=360
x=72degree
y=180-x
y=108degree
Brainliest please~
Can somebody help me with this question?
Answers
Answer:
.
Step-by-step explanation:
Which step shows the result of applying the subtraction property of equality?
(12x+8)+4-3
Answers
Answer:
Value of expression = -3 / 4
Step-by-step explanation:
Given:
(12x + 8) + 4 = 3
Find:
Value of expression
Computation:
Given expression
(12x + 8) + 4 = 3
Step 1: Use Distributive property
12x + 8 + 4 = 3.
Step 2: By adding like terms.
12x + 12 = 3
Step 3: Transfer
12x = 3 - 12
Step 4: Subtract
12x = -9
Step 4: Divide both sides by 12
12x / 12 = -9 / 12
x = -3 / 4
Value of expression = -3 / 4
Tom goes to the book fair where paperback books are $3 and hardback books are $5.50. Travis
buys three paperback and four hardback books. How much change will Travis receive from a $50
bill
1.Equation/Expression:
2. Solve:
Answers
Answer:
1: 50 - (3(3) + 5.5(4))=x
2: okay so we know how much books are brought and how much each cost.
In this case paper backs are 3 dollars each and cost 3 dollars each. So 3 (3) is 9 dollars. The next scenario are hardbacks which are 5.50 each and Tom brought 4 of them. So that makes it 5.5(4) which is 22 dollars. So the total would be 9+22 which is 31 dollars. The question asks for change from a 50 dollar bill which you subtract and 50-31=19
The change would be 19 dollars
divide 3 divided by 2/5
Answers
Answer:
[tex]{ \tt{ = 3 \div \frac{2}{5} }} \\ = { \tt{3 \times \frac{5}{2} }} \\ = \frac{15}{2} [/tex]
A garden store pays $85 for a planter. The percent of markup is 35%. What is the selling price of the planter
Answers
Answer:
Step-by-step explanation:
To get the selling price.
Selling price=100÷ 100-x × 85
Where x is the markup.
Sp= 100 ÷ 100-35× 85
Sp= 100÷ 65×85
Sp= $130.7692
Given a line segment that contains the points A,B, & C in order,if AB = 5x + 4, BC = 4x - 8, and AC = 23, find the length of segment AB.
Select one:
a. 23
b. 9
c. 19
d. 3
Answers
Answer:
C
Step-by-step explanation:
AB + BC = AC , that is
5x + 4 + 4x - 8 = 23
9x - 4 = 23 ( add 4 to both sides )
9x = 27 ( divide both sides by 9 )
x = 3
Then
AB = 5x + 4 = 5(3) + 4 = 15 + 4 = 19 → C
Tom's age is divisible by 7. If Tom's age is divided by 3 or 4, the remainder will be one. Tom is less than 100 years old. What is Tom's age?
Answers
Answer:
49
Step-by-step explanation:
−3x−8y=−8 y=2−x Is (0,1)(0,1)left parenthesis, 0, comma, 1, right parenthesis a solution of the system?
Answers
Answer:
(0,1) is not the solution to the equation
Step-by-step explanation:
Given:
−3x − 8y = −8 (1)
y = 2 − x (2)
Substitute (2) into (1)
−3x − 8y = −8 (1)
- 3x - 8(2 - x) = -8
- 3x - 16 + 8x = -8
- 3x + 8x = -8 + 16
5x = 8
x = 8/5
Substitute x = 8/5 into (2)
y = 2 − x (2)
= 2 - 8/5
= (10-8) / 5
= 2/5
y = 2/5
Solution to the equation:
(x, y) = (8/5, 2/5)
Therefore,
(0,1) is not the solution to the equation
Lana is the oldest of four sisters. Her youngest sister is half her age. The other two sisters are twins $2$ years younger than Lana. When the four sisters' ages are added together, the result is $45$. If the youngest sister is $n$ years old, what is $n$?
Answers
2n+n+2n-2+2n-2=45
7n-4=45
7n=49
n=7
Find a linear function f, given f(6) = - 4 and f(-3) = - 10. Then find f(0).
f(x)=0
(Type an expression using x as the variable. Simplify your answer.)
f(0) = (Simplify your answer.)
PLZ HELP
Answers
Answer:
[tex]y = \frac{2}{3} x - 8[/tex]
f(0)=-8
Step-by-step explanation:
Slope=rise/run=(-4-(-10))/(6-(-3))=6/9=2/3=m
y=m*x+q
-4=(2/3)*(6)+q
q=-8
f(0)=(2/3)*(0)-8=-8
What is the word form of 0.604
Answers
Answer:
zero point six hundred and four
Step-by-step explanation:
Complete the function for this graph.
Answers
Answer:
y = –|x - 1| + 3
Step-by-step explanation:
The "vertex" is (1 , 3)
y = –|x - 1| + 3
which of the following equations describes the line
check all that apply (1,9) (-2, 3) A. y - 1 = 2(X-9) B. Y- 2 = 2(x-3) c. y - 3 = 2(x + 2) D. Y-3 = 2(x - 2) E. y + 2 = 2(x-3) F. - 9 = 2(x - 1)
Answers
The equation of the line that connects the two points (1,9) and (-2,3) is,
y = 2x+7
or, y-3=2x+4
or, y-3=2(x+2)
So, option c, is the correct option
Answered by GAUTHMATH
The diagram shows a right angled triangle 15cm 31 what is value of h round to 1 decimal place
Answers
explanation:
the hypotenuse is 15 cm with the opposite side being h cm.
The angle is 31°
Thus, using trigonometric ratio, we have;
h/15 = sin 31
h = 15 sin 31
h = 15 × 0.5150
h = 7.725
Approximating to 1 decimal place gives;
h = 7.7 cm
The solution of the system of equations has coordinates where x is between 2 and 3 and y is between 2 and 3. What is a reasonable approximation for each value to the tenths place? x Almost-equals 2.2, y Almost-equals 2.1 x Almost-equals 2.2, y Almost-equals 2.4 x Almost-equals 2.7, y Almost-equals 2.3 x Almost-equals 2.7, y Almost-equals 2.6
Answers
x Almost-equals 2.2, y Almost-equals 2.4
Answer:
Its B
Step-by-step explanation:
correct on edge
eeeeeeee please help!
Answers
Answer:
1) Less than
2) greater than
Step-by-step explanation:
Equation of the first line:
(y+7)/(-13+7) = x/-1
(y+7))/-6 = -x
y+7 = 6x
y= 6x - 7
Equation of the second line:
A (4/3,0) ; B (0,8)
y/8 = (x-4/3)/-4/3
y/8 = (x-4/3) * -3/4
y/8 = -3/4x + 1
y = -6x + 8
help fast pls i need it
Answers
In a triangle ABC, a=4 cm, b=3 cm and angleC=30°, find the area of triangle ABC.
a. 6
b. 1.5
c. 3
d. 3 root 3
Answers
2. What is the area of the figure below. Simplify.
Answers
Answer:
x^2 - 9
Step-by-step explanation:
length = 2x - 6 = 2(x-3)
Area = [2(x-3) * (x + 3)]/2 = (x-3)(x+3) = x^2-9
Answer: x = 9
2x -6= x +3
2x -x= 3 +6
x= 9
What is the pH of a solution with a 1.50 × 10−9 M hydroxide ion concentration? (4 points) 0.176 5.18 8.82 9.20
Answers
Answer:
5.18
Step-by-step explanation:
This is a chemistry question. However the solution to the problem is given below:
We'll begin by calculating the pOH of the solution. This can be obtained as follow:
Concentration of Hydroxide ion [OH¯] = 1.5×10¯⁹ M
pOH =?
pOH = –Log [OH¯]
pOH = –Log 1.5×10¯⁹
pOH = 8.82
Finally, we shall determine the pH of the solution. This can be obtained as follow;
pOH = 8.82
pH =?
pH + pOH = 14
pH + 8.82 = 14
Collect like terms
pH = 14 – 8.82
pH = 5.18
Therefore, the pH of the solution is 5.18
Answer:
5.18
Step-by-step explanation:
I took the test and got it right!
Help me with these 3 and explain too thank you :))
Answers
Answer:
1) 25
2) 2
3) f(g(1)) = 42
Step-by-step explanation:
1) Given that f(x) = 4x^2 + 9
If x = -2
f(-2) = 4(-2)^2 + 9
f(-2) = 4(4) + 9
f(-2) = 16 + 9
f(-2) = 25
2) Given that f(x) = 4x - 6
y = 4x - 6
Replace y with x
x = 4y - 6
MAke y the subject of the forfmula
4y = x+ 6
y = (x+6)/4
SInce x = 2
f^(-1)(2) = (2+6)/4
f^(-1)(2) = 8/4 = 2
3) If f(x) = 6x and g(x) = x+6
f(g(x)) = f(x+6)
f(x+6) = 6(x+6)
Since x = 1
f(g(1)) = 6(1+6)
f(g(1)) = 6(7)
f(g(1)) = 42
If Q is the midpoint of PR, find the coordinates of R if P(11,-2) and Q(4,3).
Answers
Answer:
R = (-3, 8).
Step-by-step explanation:
Recall the midpoint formula:
[tex]\displaystyle M=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)[/tex]
Where M is the midpoint, (x₁, y₁) is one point and (x₂, y₂) is another.
We are given that Q is the midpoint of PR, where P = (11, -2) and Q = (4, 3) and we want to find the coordinates of R.
Substitute Q for M and let P(11, -2) be (x₁, y₁). Hence:
[tex]\displaystyle (4, 3)=\left(\frac{11+x_2}{2}, \frac{-2+y_2}{2}\right)[/tex]
Split into two separate equations:
[tex]\displaystyle \frac{11+x_2}{2}=4\text{ and } \frac{-2+y_2}{2}=3[/tex]
Solve for each case:
[tex]\displaystyle 11+x_2=8\Rightarrow x_2=-3[/tex]
[tex]\displaystyle -2+y_2=6\Rightarrow y_2=8[/tex]
Therefore, our second point (x₂, y₂) is (-3, 8).
Hence, R = (-3, 8).
Answer:
(15/2),(1/2)
Step-by-step explanation:
(x1 + x2 / 2) , (y1 + y2) / 2)
(11 + 4 / 2) , (-2 + 3 / 2)
(15/2) , (1/2)
Find the value of y in 4y + 2x = 8 and 2x + 5y = 14.
8
- 6
6
-8
Answers
a. 12.3
b. 8.1
c. 0.1
Answers
Answer:
a
Step-by-step explanation:
tan(39⁰)= opposite ÷ adjacent
0.8097= 10 ÷ x
X = 10 ÷ 0.8097
X = 12.3
Please help SUMMER SCHOOL
Question
(what are the slope and the y-intercept of the line shown in the graph)
Answers
Explanation:
The y-intercept is where the line crosses the y axis and I have put the co-ordinate where it does that.
The gradient is 3 as to find the gradient you do rise/run so we do 3/1 which equals 3
To form an equation we do y=Mx+c. The c is the y-intercept and the gradient is m. Therefore the equation of this line is y= 3x+2.
A retailer incurs a fixed cost of N$ 500 when purchasing sugar for his stock. He pays N$ 10.00 per packet which he resells at N$ 15.00 per packet. How many packets should he purchase and sell in order to break even?
Answers
Answer:
100 packets
Step-by-step explanation:
Given :
Cost = fixed cost + variable cost
Fixed cost = $500
Variable cost = $10
Sales price = $15
Let :
Number of packets = x
To break even :
fixed cost + variable cost = sales made
500 + 10x = 15x
500 = 15x - 10x
500 = 5x
x = 500 / 5
x = 100
100 packets
