Question 4 (1 point)
The image shows quadrilateral ABCD.
Find the area of ABCD. Explain or show your reasoning.
Answers
Answer:
25
Step-by-step explanation:
Using the Pythagorean Theorem, we can find the side length of each side.
a^2 + b^2 = c^2
=> 3^2 + 4^2 = x^2
=> 9 + 16 = x^2
=> x = 5
By applying the same formula for each side, we will get that each side is 5 units.
So, the area = 5*5 = 25
The quadrilateral is a square and the area of square is 25 square units.
What is a quadrilateral?
A quadrilateral is 2-dimensional geometric closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points.
For the given situation,
The quadrilateral ABCD has points A(0,4), B(3,0), C(7,3), D(4,7).
The distance these points can be found by
[tex]d=\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]
AB = [tex]d=\sqrt{(3-0)^{2}+(0-4)^{2} }[/tex]
⇒ [tex]AB = \sqrt{3^{2}+4^{2} }[/tex]
⇒ [tex]AB=\sqrt{9+16}[/tex]
⇒ [tex]AB=\sqrt{25}[/tex]
⇒ [tex]AB=5[/tex]
BC = [tex]d=\sqrt{(7-3)^{2}+(3-0)^{2} }[/tex]
⇒ [tex]BC=\sqrt{4^{2}+3^{2} }[/tex]
⇒ [tex]BC=5[/tex]
CD = [tex]d=\sqrt{(4-7)^{2}+(7-3)^{2} }[/tex]
⇒ [tex]CD=\sqrt{(-3)^{2} +4^{2} }[/tex]
⇒ [tex]CD=5[/tex]
DA = [tex]d=\sqrt{(4-0)^{2}+(7-4)^{2} }[/tex]
⇒ [tex]DA=\sqrt{4^{2}+3^{2} }[/tex]
⇒ [tex]DA=5[/tex]
Since AB = BC = CD = DA, the quadrilateral is a square.
The formula of area of quadrilateral is
[tex]A=(side)^{2}[/tex]
⇒ [tex]A=5^{2}[/tex]
⇒ [tex]A=25[/tex]
Hence we can conclude that the quadrilateral is a square and the area of square is 25 square units.
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Related Questions
John ran a race in 36 minutes. If each lap takes 9 minutes to run, write and solve an equation to find out how many laps John had to run.
SHOW YOUR WORK AND SOLVE PLEASE
Answers
Answer:
4 laps
Step-by-step explanation:
Solved using a proportion.
[tex]\frac{1}{9} = \frac{y}{36}[/tex]
9 × y = 1 × 36
9y = 36
9y ÷ 9 = 36 ÷ 9
y = 4
Plz help me with this one!
Answers
Step-by-step explanation:
[tex]y = x + 5 \: \: \: \: y = - 3x + 1 \\ y = x + 5 \: \: \: \: x + 5 = - 3x + 1 \\ y = x + 5 \: \: \: \: 4x = - 4 \\ y = x + 5 \: \: \: \: x = - 1 \\ y = 4 \: \: \: \: x = - 1[/tex]
Bentley had $25 to spend on 5 paintbrushes for his art class. After buying them, Bentley had $5 left. How much did each of the paintbrushes cost?
Answers
Answer:
$4
Step-by-step explanation:
$25-$5=20
20 divided by 5 = 4
I NEED HELP!
The function f(x) is a quadratic function and the zeros of f(x) are - 2 and 5. The y-intercept of f(x) is 30. Write the equation of the quadratic polynomial in standard form.
f(x)=___________
Answers
Answer:
Step-by-step explanation:
First of all you have to put the zeros into factor form.
y1 = (x + 2)(x - 5)
Notice that the x changes sigh. You say that the zeros are -2 and 5. To get y1 to go to zero, you must make x the opposite sign of what you are given.
Now you have to expand the factored form to get the standard form
y = x^2 + 2x - 5x - 10
y = x^2 - 3x - 10
That's not the right answer.
f(0) = 30 but you have - 10 at the end so you have to multiply the factored form by - 3
-3(f(x)) = -3(x + 2)(x - 5)
-3(f(x)) = -3(x^2 - 3x - 10)
f(x) = -3x^2 + 9x + 30
f(0) = -3(0)^2 + 9(0) + 30
f(0) = 30
The quadratic still has roots of (x +2)(x - 5) but that 3 makes the y intercept = 30.
See the graph below.
6 grade math pls help
Answers
answer
measure of o is 75
and n is same as o as the sides are same
hope this helps you
how much markup is $75 to $180
Answers
Answer:
105
Step-by-step explanation:
75+105 =180
A number "X" greater than 8
Answers
Answer:
X > 8
Step-by-step explanation:
Using the keywords greater than helps you.
The median for the 5 numbers 2647, 1956, 2250, 2141, and x is 2141. What is the largest possible value for the number x?
Answers
Answer:
2140
Step-by-step explanation:
Median can be described as the number that lies in the middle of a set of arranged observations. the observations can be arranged in ascending or descending order
in a set of 5 numbers, the median would be the 3rd number
the median is 2141. there was to be 2 numbers before and after 2141
1956, x 2141, 2250, 2647
the largest possible value of x is 2140. this is the largest number that is less than 2140
PLEASE HELP MEEEEE PLEASE!
Answers
Answer: my best guess would be c
Step-by-step explanation: I hope you figure this out maybe use Socratic app that might help
Answer:
(-2,2)
Step-by-step explanation:
the red line is y = x + 4 ( we know this as x = -4 is the x intercept)
the green one is y = -x (it intercepts in origin)
so, we equal the two equations to each other to get the interception point:
x + 4 = - x
4 = -2x
x = -2
we substitute x = -2 in any of the equations we get
y = -2 + 4 = 2 or y = -(-2) = 2
so the point is (-2,2) which is option C.
The low temperature at 6:45 A.M. was −22°F. At 3:15 P.M. the temperature was 5°F. What was the range of temperature for the day? A −27°F B −17°F C 17°F D 27°F
Answers
Answer:
D
Step-by-step explanation:
-22°F+27°F=5°F
have a nice day or evening
Answer:
D
Step-by-step explanation:
I took the test
Can someone please help me
Answers
You take each price of the games so, 1x2=2 2x2=4 2.25x2=4.5. Then add it up = 10.50. Since you already used ten you do 20-10.50 and get 9.50
How do you work the problem 6y < 18 out
Answers
Answer:
y<3
Step-by-step explanation:
6y<18
y<18/6
y<3
I hope this helps
Answer: you can see what number times 6 gets you 18 so it would be y<3
Step-by-step explanation:
how do i solve this question
Answers
Answer:
18.18
Step-by-step explanation:
total sum of angle of quadrilateral is 360
70+60+ 7x-4+4x-3=360
160-7 +11x =360
153 +11x =360
11x=360-153
x=207/11
x=18.18
A playground is rectangular with a length of 12 miles. If the area of the playground is 58 square miles, what is its width? Input your answer as a fraction.
Answers
Answer:
4 5/6 miles
Step-by-step explanation:
Area of a rectangle = length x width
58 = 12 x width
to find width, divide both sides of the equation by 12
58/12 = 4 whole number and 10 would remain
4 10/12
to simply, divide numerator and denominator by 2
4 5/6 miles
Determine the opposite of 3p^7-8p
Answers
Step-by-step explanation:
Maybe you should flip flop
add 4x²y,-2xy²,-5xy²,3x²y plz explain
Answers
5xy^2 +
3x^2y
_____________
12x^5y^4-2xy^2
This is so because 4+5+3 is 12, then using laws of indices to add your x and y you get x^5 and y^4
To simplify your answer to the lowest you have it in the form of
3x^2y^2(4x^2y - 2xy^2)
If you multiply this as well you get the same answer I got with the addition
1. Mr. Jay has 24 students and 75% of them are boys. How many are boys?
Answers
Answer:
18
Heart if this helped
I need help fast please
Answers
Answer:
-2/3
Step-by-step explanation:
8^(x+2) =8^-2x
since the base are the same we deal with the exponent
x+2=-2x
x= -2/3
HELP! I NEED THIS QUESTION ANSWERED ASAP!!!!!
HERE!
Angle X measures 53°
What type of angle is angle X?
Answers:
1 ) Obtuse
2) Right
3) Acute
Answers
Answer:
3 ) Acute
Step-by-step explanation:
Acute Angle - An angle less than 90 degrees.
Right Angle - An angle that is exactly 90 degrees.
Obtuse Angle - An angle more than 90 degrees and less than 180 degrees.
Straight Angle - An angle that is exactly 180 degrees.
Answer:
3)Acute
Step-by-step explanation:
any angle that is under a 90 degree angle or a right angle, is an acute angle. any angle that is above 90 degrees or a right angle is an obtuse andgle
finding area of circle with radius , giving brainliest :)) pls help asap
Answers
Answer:
number 2 is the answer or 4*pi inches² or 12.6
Step-by-step explanation:
HELP MEEEEEEEEEEEE 3.0
Answers
Answer:
I think that J would be the answer , It is more reliable than the left ones .
Hope it was helpful , good luck ^^
Which statement about the graphs is true? NEED HELP!
Graph A is a valid density curve because the part of the graph from 2 to 6 is below the horizontal axis.
Graph A is not a valid density curve because the part of the graph from 1 to 2 is above the horizontal axis.
Graph B is not a valid density curve because part of the horizontal axis has negative values.
Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.
Answers
Answer:
Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.
Step-by-step explanation:
A density curve is a graph that shows probability.
There are a few properties that those curves have:
The curves are normalized, which means that the area inside the curve is always equal to 1 (or the 100% of possibilities).
And the probabilities are always defined with positive numbers between 0 and 1, which means that we can not have a density curve with elements below the horizontal axis.
From this, we can conclude that graph A is not a density curve (but neither of the two given options for graph A are correct, then we can discard these).
Now let's look at graph B.
We can see that all points are above the horizontal axis, so that is good.
Now let's compute the area inside the curve.
We can see two triangles, remember that the area of a triangle of base b and height h is:
A = (b*h)/2
To calculate the base in the image, just take the difference between the rightmost vertex and the left vertex.
The base of the left triangle is b = (-3 - (-5)) = 2, and the height is h = 0.25
Then the area is:
A1 = (2*0.25)/2 = 0.25
The base of the right triangle is b = (3 - (-3)) = 6, and the height is h = 0.25
Then the area of this triangle is:
A2 = (6*0.25)/2 = 0.75
If add these areas, we get:
Total area = A1 + A2 = 0.25 + 0.75 = 1
Total area = 1
So we have an area under the curve equal to 1, which means that graph B is a valid density curve.
And the correct option is then:
Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.
which number line shows the solution to the inequality -2x-3> -11
Answers
The solution to the inequality is x is less than 4.
What is inequility ?
An inequality is a mathematical statement that expresses a relationship between two values or expressions that are not necessarily equal. Inequalities are often used in mathematics to compare values, express constraints or limitations, and solve problems involving ranges of values.
To solve the inequality -2x - 3 > -11, we can start by isolating the variable x.
-2x - 3 > -11
Add 3 to both sides:
-2x > -8
Divide both sides by -2 (and flip the inequality because we're dividing by a negative number):
x < 4
So the solution to the inequality is x is less than 4.
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If each square in the following floor plan represents 2.5 feet, what are the dimensions of the living room?
Answers
1.7. In a Maths class, the girl to boy ratio is 7:5.
If there are 20 boys, how many girls are in the class?
Answers
Answer:
28 girls
Step-by-step explanation:
Let total students be ‘X’
No of girls = (X-20)
Girls/Boys=7/5=(X-20)/20
7(20) =5(X-20)
140=5X-100
5X=240
X = 240/5
X =48
So, Total Students are 48
No of girls = (X-20) = 48-20 = 28
PLEASE HELP I HAVE NO IDEA WHAT TO DO!!!
Answers
Answer: multiply and round I'm pretty sure tell me if u want me to multiply for u
Step-by-step explanation:
Freddy exercise 3.5 hours per day 4 days last week he burned 440 calories per hour while exercising how many calories did Freddie burn by exercising last week
Answers
Answer:
6,160 calories
Step-by-step explanation:
total hours of exercising = 3.5 x 4 = 14
burns 440 calories per each hour
total calories burned is 440 x 14
HELP ME IN NUMBER 1 AND 2
Answers
Answer:
Number is is A Number 2 is 77 trust ik math
Please need help you know this
Answers
Answer:
Rule: Output = 2 * input + 1
Right blank: Output = - 1
Left blank: Input = 4
Step-by-step explanation:
Rule
Start with the rule
Output = 2 * input + 1
Let the output = y
Let the input = x
y = 2x + 1
Now
Right Blank
x = - 1
y = 2*-1 + 1
y = -2 + 1
y = - 1
That's the output for -2
Left Blank
The second blank asks you to solve for the input (x) The output (y) is 9
9 = 2x + 1 Subtract 1 from both sides
9-1 = 2x Combine
8 = 2x Divide by 2
8/2 = 2x/2
x = 4
On a number line, show all values of x for which |x|>3