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2 years ago

Based only on the information given in the diagram, it is guaranteed that ABC XYZ

Mathematics

2 answers:

serious [3.7K]2 years ago

5 0

This statement is true

Scilla [17]2 years ago

3 0

Answer:

Statement is true.

Step-by-step explanation:

The given triangles ΔABC and ΔXYZ will be similar if the two angles of these triangles are equal Or all sides of both the triangles are equal Or two corresponding sides and the angle between these lines are same.

Here in ΔABC

∠ACB = 52°

∠ABC = 90°

Then we can find the third angle ∠CAB = 180°-(∠ACB+∠ABC)

= 180 - (52+90)

= 180 - 142

= 38°

Similarly in ΔXYZ, ∠YXZ = 38°, ∠XYZ = 90°

Then ∠YZX = 180-(∠YXZ+∠XYZ)

= 180-(90+38) = 180-128 = 52°

Now we can say that in two triangles

∠ACB = ∠YZX =52°

∠CAB = ∠YXZ = 38°

Therefore These triangle are similar and the statement is true.

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A boat tour guide expects his tour to travel at a rate of x mph on the first leg of the trip. On the return route, the boat trav

Georgia [21]

The intervals included in solution are:

$\frac{1}{x} + \frac{1}{x}-10\ge \frac{2}{24}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:0$

Solution:

Given that,

A boat tour guide expects his tour to travel at a rate of x mph on the first leg of the trip

On the return route, the boat travels against the current, decreasing the boat's rate by 10 mph

The group needs to travel an average of at least 24 mph

Given inequality is:

$\frac{1}{x} + \frac{1}{x} - 10\geq \frac{2}{24}$

We have to solve the inequality

$\frac{1}{x} + \frac{1}{x} - 10\geq \frac{2}{24}\\\\\frac{2}{x} - 10\geq \frac{2}{24}$

$\mathrm{Subtract\:}\frac{2}{24}\mathrm{\:from\:both\:sides}\\\\\frac{2}{x}-10-\frac{2}{24}\ge \frac{2}{24}-\frac{2}{24}\\\\Simplify\\\\\frac{2}{x}-10-\frac{2}{24}\ge \:0$

$\frac{2}{x}-\frac{10}{1}-\frac{2}{24} \geq 0\\\\\frac{ 2 \times 24}{x \times 24} -\frac{10 \times 24}{1 \times 24} - \frac{2 \times x }{24 \times x}\geq 0\\\\\frac{48}{24x}-\frac{240x}{24x}-\frac{2x}{24x}\geq 0\\\\Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions\\\\\frac{48-240x-2x}{24x}\geq 0\\\\Add\:similar\:elements\\\\\frac{48-242x}{24x}\ge \:0$

$\mathrm{Multiply\:both\:sides\:by\:}24\\\\\frac{24\left(48-242x\right)}{24x}\ge \:0\cdot \:24\\\\Simplify\\\\\frac{48-242x}{x}\ge \:0\\\\Factor\ common\ terms\\\\\frac{-2\left(121x-24\right)}{x}\ge \:0\\\\\mathrm{Multiply\:both\:sides\:by\:}-1\mathrm{\:\left(reverse\:the\:inequality\right)}$

When we multiply or divide both sides by negative number, then we must flip the inequality sign

$\frac{\left(-2\left(121x-24\right)\right)\left(-1\right)}{x}\le \:0\cdot \left(-1\right)\\\\\frac{2\left(121x-24\right)}{x}\le \:0\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{\frac{2\left(121x-24\right)}{x}}{2}\le \frac{0}{2}\\\\Simplify\\\\\frac{121x-24}{x}\le \:0$

$\mathrm{Find\:the\:signs\:of\:the\:factors\:of\:}\frac{121x-24}{x}\\$

This is attached as figure below

From the attached table,

$\mathrm{Identify\:the\:intervals\:that\:satisfy\:the\:required\:condition:}\:\le \:\:0\\\\0$

Therefore, solution set is given as:

$\frac{1}{x} + \frac{1}{x}-10\ge \frac{2}{24}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:0$

8 0

1 year ago

Read 2 more answers

Yen paid $10.50 for 2.5 pounds of pretzels. What price did she pay for each pound of pretzels?

Furkat [3]

Answer:

The first step is to multiply by a power of 10, so the divisor is a whole number.

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

ALGEBRA Jake Duffy drove 12,568 miles

kirza4 [7]

Answer:

The cost per mile that Jack Duffy charge $0.278 per miles , i.e option B

Step-by-step explanation:

Given as :

The distance drove by Jack Duffy = d = 12,568 miles

The fixed costs totaled = $1,485.00

The variable cost totaled = $2,015.75

Let The cost per mile that Jack Duffy charge = $x cost per miles

Now, According to question

The totaled cost = The fixed costs + The variable cost

Or, The totaled cost = $1,485.00 + $2,015.75

I.e The totaled cost = $3500.75

Now,

The cost per mile that Jack Duffy charge = $\dfrac{\extrm Total cost}{\textrm Total Distance}$

I.e x = $\dfrac{3500.75}{12568}$

∴ x = $0.278 per miles

So,The cost per mile that Jack Duffy charge = x = $0.278 per miles .

Hence,The cost per mile that Jack Duffy charge $0.278 per miles , i.e option B Answer

5 0

1 year ago

Agent Hunt transferred classified files from the CIA mainframe onto his flash drive. The drive had some files on it before the t

topjm [15]

Answer: The drive was 24.32% full when the transfer began.

Step-by-step explanation:

Given: The rate of transferring file = 4.44 megabytes per second.

After 32 seconds, the amount of data on the drive = 384 megabytes

The amount of transferred data = $32\times4.4=140.8$ megabytes

Therefore, the amount of data in the drive at the beginning is given by :-

$\text{Beginning amount=Amount after 32 seconds -Amount transferred}\\\\\Rightarrrow\ \text{Beginning amount=}384-140.8=243.2$

The drive had a maximum capacity of 1000 megabytes.

$\frac{243.2}{1000}\times100=24.32\%$

Hence, the drive was 24.32% full when the transfer began.

4 0

1 year ago

Read 2 more answers

Check each set that includes the number shown.

zavuch27 [327]

Answer:

Fourth option.

Sixth option.

Step-by-step explanation:

We know that:

- Any number you can find on the number line, is a Real number.

- Integers contains positive numbers, negative numbers and zero. Every Integer is a Rational number.

- A Rational number is that number that can be written in the following form:

$\frac{a}{b}$

Where "a" and "b" are integers ( $b\neq 0$ ).

- An Irrational number cannot be written as a simple fraction.

- A Whole number is any of the numbers { ${0, 1, 2, 3...}$ }. Every Whole number is a Rational number.

- Natural numbers contain the set of positive integers{ ${1, 2, 3...}$ } or to the set of nonnegative integers { ${0, 1, 2, 3...}$ }, Every Natural number is a Rational number.

Based on this, since $\frac{5}{9}$ is in the form $\frac{a}{b}$ where $a=5$ and $b=9$ , it is a Rational Number and therefore a Real number.

7 0

1 year ago