Find the approximate perimeter of rectangle ABCD plotted below.
A(-2,6)
B(3,3)
D(-8,-4)
C(-3,-7)
Answers
Answer:
35 units
Step-by-step explanation:
Perimeter of rectangle ABCD =2(L + W)
L = AD or BC (we only need to calculate one of the two)
W = AB or DC. (we only need to calculate one of the two).
Distance between A(-2, 6) and D(-8, -4):
\( AD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)
Let,
\( A(-2, 6) = (x_1, y_1) \)
\( D(-8, -4) = (x_2, y_2) \)
\( AD = \sqrt{(-8 -(-2))^2 + (-4 - 6)^2} \)
\( AD = \sqrt{(-6)^2 + (-10)^2} \)
\( AD = \sqrt{36 + 100} = \sqrt{136} \)
\( AD = 11.7 \) (nearest tenth)
Distance between A(-2, 6) and B(3, 3):
\( AD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)
Let,
\( A(-2, 6) = (x_1, y_1) \)
\( B(3, 3) = (x_2, y_2) \)
\( AB = \sqrt{(3 -(-2))^2 + (3 - 6)^2} \)
\( AB = \sqrt{(5)^2 + (-3)^2} \)
\( AB = \sqrt{25 + 9} = \sqrt{34} \)
\( AB = 5.8 \) (nearest tenth)
Perimeter of rectangle ABCD =2(AD + AB)
= 2(11.7 + 5.8)
= 2(17.5)
= 35 units
Related Questions
Factor the following:
5∙(a+3)^2-(a+3)
Answers
Answer:
(a+3)(5a+14)
Step-by-step explanation:
Factor the polynomial.
(a+3)(5a+14)
ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°.
Answers
The length of side AB in right angled triangle ABC will be 48 cm.
What is a right angled triangle?Every triangle with one 90° angle is said to have a right angle. The triangle with a right angle is known as a right triangle because a right angle is 90 degrees.The longest side of a right angle is known as the hypotenuse, and it is opposite the right angle.
Given,
∠B= 90°, AC = 96 cm, ∠C = 30°
Now, we know, Trignometric ratio sin θ in triangle can be given by-:
sin θ = \(\frac{perpendicular}{hypotenuse}\)
From given figure,
Perpendicular= AB= ?
and Hypotenuse= AC = 96
and θ= 30°
Hence,
sin 30° =\(\frac{perpendicular}{hypotenuse}\)= \(\frac{AB}{96}\)
\(\frac{1}{2} = \frac{AB}{96}\) (∵ sin 30°= 1/2)
\(AB=\frac{96}{2}\)
\(AB= 48 cm\)
Thus, AB= 48 cm
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Correct Question:ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°. Find AB = ?
000KS
c. Sumana runs a tea shop and she buys 7.5L of milk everyday. If she
uses 4.75L of milk in the morning and the remaining milk in the
evening. Find the quantity of milk she uses in the evening
Answers
Answer:
2.75 L
Step-by-step explanation:
This is the problem of subtraction.
Total Milk sumana has = 7.5 l
Milk used in the morning = 4.75 L
Milk left for evening = Total Milk sumana has - Milk used in the morning
Milk left for evening = 7.5 l - 4.75 l = 2.75 L
Help pls
Stuck on this question
Answers
Answer:
x = 35
Step-by-step explanation:
since the figures are similar then the ratios of corresponding parts are in proportion, that is
\(\frac{x}{10}\) = \(\frac{14}{4}\) = \(\frac{7}{2}\) ( cross- multiply )
2x = 7 × 10 = 70 ( divide both sides by 2 )
x = 35
which value of x makes the equation 2+4(6-2x)
Answers
Answer:
8=8 so it is true
Step-by-step explanation:
PLS HELP I’LL MARK BRAINLIEST!!! ALSO THE ANSWER IS NOT 118!
Answers
Answer:
B. 128
Step-by-step explanation:
so the sum of the interior angle is 180
180 - 76 is 104
since both sides are the same divide 104 with 2 to get 52
to find x = 180 - 52 = 128
what is 11/2 times 1/3 as a fraction
Answers
Answer:
11/2 times 1/3 is 11/6
Step-by-step explanation:
11/2 times 1/3,
We have to multiply the numerators and denominators,
\((11/2)(1/3) = (11*1)/(2*3) = 11/6\\11/6\)
hence we get 11/6
What simple interest rate would you pay if you borrowed $5000 and paid back $6000 as promised after 5 years?
Enter the rate as a %.
(Use integers or decimals for any numbers in the expression.)
Answers
Answer:
4%
Step-by-step explanation:
6000 x 100 / 5000 = 120
after 5 years the total interest is 20%
each year interest = 4%
( 4 x 5 =20 )
is (5 , -11) a solution to a function y= -2x+1
Answers
Answer:
No
Step-by-step explanation:
y = -2x + 1
(-11) = -2(5) +1 \ Plug-in the values from the point given
-11 = -10 + 1 \ Reduce
-11 = -9 \ Simplify
-11 ≠ -9 \ Determine the valididity
please help me with my online classwork!
Answers
Answer:
840 cm²---------------------------
There are two triangular faces with base of 16 cm and height of 15 cm and three rectangular faces.
Find the sum of areas of all five faces:
S = 2*(1/2)*16*15 + (17*2 + 16)*12 = 240 + 600 = 8405 3/10 simplified jdjehehshhss
Answers
Hey there!
5 3/10
= (5 * 10 + 3)/10
= (50 + 3)/10
= 53/10
Therefore, your answer MIGHT be:
53/10
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
4/6+1/4 =
Pliss help me
Answers
1/4 can be 6/24
when you add it equals 22/24 simplified into 11/12
Answer:
11/12.
Step-by-step explanation:
The lowest common denominator of 6 and 4 is 12, so we have
4/6 + 1/4
= 4*2 / 6*2 + 1*3 / 4*3
= 8/12 + 3/12
= 11/12.
Aiden runs a farm stand that sells apples and strawberries. Each pound of apples sells
for $2 and each pound of strawberries sells for $3. Aiden made $80 from selling a
total of 35 pounds of apples and strawberries. Write a system of equations that could
be used to determine the number of pounds of apples sold and the number of pounds
of strawberries sold. Define the variables that you use to write the system.
Answers
Answer:
Step-by-step explanation:
SHOW WORK PLEASE AND THANK YOU
Two bikers start at the same place and same time. The first biker rides east at a constant velocity of 5 miles per hour and the second biker rides north at a constant velocity of 12 miles per hour. Approximately how fast (in mph) is the distance between them changing after 3 hours?
A. 5
B. 7
C. 12
D. 13
E. 17
Answers
9514 1404 393
Answer:
D. 13
Step-by-step explanation:
The distance between the bikers is the hypotenuse of a right triangle whose legs are a linear function of time. It will be ...
d(t) = √((5t)² +(12t)²) = √((25 +144)t²) = 13t
The distance between the bikers is increasing at the constant rate of 13 miles per hour. The rate is still 13 miles per hour after 3 hours.
Question number 13 needs to answered
Answers
Final speed after slowing down by 15 miles per hour and reducing the speed by one third is 25 miles per hour.
Let's break down the steps to determine the final speed:
Step 1: Convert the speed from miles per minute to miles per hour.
Since you're driving one and a half miles per minute, we need to convert it to miles per hour. There are 60 minutes in an hour, so we multiply 1.5 by 60 to get 90 miles per hour.
Step 2: Slow down by 15 miles per hour.
Subtract 15 from the initial speed of 90 miles per hour, resulting in 75 miles per hour.
Step 3: Reduce the speed by one third.
To find one third of 75 miles per hour, we divide it by 3, which gives us 25 miles per hour.
Therefore, the final speed after slowing down by 15 miles per hour and reducing the speed by one third is 25 miles per hour.
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which is it? please help me and i will give brainliest
Answers
Answer: A, 1/2
Step-by-step explanation:
he is simply using 1 cup of bs for each cup of ws so when you do it its i cup of ws then its hald of 1 bs
Answer:
it is 1/2 i.e. the first option
this is simple ratio method;
white : brown
2 : 1
1 : x
x = 1/2 cups
Hope this helps!
I would really appreciate if you mark me brainliest as I have been trying to get there for a veryyy long time now :)
Please solve this for 15 points
Answers
Answer:
on the outside of the bracket. The divisor is the number you're dividing by.Set up the division problem with the long division symbol or the the dividend, on the inside of the bracket. The dividend is the number you're dut 32, the divisor, on the outside of the bracket. The divisor is the number you're dividing by.Set up the division problem with the long division symbol or the long division brackPut 487, the dividend, on the inside of the bracket. The dividend is the number yoPut 32, the divisor, on the outside of the bracket. The divisor is the number you're dividing by.
Step-by-step explanation:
I need a help with this hw
Answers
The values of the trigonometric ratios are: a) - 7/5, b) -75 c ) -1/5 d ) -25/12
What is trigonometric ratio?
Trigonometric ratios are measurements of the lengths of two sides of a triangle. There are three basic trigonometric ratios: sine, cosine, and tangent. Sine ratios are the ratios of the length of the side opposite the angle they represent over the hypotenuse
the give parameters are:
tanα = -4/3 where π/2 <α<π and sinβ = √3/2, 0<β<π/2
a) sin(α+β)
Using the trig ratios tan = opp/adj
but from pyth. rule, 4² + 3² = h²
16+9 = h²
h = √25 = 5
Now from trig Sin(α+β)
4/5 + 3/5
=- 7/5
b) cos(α+β)
cos = ad/hypo
4/5 + 3/5
= -7/5
c) Sin(α-β)
4/5 - 3/5
-1/5
d) tan(α-β)
= -4/3 - 3/4
= (-16 - 9)/ 12
-25/12
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Anna drives her car at a speed of 70 km per hour. How much distance will she cover in 3 hours 30 minutes?
Answers
Distance» \(speed \times time\)
Distance» \(70 \times \frac{7}{2} \)
Distance» \( \frac{490}{2} \)
Distance» 245
Answer:
245 units
Step-by-step explanation:
Anna drives her car at a speed of = 70 kmph
To Find:
How much distance will she cover in 3 hours 30 minutes.
Solution:
We'll use here the formula of Speed,then plug the values which are given.
Speed = Distance/Time
Speed = 70 kmphDistance = 3 hr 3 mins = 7/2 hrs70 = D/7/2
7/2*70 = Distance
7*35 = Distance
Distance = 245
We can conclude that Anna can cover 245 units in 3 hrs 30 mins.
Kimora drove with frankie to her mothers house which is 310 miles away. If it took them 6 hours, what was their average speed ?
Answers
Answer:
51.6 was the average speed
Step-by-step explanation:
speed= distance/time
I'd like to know what is -5.33333333333 as a fraction please help me thank you very much :)
Answers
Answer:
-5 33333333333/100000000000
Step-by-step explanation:
Answer:
-5 3333333/10,000,000
Step-by-step explanation:
all u have to do is divide 5.33333333333 by how much the places there are
ASAP
What is the sum of 16.87 + (–98.35)?
–115.22
–81.48
81.48
115.22
Answers
Solution,
16.87+(-98.35)
=16.87-98.35
= -81.48
Hope it helps
Good luck on your assignment
Answer:-81.48
Step-by-step explanation:
16.87 + (–98.35)
-81.48
If you stumble in other questions like there you can use a calculator or ask me. :D hope that helps
which is a equivalent expression to 3^3x3^3x3?
Answers
\(\huge\text{Hey there!}\)
\(\mathsf{3^3\times3^3\times3}\)
\(\mathsf{3^3 = 3 \times3\times3 = 9\times 3 = \bf 27}\)
\(\mathsf{27\times27\times3 =\ ? }\)
\(\mathsf{27\times27 = \bf 729}\)
\(\mathsf{729\times 3}\)
\(\mathsf{= \bf 2,187}\)
\(\large\text{So you are looking for: \bf 2,187}\)
\(\large\text{Option A.}\)
\(\mathsf{3^6}\)
\(\mathsf{= 3\times3\times3\times3\times 3\times3}\)
\(\mathsf{3\times 3 = \bf 9}\)
\(\mathsf{= 9\times 9\times 9}\)
\(\mathsf{9\times9 = \bf 81}\)
\(\mathsf{= 81\times9}\)
\(\mathsf{= \bf 729}\)
\(\large\text{So Option A is NOT equivalent because it is too small }\)
\(\large\text{Option B.}\)
\(\mathsf{3^7}\)
\(\mathsf{= 3\times3\times3\times3\times3\times3 \times3}\)
\(\mathsf{3\times 3 = \bf 9}\)
\(\mathsf{= 9\times9\times9\times3}\)
\(\mathsf{9\times9 = \bf 81}\)
\(\mathsf{81\times9\times3}\)
\(\mathsf{81\times 9 = \bf 729}\)
\(\mathsf{729\times3}\)
\(\mathsf{= \bf 2,187}\)
\(\large\text{Option B. could possibly be your answer}\)
\(\mathsf{3^9}\)
\(\mathsf{= \bf 19,683}\)
\(\large\text{Option C. Can’t be your answer because it’s too big!}\)
\(\mathsf{3^{12}}\)
\(\mathsf{= \bf 531,441}\)
\(\large\text{Option D. cannot be your answer because it is way too big}\\\ \large\text{similar to your original answer (2,187)}\)
\(\boxed{\boxed{\large\textsf{Answer: \huge Option B.}}}\huge\checkmark\)
\(\text{Good luck on your assignment and enjoy your day!}\)
~\(\frak{Amphitrite1040:)}\)
Answer: ur answer is B mark me brainliest
Step-by-step explanation:
A factory manager wishes to install types of machines, small and large. A small machine needs 2 operators and occupies 4m² of floor space. A large machine needs 3 operators and accupies 8m³of floor space. There are up to 30 operators available and 72m² of floor space. At Least 4small machines and at least 5 large machines must be installed.
a) Taking X to be the number of small machine, and y as the number of large machine to be installed, write down. the four major inequalities required.
b) Draw a graph to show the region satisfying the inequalities
c) Determine the maximum number of machines he can install .
d) If the profit made by each small machine is 250,000 and by the large type is 300,000 per week, find the maximum profit the factory can make in one week and the number of machines of each type that should be installed.
Answers
a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72
b) We have drawn the graph.
c) The maximum number of machines that can be installed is 11.
d) The maximum profit is 2,500,000.
What is inequality?
An inequality is a mathematical statement that shows the relationship between two values where one value is either greater than or less than the other value. It is represented by symbols such as >, <, ≥, or ≤. For example, if x is a variable and we want to express that x is greater than 5, the inequality would be written as x > 5.
a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72
b) To graph the region, we can plot the lines that define the inequalities and shade the area that satisfies all of them.
c) Solving the system of inequalities graphically, we find the maximum number of machines that can be installed is 11 (6 small and 5 large).
d) To find the maximum profit, we need to substitute the number of machines into the profit equation. P = 250,000X + 300,000Y. Plugging in X = 6 and Y = 5, we find the maximum profit to be 2,500,000.
Hence,
a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72
b) We have drawn the graph.
c) The maximum number of machines that can be installed is 11.
d) The maximum profit is 2,500,000.
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Are the following figures similar?
Trapezoids ABCD and EFGH are shown. Angle A equals 137 degrees, Angle B equals 90 degrees, Angle C equals 90 degrees, Angle D equals 43 degrees, Angle E equals 136 degrees, Angle F equals 90 degrees, Angle G equals 90 degrees, Angle H equals 44 degrees.
Answers
No, the trapezoids are not similar because their corresponding angles do not have the same measures.
The given trapezoids ABCD and EFGH can be analyzed to determine if they are similar. Similarity in geometric figures implies that their corresponding angles are congruent, and their corresponding sides are proportional.
Let's examine the angles of the trapezoids:
In trapezoid ABCD:
Angle A = 137 degrees
Angle B = 90 degrees
Angle C = 90 degrees
Angle D = 43 degrees
In trapezoid EFGH:
Angle E = 136 degrees
Angle F = 90 degrees
Angle G = 90 degrees
Angle H = 44 degrees
By comparing the angles, we can observe that angles B and F are both right angles (90 degrees) in both trapezoids. Additionally, angles C and G are also right angles (90 degrees) in both trapezoids.
However, angles A and E, as well as angles D and H, do not have the same measures. Angle A measures 137 degrees in trapezoid ABCD, while angle E measures 136 degrees in trapezoid EFGH. Similarly, angle D measures 43 degrees in trapezoid ABCD, while angle H measures 44 degrees in trapezoid EFGH.
Since the corresponding angles in the two trapezoids do not have the same measures, we can conclude that trapezoids ABCD and EFGH are not similar.
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Do the following lengths form a right triangle?
Answers
Answer:
Yes, they do
Step-by-step explanation:
Because
6+8=14>9
6+9=15>8
8+9=17>6
The equation y = 1/4x represents a proportional relationship. What is the constant of proportionality?
Answers
Answer:
The constant of proportionality is k=1/4
Step-by-step explanation:
For the equation y=kx, y varies directly with x with the constant of proportionality k. Therefore, k=1/4 is the answer.
i need helppppp please answer correctlyyyy Multiply (−4) × (−2) × (−5).
Answers
Answer:
-40hope this helps...........
First Multiplying an odd number of negative terms makes the product negative then To make the calculation easier, first multiply the numbers that result in multiples of 10 then multiply the numbers 4x10 =40
The question is asked in the attached file,. Kindly someone answer it in the best way.
Answers
According to the Empirical Rule, 99.7% of the measures fall within 3 standard deviations of the mean in the normal distribution.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.More can be learned about the Empirical Rule at https://brainly.com/question/10093236
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The length of the longer leg of a right triangle is 4ft more than twice the length of the shorter leg. The length of the hypotenuse is 6ft more than twice the length of the shorter leg. Find the side lengths of the triangle.
a. Find the length of the shorter side
b. Find the length of the longer side
c. Find the length of the hypotenuse
d. Find the side lengths of the triangle.
Answers
Answer: Shorter side = 10 feet
Longer side = 24 feet
Hypotenuse = 26 feet
The side lengths of the triangle are 10ft, 24ft and 26ft.
Step-by-step explanation:
Let the length of the shorter leg be x.
The length of the longer leg of a right triangle is 4ft more than twice the length of the shorter leg. This will be: = 2x + 4
The length of the hypotenuse is 6ft more than twice the length of the shorter leg. This will be: = 2x + 6
Note that the square of the hypothenuse will be equal to the square of the other two sides. This will be:
x² + (2x + 4)² = (2x + 6)²
x² + (2x + 4)(2x + 4) = (2x + 6)(2x + 6)
x² + 4x² + 8x + 8x + 16 = 4x² + 12x + 12x + 36
x² + 4x² + 16x + 16 = 4x² + 24x + 36
5x² + 16x + 16 = 4x² + 24x + 36
Collect like terms
5x² - 4x² + 16x - 24x + 16 - 36 = 0
x² - 8x - 20 = 0
x² - 10x + 2x - 20 = 0
x(x - 10) + 2(x - 10) = 0
Therefore, x - 10 = 0
x = 10
a. length of the shorter side = 10ft
b. Length of the longer side = 2x + 4 = 2(10) + 4 = 20 + 4 = 24ft
c. length of the hypotenuse = 2x + 6 = 2(10) + 6 = 20 + 6 = 26ft
d. The side lengths of the triangle are 10ft, 24ft and 26ft.
Answer:
egg
Step-by-step explanation:
yes