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tino4ka555 [31]
3 years ago
8

Triangle A B C is shown. Angle A B C is a right angle. An altitude is drawn from point B to point D on side A C to form a right

angle. The length of A D is x, the length of D C is 4 x, and the length of B D is 10.
What is the value of x?

a. 2 units
b. 3 units
c. 5 units
d. 8 units
Mathematics
1 answer:
Anika [276]3 years ago
3 0

Answer:

C. - X = 5 units

Step-by-step explanation:

We need to solve for x from the given figure.

In ΔADB and ΔCDB

 ∠ABD=∠BCD         (Corresponding angle of two right triangle)

 ∠ADB=∠CDB         (Each 90°)

∴  ΔADB ≈ ΔCDB  By AA similarity

If two triangles are similar then ratio of their corresponding height are same.

Substitute the value of side into the expression

Cross multiply and solve for x

x can't be negative because side of triangle is positive.

Hence, The value of x is 5 units.

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Please help Which of the following inequalities is graphed on the coordinate plane?
Gekata [30.6K]

Answer:

The inequality which represents the graph is y ≤ -2x + 1 ⇒ A

Step-by-step explanation:

To solve the question you must know some facts about inequalities

  • If the sign of inequality is ≥ or ≤, then it represents graphically by a solid line
  • If the sign of inequality is > or <, then it represents graphically by a dashed line
  • If the sign of inequality is > or ≥, then the area of the solutions should be over the line
  • If the sign of inequality is < or ≤, then the area of the solutions should be below the line

Let us study the graph and find the correct answer

∵ The line represented the inequality is solid

∴ The sign of inequality is ≥ or ≤

→ That means the answer is A or B

∵ The shaded area is the area of the solutions of the inequality

∵ The shaded area is below the line

∴ The sign of inequality must be ≤

→ That means the correct answer is A

∴ The inequality which represents the graph is y ≤ -2x + 1

3 0
3 years ago
He paid $5.83 to make each shirt and sold each shirt at a marked-up price.
Naddika [18.5K]

we know he made a profit of 1834 for 200 shirts, let's divide those to see how much profit per shirt

\cfrac{1834}{200}\implies \cfrac{917}{100}\implies 9.17

so he made a profit of 9.17 per shirt, now profit is surplus value, value beyond the cost, we know its cost was 5.83 per shirt, so if we take 5.83 to be 100%, how much is 9.17 off of it in percentage?

\begin{array}{ccll} amount&\%\\ \cline{1-2} 5.83&100\\ 9.17&x \end{array}\implies \cfrac{5.83}{9.17}=\cfrac{100}{x}\implies 5.83x=917 \\\\\\ x=\cfrac{917}{5.83}\implies x \approx 157.29

7 0
2 years ago
Can someone please help<br><br>find slope/rate of change <br>a. 1/3<br>b. 3<br>c. 30<br>d. 10​
Lera25 [3.4K]

Answer:

Answer should be 1/4, since it's not there I would suggest 1/2.

Step-by-step explanation:

Its rise/run therefore it going up one and moving four.

3 0
3 years ago
Given a triangle with sides measuring 18 inches, 21 inches, and 14 inches find the measure of the angle with the greatest measur
USPshnik [31]
B :81 EXPLANATION
The angle with the greatest measure corresponds to the longest:
Since we know the three side lengths, we use the cosine rule to obtain;
{a}^{2} = {b}^{2} + {c}^{2} - 2bc \cos(A)
where a=21, b=18 and c=14
{21}^{2} = {18}^{2} + {14}^{2} - 2 \times 18 \times 14\cos(A)
44 1= 324+ 196 - 504\cos(A)
44 1= 520 - 504\cos(A)
44 1 - 520 = - 504\cos(A)
- 79 = - 504\cos(A)
\cos(A) = 0.1567
A = \cos ^{ - 1} (0.1567) = 80.98 \degree
7 0
3 years ago
In a standard Normal​ distribution, if the area to the left of a​ z-score is about 0.3500​, what is the approximate​ z-score? Dr
wlad13 [49]

Answer:

z-score=0.385

(See attached picture)

Step-by-step explanation:

The procedure to find the z-score will depend on the resources we have available. I have a table with the area between the mean and the value we wish to normalize, so the very first thing we need to do is precisely find this area we need to analyze.

Everything to the left of thte mean will represent 50% of the data, so we start by subtracting:

50%-35%=15%

so we need to look in the table for the value 0.15.

In my table I can see that for an area of 0.15, the z-score will be between 0.38 (z-score of 0.1480) and 0.39 (z-score of 0.1517).

By doing some interpolation, you can determine a more accurate value of the z-score to be 0.385.

4 0
3 years ago
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