Answers
Answer:
A. 1/3
B. √10
C. -1, 1
D. √8, 6
E. congruent and opposite pairs parallel
F. perpendicular, not congruent
G. rhombus, explanation below
Step-by-step explanation:
Hey there! I'm happy to help!
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A.
Slope is the rise over the run. Let's look at F to G.
We are going from -1 to 2 on our x-axis (run), so our run is 3 units.
Our rise is 1 unit as we go from 2 to 3 on the y-axis.
[tex]slope=\frac{rise}{run} =\frac{1}{3}[/tex]
This slope is the same for all of the sides.
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B.
We will use the distance formula (which is basically just the Pythagorean Theorem) to calculate the length of each side. Let's go between F and G again, but this distance is the same for all the sides.
[tex]\sqrt{(x_{2}-x_1)^2+(y_{2}-y_1)^2 } \\\\(x_1,y_1)=(-1,2)\\\\(x_2,y_2)=(2,3)\\\\\\\sqrt{(2+1)^2+(3-2)^2 } \\\\\sqrt{(3)^2+(1)^2 }\\\\\sqrt{9+1 }\\\\\sqrt{10}[/tex]
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C.
The diagonals are the lines that connect the non-adjacent vertices.
Our two diagonals are FH and GE.
-----------------------------
FH
We go from x-value -1 to 1 from F to H, so our run is 2.
We go from y-value 2 to 0. so our rise is -2.
[tex]slope=\frac{rise}{run} =-\frac{2}{2} =-1[/tex]
-----------------------------
GE
We go from x-value -2 to 2 from E to G, so our run is 4.
We go from y-value -1 to 3. so our rise is 4.
[tex]slope=\frac{rise}{run} =\frac{4}{4} =1[/tex]
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D.
Let's use the distance formula on each of our diagonals.
-----------------------------
FH
[tex]\sqrt{(x_{2}-x_1)^2+(y_{2}-y_1)^2 } \\\\(x_1,y_1)=(-1,2)\\\\(x_2,y_2)=(1,0)\\\\\\\sqrt{(1+1)^2+(0-2)^2 } \\\\\sqrt{(2)^2+(-2)^2 }\\\\\sqrt{4+4 }\\\\\sqrt{8}[/tex]
-----------------------------
GE
[tex]\sqrt{(x_{2}-x_1)^2+(y_{2}-y_1)^2 } \\\\(x_1,y_1)=(-2,-1)\\\\(x_2,y_2)=(2,3)\\\\\\\sqrt{(2+2)^2+(3+1)^2 } \\\\\sqrt{(4)^2+(4)^2 }\\\\\sqrt{16+16 }\\\\\sqrt{36}\\\\6[/tex]
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E.
They are congruent as they all have the same length (√10) and the opposite sides are parallel as they have the same slope (1/3)
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F.
They are perpendicular diagonals as their slopes are negative reciprocals (1 and -1), and they are not congruent as they have different lengths (√8 and 6).
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G.
Parallelogram- quadrilateral with opposite pairs of parallel sides.
Rhombus- a parallelogram with four equal sides
Square- a rhombus with four right angles
We can see that this is a parallelogram as we saw that the opposite sides are parallel due to having the same slope, and the perpendicular diagonals show that as well. This is also a rhombus because if we use that distance formula on all the sides, it will be the same. It is not a square though because it does not have four right angles, so this is a rhombus.
-----------------------------------------------------------------
Have a wonderful day and keep on learning!
Related Questions
Hi, please help me with this question.
what is 45+46+47+ ... +53+54?
Answers
Answer:
245Step-by-step explanation:
1). 91 + 41 + 53 + 54 {Simplify}
2). 138 + 53 + 54 {Simplify}
3). 191 + 54 {Simplify}
4). 245 {Add}
9514 1404 393
Answer:
495
Step-by-step explanation:
There are several ways to figure this:
1) Multiply the average value by the number of numbers. The average number in an arithmetic sequence is the average of the first and last numbers in the sequence.
average = (54+45)/2 = 49.5
number of numbers = 54 -45 +1 = 10
Total = 49.5 · 10 = 495
__
2) Add the numbers pairwise. It works best to work toward the middle from the ends:
45 +54 = 99
46 +53 = 99
47 +52 = 99
48 +51 = 99
49 +50 = 99
Total = 5 · 99 = 495
__
3) Subtract the sum of numbers to 44 from the sum of numbers to 54.
The sum of numbers 1 to n is (n)(n+1)/2.
(54)(55)/2 -(44)(45)/2 = (27)(55) -(22)(45) = 1485 -990 = 495
__
4) Use a spreadsheet or calculator to add them. (see attached)
Cuanto es 2/9 - 4/15
Answers
Answer:
Step-by-step explanation:
Common denominator is 45
(45/9)*2 = 10 and (45/15)*4 = 12
10/45 - 12/45 = - 2/45
If 8 ounces of cereal cost $2.99, then 16 ounces of cereal cost $5.98
Answers
Consider the sequence of steps to solve the equation: 3(x − 4) + 5x = 9x − 36 Given ⇒ 3(x − 4) + 5x = 9x − 36 Step 1 ⇒ 3x − 12 + 5x = 9x − 36 Step 2 ⇒ 3x + 5x − 12 = 9x − 36 Step 3 ⇒ 8x − 12 = 9x − 36 Step 4 ⇒ 8x − 8x − 12 = 9x − 8x − 36 Step 5 ⇒ 0 − 12 = x − 36 Step 6 ⇒ −12 = x − 36 Step 7 ⇒ −12 + 36 = x − 36 + 36 Step 8 ⇒ 24 = x + 0 Step 9 ⇒ 24 = x Which property yields Step 2? A) Additive Inverse Property B) Additive Identity Property C) Addition Property of Equality D) Commutative Property of Addition
Answers
Answer:
Commutative Property of Addition
Step-by-step explanation:
3(x − 4) + 5x = 9x − 36
3x − 12 + 5x = 9x − 36 Distribute
3x + 5x − 12 = 9x − 36 Commutative Property of Addition
I don’t get this how do these things work please explain
Answers
Answer:
Ok, so:
-The number of people who like tea are represented in the first column.
-The number of people who dislike tea are represented in the second column.
-The number of people who like coffee are represented in the first row.
-The number of people who dislike coffee are represented in the second row.
This works like a multiplication chart:
People who like tea and coffee are represented in the top left square. People who dislike tea and coffee are represented in the box that coordinates to T' and C' (If you find T' and C' and run your fingers along the column/row until they run into each other, you'll find it.) The same is true for other combinations.
At the bottom of the first column is the total number of people who like tea. At the right-most part of the first row, is the total number of people who like coffee.
(52 people like tea, 80 people were surveyed)
I hope this helps you understand, please ask any clarifying questions you need! : )
A restaurant divides its daily tips equally among 8 employees.
If the daily tips were $743.36, how much should each employee receive?
a
O $92.92
O $102.92
O$93.02
O $91.92
Answers
Answer:
Step-by-step explanation:
The daily tips were 743.36
8 people divided the money
Tips = 743.36 / 8 = 92.92
I can't explain how the others were obtained. The answer is A
Answer this question and turn it in HERE or on paper in the TURN-IN BOX by Friday for +2 Practice points. 0, 1, 1, 2, 3, 5, 8,... What are the next three numbers? Explain!
Answers
Answer:
13, 24, and 34
Step-by-step explanation:
0, 1, 1, 2, 3, 5, 8, 13, 24, 34, . . .
0+ 1 = 1
1+ 1 = 2
2+ 1 = 3
3+ 2 = 5
5+ 3 = 8
8+ 5 = 13
13+ 8 = 24
24+ 13 = 34
start at 1, then add the number behind it to move forward one space. repeat process.
why is the graph dashed line Rather than solid line?
Answers
Answer: Inqualities that use < and> with a line under them means solid line
Step-by-step explanation: whereas < and> by themselves is dashed
Leroy's total job benefits were $50,150 last year. His total job expenses for traveling and for professional development for the year were $3,500. Which of the following represents his total employment compensation?
a.
$46,650
b.
$47,650
c.
$50,150
d.
$53,650
Please select the best answer from the choices provided
A
B
C
D
Answers
Answer:
D. 53,650
50,150+3,500=53,650
Please Answer ASAP
The first term of a GP is 1, the sum of the third and fifth term is 90. Find the
common ratio.
Answers
hence, the common ratio of the given G.P. is 3 or −3.
Answer:
common ratio is -3 or 3
Step-by-step explanation:
[tex]u_1=1\\\\u_3=u_1*r^2=r^2\\\\u_5=u_1*r^4=r^4\\\\r^2+r^4=90\\\\r^4+r^2-90=0\\\Delta=1+4*90=361=19^2\\\\r^2=\dfrac{-1-19}{2} =-10 (exclude\ a\ square\ is\ positive)\\or\\r^2=\dfrac{-1+19}{2}=9\\r^2-9=0\\(r-3)(r+3)=0\\So\ r=-3\ or\ r=3\\[/tex]
please help its urgent
Answers
Step-by-step explanation:
tn=3n+8
t1=3*1+8
=3+8
=11
t7=3*7+8
=21+8
=29
t14=3*14+8
=42+8
=50
A number is divided by 2, and then the quotient is increased by 8. The result is 33.
Answers
Answer:
33
Step-by-step explanation:
please let me know if I’m correct
hope this helps
Given that tan x=5/12, what is the value of sin x + cos x?
Answers
Answer:
17/13
Step-by-step explanation:
the answer is in the image above
Mark is mixing different color paints for a mural
he has been asked to paint in the school
gymnasium. To create the color purple he wants,
Mark mixes r gallons of red paint with b gallons of
blue paint. Red paint costs $25 per gallon and
blue paint costs $22 per gallon. He also needs $65
to spend on paint supplies.
Mark knows the cost of his paint and supplies can
be found using the expression
Answers
Answer:
25r+22b+65s
Step-by-step explanation:
ok so like uhh yea
Solve for h in the equation 15-2h=6
Answers
Answer:
h=4.5
Step-by-step explanation:
15-2h=6 Get rid of any constants of the side of the variable.
-15 -15
-2h=-9 Divide -2 from both sides to isolate h.
/-2 /-2
h=4.5
Hope this helped you out! Have a wonderful day :)
ok this is the last one i swear , i’m so bad at finding mistakes
Answers
Answer:
there is no mistake
Step-by-step explanation:
this seems weird ik but i dont think there is even a mistake? the answer is definitely -7/2 or -3.5
Find the mean of 9, 10, 3, 9, 2, 3 graphically.
Answers
Answer:
18
Step-by-step explanation:
add all number and simply divide it by 2
Picture shown!
Complete the remainder of the table for the given function rule:
y=-x-9
x | -2 -1 0 2
y |-7 [?] [ ?] [? ] [? ]
Answers
Step-by-step explanation:
-8
-9
-10
-11
just subtituted the remaining values of x.
Answer:
x= -1 —> y= –8
x=0 —> y= –9
x=1—> y= –10
x=2—>y= —11
Step-by-step explanation:
x= -1 —>y= -(-1)-9= +1-9 = –8
x=0 —> y= -(0)-9= –9
x=1—> y= -(1)-9= -1-9= –10
x=2—>y= -(2)-9 = —11
I hope I helped you^_^
The sum of three numbers is 124. The second is 10 less than the first. The third number is 4 times the second. What are the numbers?
Answers
Step-by-step explanation:
numbers
first = X
second = (x-10)
Third = 4(x-10)
x + (x-10) + 4(x-10) = 124
2x -10 + 4x-40 =124
6x - 50 = 124
6x = 124 + 50
6x = 174
x= 29
therefore the ;
first number = 29
second = (x-10) = 29-10 = 19
third= 4(x-10) = 4(29-10)= 76
find product of :(2x-y)(2x+3y).
Answers
Answer: 4x² + 4xy - 3y²
Concept:
When encountering questions that ask for simplifying algebraic expressions, using the FOIL method would be easier:
First, which means multiplying the first terms together;Outer, which means that we multiply the outermost terms when the binomials are placed side by side;Inner, which means multiply the innermost terms together;Last, which means that we multiply the last term in each binomial together.Solve:
Given
(2x - y) (2x + 3y)
Expand parentheses and apply the FOIL method
=4x² + 6xy - 2xy - 3y²
Combine like terms
=4x² + (6xy - 2xy) - 3y²
=[tex]\boxed{4x^2+4xy-3y^2}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
F=ma find out f if m-26 and a-3 please help
Answers
Answer:
78
Step-by-step explanation:
26 + 26 + 26 = 78
Many numbers in real life are very large or very small. For example the distance from the earth to the sun is about 93,000,000 miles and midth of human hair is about 0.007 cm.
Answers
Answer:
yes, you are telling right.
I need help ASAP IM IN SCHOOL!!!
Answers
Answer:
-4, -9/4, 1/2, sqrt5, 3.7
4
Select the correct answer.
Identify the system of linear equations from the tables of values given below.
х
у
х
у
.
0
2
0
1
-4
0
-2
0
6
5
-4
-1
-6
-1
2.
2.
Answers
Answer:
x 3:7 y 5:9 :)
Step-by-step explanation:
An artist mixes 1.6 ounces of green paint with 1.85 ounces of white paint. She then divides the paint into 6 equal parts.
How much paint is in each part?
Answers
Answer:
0.575 ounce
Step-by-step explanation:
Total paint
= Green paint + white paint
= 1.6 ounces + 1.85 ounces
= 3.45 ounces
Paint in each part if divided into 6 parts equally
= 3.45 ounces/6
= 345 ounces/600
= 23/40
= 0.575 ounce
The amount of green and white paint in each part is 0.27 ounces and 0.31 ounces respectively.
What are the ratio and proportion?The ratio is the division of the two numbers.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
Amount of green paint = 1.6 ounces
Amount of white paint = 1.85 ounces
Total paint = 1.6 + 1.85 = 3.45
The ratio of green paint to total paint = 1.6/3.45 = 0.46
Now, this ratio must be maintained in each part after dividing it into 6 equal parts.
Total paint in each section after dividing = (1.6 + 1.85)/6 = 0.58
With the same ratio,
Green paint / Total paint = 0.46
Green paint / 0.58 = 0.46
Green paint = 0.27 ounces
White paint = total paint - green paint
White paint = 0.58 - 0.27 = 0.31 ounces
Hence "The amount of green and white paint in each part is 0.27 ounces and 0.31 ounces respectively".
For more information about ratios and proportions,
brainly.com/question/26974513
#SPJ5
HELP PLEASE
a rectangle room has an area of 400 square feet. the length is 7 feet less than twice the width. find the dimensions of the room.
Answers
Answer: 16 feet is the width and 25 is length
Step-by-step explanation:
x*(2x-7)=400
Word problem written in numerical form^^^^
Solve for x to get 16
length = 2(16)-7= 25
Check our work
16*25=400 yay
What is the area of this figure?
5 yd
2 yd
2 yd
5 yd
3 yd
5 yd
4 yd
4 yd
Write your answer using decimals, if necessary.
square yards
PLS IT 11 points
Answers
the answer is 47yd²
hope it help n please give me brain.. thanks
I need workings pls.and I want you to understand my questions
1.)log base 16 0.25
2.)log base 7 ¹/7
3.)log base 4 ⅛
Answers
Answer:
-1/2 , -1, -3/2
Step-by-step explanation:
1.)log base 16 1/4
log base 16 [tex]4 ^{-1 }[/tex] =x
[tex]16 ^{x} = 1/4[/tex]
x = -1/2
2.)log base 7 ¹/7
log base 7 [tex]7^{-1}[/tex] = x
7^x = 7^-1
x = -1
3.)log base 4 ⅛
4^x = 1/8
[tex]2^{2x} = 2^{-3}[/tex]
2x = -3
x = -3/2
Answer:
Step-by-step explanation:
1. Let a = log16 0.25, then:
0.25 = 16 ^ a = 16^-0.5
So the answer is -0.5.
2. log7 1/7
1/7 = 7^-1
Answer is -1.
3. log4 1/8
1/8 = 4^(-1.5)
Answer is -1.5
[tex]\frac{-3+-6}{3}[/tex]
whats the answer to that?
Answers
Answer:
-3
Step-by-step explanation:
A postive and a negative becomes a negative.
So -3 + - 6 becomes
-3 - 6
= -9
The -9 is over 3, which is 9/3 negated, so 3 negated which is -3.
if M={a,b,c,d} and N={c,b,e,f},find the value of M-N
Answers
Answer:
M-N= {a,d}
Step-by-step explanation:
subtract the common elements
(a, d)
(
Step-by-step explanation:
because a and d are not in N ,