MATHEMATICS HIGH SCHOOL

Calculate the length of AB. Round to the nearest tenth.

Answers

Answer 1

Answer:

Answer:

AB = 10.06 cm

Step-by-step explanation:

Consider the given figure,

We have to find the length of side AB.

Lets rename the figure first, ABCD forms a rectangle. So , CB = DA = 12 cm

Also, EA = ED +DA ⇒ 15 = ED + 12 ⇒ ED = 15 - 12 ⇒ ED = 3 cm

Pythagoras theorem states that in a right triangle the sum of square of base and perpendicular is equal to square of hypotenuse.

Using, Pythagoras Theorem on Δ EDC,

$(EC)^2=(ED)^2+(DC)^2$

ED = 3 cm , EC = 10.5, Substitute, we get,

$\Rightarrow (10.5)^2=(3)^2+(DC)^2$

Solve for DC, we get,

$\Rightarrow 110.25=9+(DC)^2$

$\Rightarrow 110.25-9=(DC)^2$

$\Rightarrow (DC)^2=101.25$

$\Rightarrow DC=√(101.25)$

$\Rightarrow DC=10.06$

Since, ABCD is a rectangle. Thus, DC = AB

Hence, AB = 10.06 cm

Answer 2

Answer:

Answer:

AB =10.06 ≈10.1 units

Step-by-step explanation:

To answer this question we must draw a parallel line to the side AB, closing a triangle, so that we can visualize a triangle, and a square.

1) After drawing this red line. Since it's parallel we can assume it is the same length as AB. And as we have a Rectangular Triangle we can apply the Pythagoras Theorem.

The Parallelism assure us that the segment to the left below the red line measures the same if the angle is the same, namely 90º.

$10.5^(2)=3^(2)+h^(2) \n 110.25=9+h^(2) \n 110.25-9=9+h^(2) -9\n 101.25= h^(2)\n h=√(101.25)\n h=10.06 u$

Since h=AB Therefore AB=10.06 units

Related Questions

Bilquis practices the piano 903 minutes in 3 weeks. Assuming she practices the same amount every week, how many minutes would she practice in 5 weeks?
Which equation can pair with 3x + 4y = 8 to create a consistent and independent system?
Simplify. Write each answer in scientific notation. 15. (6 ˣ 10^-5)^3 19. 3 ˣ 10^-2 / 8 ˣ 10^-1 20. 4.1 ˣ 10^-4 / 1.28 ˣ 10^-5 21. 1.91 ˣ 10^3 / 5 ˣ 10^-4
Is (-2) to the 27th power positive or negative and how would you know?
F(x) = 7x + 7, g(x) = 6x2Find (fg)(x).

Factor : 49c^2 - 25d^6

Answers

49c^2 - 25d^6
(7c)^2 - (5d^3)^2
(7c + 5d^3)(7c - 5d^3)

The answer is: (7c + 5d^3)(7c - 5d^3).

Hello,

$49c^(2)-25d^(6)=(7c)^2-(5d^3)²=[7c-5d^3][7c+5d^3]$

2x-[4-3(2^5+18y)] simplify

Answers

$2x-[4-3(2^5+18y)]\n\n=2x-[4-3(32+18y)]\n\n=2x-(4-96-54y)\n\n=2x-(-92-54y)\n\n=2x+92+54y$

= 2x - [4 - (96 + 54y)]
= 2x - 4 + 96 + 54y
= 2x + 54y + 92

Find the non-extraneous solutions of the square root of the quantity x plus 9 minus 5 equals quantity x plus 4.

Answers

( x+9) - 5= ( x+4 ) Try this it should help you ^^

Solve Mathematics question, in photo. Please

Answers

(-2,3) if you just plug in X and y you get both -4 and 12

One of diagonals of a parallelogram is its altitude. What is the length of this altitude, if its perimeter is 50 cm, and the length of one side is 1 cm longer than the length of the other?

Answers

The length of that altitude is 5 cm.

Explanation

According to the below diagram, $ABCD$ is a parallelogram with diagonal $\overline{AC}$ as its altitude.

Suppose, the length of side $\overline{AB}$ is $x$ cm.

As the length of one side is 1 cm longer than the length of the other, so the length of side $\overline{BC}$ will be: $(x+1) cm$

Given that, the perimeter of the parallelogram is 50 cm. So, the equation will be.....

$2[x+(x+1)]=50\n \n 2(2x+1)=50\n \n 4x+2=50\n \n 4x=48\n \n x= 12$

So, the length of $\overline{AB}$ is 12 cm and the length of $\overline{BC}$ is (12+1)= 13 cm.

Suppose, the length of the altitude( $\overline{AC}$ ) is $h$ cm.

Now, in right angle triangle $ABC$ , using Pythagorean theorem....

$(AC)^2+(AB)^2= (BC)^2\n \n h^2+(12)^2= (13)^2\n \n h^2+144= 169\n \n h^2= 25\n \n h= √(25)= 5$

So, the length of that altitude is 5 cm.

X + y = 1,000
0.06x = 0.04y

Answers

If:
x + y = 1000
then:
y = 1000 - x

We can plug that into the other equation to solve for a value of x.
0.06x = 0.04y
0.06x = 0.04(1000-x)
0.06x = 40-0.04x
0.1x = 40
x = 400

We can then solve for y:
y = 1000 - 400
y = 600

Therefore, x = 400 and y = 600.

Other Questions

(07.02 MC)An equation is shown below: 5(3x − 4) = 1 Which of the following correctly shows the first two steps to solve this equation? Step 1: 15x − 20 = 1; Step 2: 15x = 21 Step 1: 15x − 4 = 1; Step 2: 15x = 5 Step 1: 8x + 1 = 1; Step 2: 8x = 0 Step 1: 8x − 9 = 1; Step 2: 8x = 10

Skateboard Revenue: A skateboard shop sells about 50 skateboards per week for the price advertised. For each $1 decrease in price, about 1 more skateboard per week is sold. The shop's revenue can be modeled by y=(70-x) (50+x). Use vertex form to find how the shop can maximize weekly revenue. [I can get this into vertex form, but I'm not understanding how to read the vertex form of the equation to answer the question]

When it goes on sale for $1,600, Mikah buys a new plasma television that is valued at $1,800. He takes $300 from his savings account to use as a down payment and finances the rest. Choose the true statement.a. Mikah's assets increased by $1,300. b. Mikah's assets increased by $1,500. c. Mikah's assets increased by $1,600. d. Mikah's assets increased by $1,800.

Emily is 280 miles away from home. She is traveling back at a rate of 40 miles per hour. Determine which graphs and which equation represents Emily’s distance from home, D, after Emily travels h hours.