Find the approximate perimeter of rectangle ABCD plotted below.
A(-2,6)
B(3,3)
D(-8,-4)
C(-3,-7)

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

Answer:

hope this helps...........

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.

Answer:

51.6 was the average speed

Step-by-step explanation:

speed= distance/time

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

The values of the trigonometric ratios are: a) - 7/5, b) -75 c ) -1/5  d ) -25/12

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

Learn more about trigonometric ratios on https://brainly.com/question/23130410

#SPJ1

Answer:

8=8 so it is true

Step-by-step explanation:

Answer:

(a+3)(5a+14)

Step-by-step explanation:

Factor the polynomial.

(a+3)(5a+14)

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

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:)

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.

Answer:

Step-by-step explanation:

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.

For more such question on Speed

https://brainly.com/question/553636

#SPJ8

\(\huge\text{Hey there!}\)

\(\mathsf{3^3\times3^3\times3}\)

\(\mathsf{3^3 = 3 \times3\times3 = 9\times 3 = \bf 27}\)

\(\mathsf{27\times27\times3 =\ ? }\)

\(\mathsf{27\times27 = \bf 729}\)

\(\mathsf{729\times 3}\)

\(\mathsf{= \bf 2,187}\)

\(\large\text{So you are looking for: \bf 2,187}\)

\(\large\text{Option A.}\)

\(\mathsf{3^6}\)

\(\mathsf{= 3\times3\times3\times3\times 3\times3}\)

\(\mathsf{3\times 3 = \bf 9}\)

\(\mathsf{= 9\times 9\times 9}\)

\(\mathsf{9\times9 = \bf 81}\)

\(\mathsf{= 81\times9}\)

\(\mathsf{= \bf 729}\)

\(\large\text{So Option A is NOT equivalent because it is too small }\)

\(\large\text{Option B.}\)

\(\mathsf{3^7}\)

\(\mathsf{= 3\times3\times3\times3\times3\times3 \times3}\)

\(\mathsf{3\times 3 = \bf 9}\)

\(\mathsf{= 9\times9\times9\times3}\)

\(\mathsf{9\times9 = \bf 81}\)

\(\mathsf{81\times9\times3}\)

\(\mathsf{81\times 9 = \bf 729}\)

\(\mathsf{729\times3}\)

\(\mathsf{= \bf 2,187}\)

\(\large\text{Option B. could possibly be your answer}\)

\(\mathsf{3^9}\)

\(\mathsf{= \bf 19,683}\)

\(\large\text{Option C. Can’t be your answer because it’s too big!}\)

\(\mathsf{3^{12}}\)

\(\mathsf{= \bf 531,441}\)

\(\large\text{Option D. cannot be your answer because it is way too big}\\\ \large\text{similar to your original answer (2,187)}\)

\(\boxed{\boxed{\large\textsf{Answer: \huge Option B.}}}\huge\checkmark\)

\(\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer: ur answer is B mark me brainliest

Step-by-step explanation:

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

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

The length of side AB in right angled triangle ABC  will be 48 cm.

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

Learn more about right angled triangle here:

https://brainly.com/question/3772264

#SPJ1

Correct Question:ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°. Find AB = ?

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

70 = 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.

Answer:

---------------------------

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:

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 :)

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.

To learn more about the inequalities, visit:

https://brainly.com/question/24372553

#SPJ1

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.

for such more question on trapezoids

https://brainly.com/question/22351006

#SPJ8

According to the Empirical Rule, 99.7% of the measures fall within 3 standard deviations of the mean in the normal distribution.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

More can be learned about the Empirical Rule at https://brainly.com/question/10093236

#SPJ1

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

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 )

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

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:

Answer:

Yes, they do

Step-by-step explanation:

Because

6+8=14>9

6+9=15>8

8+9=17>6

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.

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