On your paper, construct a rectangle on a coordinate plane that satisfies these criteria.
• The sides of the rectangle are either vertical or horizontal.
• The perimeter of the rectangle is 42 units.
• Each of the vertices lies in a different quadrant.
What are the coordinates of the vertices of your rectangle? Explain how you know the perimeter of your rectangle is
42 units
Answers
Answer:
[tex]A = (5,3)[/tex]
[tex]B = (-5,3)[/tex]
[tex]C = (-5,-8)[/tex]
[tex]D = (5,-8)[/tex]
Step-by-step explanation:
Required
[tex]Perimeter = 42[/tex]
Construct a rectangle whose perimeter is 42 units and satisfies the given conditions.
First, name the rectangle ABCD.
Such that:
[tex]A = (x_1,y_1)[/tex]
[tex]B = (x_2,y_2)[/tex]
[tex]C = (x_3,y_3)[/tex]
[tex]D = (x_4,y_4)[/tex]
For the rectangle to be either horizontal or vertical, then:
[tex]y_1 = y_2[/tex] and [tex]y_3 = y_4[/tex]
We have that:
[tex]Perimeter = 42[/tex]
Replace perimeter with its formula
[tex]2(AB + BC) = 42[/tex]
Divide both sides by 2
[tex]AB + BC = 21[/tex]
This implies that, the distance between adjacent sides (through the edges) must be equal to 21
Having said that: a set of coordinates that satisfy the given conditions are:
[tex]A = (5,3)[/tex] -- First quadrant
[tex]B = (-5,3)[/tex] -- Second quadrant
[tex]C = (-5,-8)[/tex] -- Third quadrant
[tex]D = (5,-8)[/tex] -- Fourth quadrant
The above quadrants satisfy the condition:
[tex]y_1 = y_2[/tex] and [tex]y_3 = y_4[/tex]
HOW TO KNOW THE PERIMETER IS 42
To do this, we simply calculate the distance between the edges and add them up
Distance is calculated as:
[tex]D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2[/tex]
For AB
[tex]A = (5,3)[/tex]
[tex]B = (-5,3)[/tex]
[tex]D_1 = \sqrt{(5 - (-5))^2 + (3 - 3)^2}= \sqrt{(10)^2 + (0)^2} = \sqrt{100} = 10[/tex]
For BC
[tex]B = (-5,3)[/tex]
[tex]C = (-5,-8)[/tex]
[tex]D_2 = \sqrt{(-5 - (-5))^2 + (3 - (-8))^2}= \sqrt{(0)^2 + (11)^2} = \sqrt{121} = 11[/tex]
For CD
[tex]C = (-5,-8)[/tex]
[tex]D = (5,-8)[/tex]
[tex]D_3 = \sqrt{(-5 -5)^2 + (-8 - (-8))^2}= \sqrt{(-10)^2 + (0)^2} = \sqrt{100} = 10[/tex]
For DA
[tex]D = (5,-8)[/tex]
[tex]A = (5,3)[/tex]
[tex]D_4 = \sqrt{(5 -5)^2 + (-8 -3)^2}= \sqrt{(0)^2 + (11)^2} = \sqrt{121} = 11[/tex]
So, the perimeter is:
[tex]P = D_1 + D_2 + D_3 + D_4[/tex]
[tex]P = 10 + 11 + 10 +11[/tex]
[tex]P = 42[/tex]
See attachment for rectangle
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3,5,8. I think.
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Answer:
first: x=1.3024
second: x=12.29
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Step-by-step explanation:
sin 19=x/4
0.3256=x/4
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consider the line y=6/7x-7
find the equation of the line that is perpendicular to the line and passes through the points (6,3)
find the equation of the line that is parallelto the line and passes through the points (6,3)
Answers
Answer:
y = -7/6x + b
Step-by-step explanation:
Perpendicular lines require the reciprocal of the slope and opposite sign to the original slope. Then, you substitute the x and y coordinates into the equation to find the y-intercept. Done.
y = 6/7x -7 (6,3)
y = -7/6x + b
3 = -7/6(6) + b
3 = -7 + b
7 7
10 = b
y = -7/6x + b
Answer:
see below
Step-by-step explanation:
If two lines are perpendicular to each other, they have opposite slopes.
The first line is y = 6/7x. Its slope is (6/7). A line perpendicular to this one will have a slope of -7/6.
Plug this value (-7/6) into your standard point-slope equation of y = mx + b.
y = -7/6x + b
To find b, we want to plug in a value that we know is on this line: in this case, it is (6, 3). Plug in the x and y values into the x and y of the standard equation.
3 = -7/6(6) + b
To find b, multiply the slope and the input of x (6)
3 = -42/6 + b
3 = -7 + b
Now, add 7 to both sides to isolate b.
10 = b
Plug this into your standard equation.
y = -7/6x + 10
This equation is perpendicular to your given equation (y = 6/7x -7) and contains point (6, 3)
If two lines are parallel to each other, they have the same slope.
The first line is y = 6/7x - 7. Its slope is (6/7). A line parallel to this one will also have a slope of 6/7.
Plug this value (6/7) into your standard point-slope equation of y = mx + b.
y = 6/7x + b
To find b, we want to plug in a value that we know is on this line: in this case, it is (6, 3). Plug in the x and y values into the x and y of the standard equation.
3 = 6/7(6) + b
To find b, multiply the slope and the input of x (6)
3 = 36/7 + b
Now, subtract 36/7 to both sides to isolate b. To make this easier to visualize, convert 3 to have a denominator of 7.
21/7 - 36/7 = b
-15/7 = b
Plug this into your standard equation.
y = 6/7x - 15/7
This equation is parallel to your given equation (y = 6/7x - 7) and contains point (6, 3)
Hope this helps!
what is the prudct of 7\9 and 6
Answers
Answer:
378
Step-by-step explanation:
9 × 7 × 6 = 378
pls mark brainliest, if not, its ok :)
Answer:
14/3, or 4.6^bar
Step-by-step explanation:
first you'd just divide 7 by 9, resulting in [tex]\frac{7}{9}[/tex], or 0.7^bar.
Then you'd multiply either by 6, resulting in the answers above. Fractions are easier than infinite numbers, so if you're able to do that, I'd suggest you do so.
Hope this helped!
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Answer:
Hi! Hope this helps!
Step-by-step explanation:
A verb is used to describe actions.
Example: I JUMPED over the rock. In this sentence the verb is JUMPED
a ver
Step-by-step explanation:
a verb is a word used to describe an action , state , occurrence and forming the main part of a predicate of a sentence
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Answer:
8h
Step-by-step explanation:
basically your supposed to combine all of the H's. The numbers are how many there are. Just add the numbers with the same letters, and then stick the letter next to it.
2+2+4= 8
h+h+h= h
8h
Have a good day!! Be tiger fierce!!
2h + 2h = 4h +4h = 8h
A map uses a scale of 1 in :20mi. Find the the actual distance of 5.5 inches on the map. help me
Answers
Answer:
110
Step-by-step explanation:
5.5 x 20 = 110
which fraction is 16/64 in lowest terms
PLEASE SHOW HOW U DID UR PROBLEM
Answers
Answer:
16/64 simplified to lowest terms is 1/4
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 16 and 64 is 16
Divide both the numerator and denominator by the GCD
16 ÷ 16
64 ÷ 16
Reduced fraction:
1/ 4
Answer:
1/4
Step-by-step explanation:
Steps to simplifying fractions
Find the GCD (or HCF) of numerator and denominator
GCD of 16 and 64 is 16
Divide both the numerator and denominator by the GCD
16 ÷ 16
64 ÷ 16
Reduced fraction:
1 / 4
Therefore, 16/64 simplified to lowest terms is 1/4.
The distance from New York City to Riverhead is approximately 150 miles. On a map whose scale is 24mi= 2inch, what is the distance between the two locations in inches?
Answers
Answer:
12.5 inches
Step-by-step explanation:
Given
[tex]Distance = 150\ miles[/tex]
[tex]Scale:= 24\ miles : 2\ inches[/tex]
Required
Determine the measurement in inches
Represent the inches equivalent with d.
So, the scale can also be calculated as:
[tex]Scale:= 150\ miles: d[/tex]
Equate both scales
[tex]150\ miles: d = 24\ miles ; 2\ inches[/tex]
Convert to fraction
[tex]\frac{d}{150\ miles} = \frac{2\ inches}{24\ miles}[/tex]
[tex]\frac{d}{150} = \frac{2\ inches}{24}[/tex]
Multiply both sides by 150
[tex]150 * \frac{d}{150} = \frac{2\ inches}{24} * 150[/tex]
[tex]d = \frac{2\ inches}{24} * 150[/tex]
[tex]d = \frac{2\ inches * 150}{24}[/tex]
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Which of the following shows the equation after both sides have been distributed
-4(x - 2) = 5(3x – 8)
A. 4x-8=15x-40
B. 4x-6=15x-3
C. 4x+8=15x-40
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Answers
Two triangles are cut from a rectangle to form a trapezoid. What is the ratio of the area of the trapezoid to the combined area of the triangles? A 18:54 C 54:18 B 18:72 D 72:18 12 in group of students is painting a background piece
Answers
The image showing the trapezoid is missing, so i have attached it.
Answer:
C 54:18
Step-by-step explanation:
Formula for area of trapezoid is;
A_trap = ½(sum of parallel sides) × height = ½(12 + (12 - (3 + 3))) × 6
A_trap = ½(12 + 6) × 6
A_trap = 54 in²
Combined area of triangle:
A_tria = 2 × ½ × 3 × 6 = 18 in²
Thus;
A_trap:A_tria = 54 in²:18 in² = 54:18
The image showing the trapezoid is missing, so i have attached it.
Answer:
C 54:18
Step-by-step explanation:
Formula for area of trapezoid is;
A_trap = ½(sum of parallel sides) × height = ½(12 + (12 - (3 + 3))) × 6
A_trap = ½(12 + 6) × 6
A_trap = 54 in²
Combined area of triangle:
A_tria = 2 × ½ × 3 × 6 = 18 in²
Thus;
A_trap:A_tria = 54 in²:18 in² = 54:18
this equality contains a viable 3(23+18)<6a
Answers
[tex]3(23+18) < 6a \\ 41 < 2a \\ a > 41/2\implies a > 20.5[/tex]
Hope this helps.
Answer: a >41/2
Step-by-step explanation: Step 1: Simplify both sides of the inequality.
123<6a
Step 2: Flip the equation.
6a>123
Step 3: Divide both sides by 6.
6a/6>123/6
a>41/2
I don’t remember doing this so can someone please help me!!!
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Answer:
Step-by-step explanation:
10. m-56
11. 4r+3
Drag each tile to the correct box.
Match each equation with its solution.
x = -0.4
x = 10
x = 2
x = -10
Equation
Solution
x − 6 = -4
arrowRight
x + 3 = -7
arrowRight
5x = -2
arrowRight
0.5x = 5
arrowRight
Answers
x - 6 = - 4
Answer: x = 2
x + 3 = -7
Answer: x = -10
5x = -2
Answer: x = -0.4
0.5x = 5
Answer: x = 10
The solutions to the equations as arranged are 2, -10, -0.4 and 10 respectively
Solving equationsGiven the following equations
x − 6 = -4
Add 6 to both sides
x - 6 + 6 = -4 + 6
x = -4 + 6
x = 2
For the equation x + 3 = -7
Subtract 3 from both sides
x + 3 -3 = -7 - 3
x = -10
For the equation 5x = -2
x = -2/5
x = -0.4
For the equation
0.5x = 5
x = 5/0.5
x =10
Hence the solutions to the equations as arranged are 2, -10, -0.4 and 10 respectively
Learn more on equation here: https://brainly.com/question/2972832
#SPJ2
36-40. The probability that a fatal car accident is alcohol related is over 40%. The probability that a fatal accident happens at night is 5 times more than the probability that it happens during the day.
What should drivers do to stay safe on the road? Write a probability facts that is based in your real life events?
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Please help me one more time
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Answer: 24
Yes (x-2) is a factor. There is a remainder.
Step-by-step explanation:
2³-8•2²+14•2-4
8-8•4+14•2-4
0•4+14•2-4
0+14•2-4
14•2-4
28-4
24
Hope this helps if so plz mark me brainly
2x+3y=12
if y=8
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Answers
Answer:
-6
Step-by-step explanation:
2x + 3(8) = 12
2x + 24 = 12
2x = 12 - 24
2x = -12
x = -12/2
x = -6
2x+3y=12
2x+3(8)=12
2x+24=12
-24 -24
2x=-12
\2 \2
x=-6
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Answer:
rawrrrrrr
Step-by-step explanation:
rawrrrrrrrrrrrrrrrr
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Answer:
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Answer:
So the given equation is h= -5t^2+40t
the first question asks when it will be 75 meters above the ground. So plug in 75 for h and find t
75= -5t^2+40t
start by dividing everything by 5
15= -x^2 + 8x
then you can add x squared to both sides and subtract 8x
x^2 - 8x + 15 =0
then you can plug it into the quadratic formula, which is a pain to type so I did it on paper.
x = 5 or 3
so it will be 75 meters above the ground at 3 seconds and 5 seconds
Rewriting the equation
ok so I accidentally already factored it when I divided everything by 5...
I believe the answer here is x^2 - 8x + 15 =0
The meaning of the x intercepts is when h=0 or the object is 0 meters above the ground (basically when it starts and when it ends)
the maximum height is greater than 75 because it gets to 75 meters 3 seconds after it is thrown, and continues going higher before it comes back to 75 two seconds later.
The object is airborne for 8 seconds because the second x intercept is at (8,0)
a salesperson earns a commission of $476 for selling $3400 in merchandise. what is the commission rate?
Answers
Answer:
Step-by-step explanation:
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Use the tangent to find the length of side PR.Express your answer to the nearest tenth.
Answers
Answer:
PR = 4.9
Step-by-step explanation:
For given angle Q, RQ is the adjacent leg, and PR is the opposite leg.
We recall the meaning of the tangent ratio.
tan A = opp/adj
Here we have
tan Q = opp/adj
tan 51 deg = PR/4.0
PR = 4.0 * tan 51 deg = 4.9
Answer: PR = 4.9
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Answer:
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Step-by-step explanation:
im sorry if this is incorrect.
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Answer:
The answer is A!
Step-by-step explanation:
Its correct, I took the quiz :)
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Answer:
the ball is to help with reflexes you have to dodge the ball so you dont get hit
i think
