5. Triangle ABC is a right triangle with CD and AB angle C is a right triangle.
By the ,(.......) △ACB∼△ADC and △ACB∼△CDB. Since similar triangles have (........) sides, BCBA=BDBC and ACAB=ADAC . Using cross multiplication gives the equations (BC)2=(BD)(BA) and (AC)2=(AD)(AB). Adding these together gives (BC)2+(AC)2=(BD)(BA)+(AD)(AB). Factoring out the common segment gives (BC)2+(AC)2=(AB)(BD+AD). Using (........) gives (BC)2+(AC)2=(AB)(AB), which simplifies to (BC)2+(AC)2=(AB)2 .

First paranthese
SAS or AAS or SSS

Second paranthese
Congruent or proportional

Third paranthese
SA or CPCTC

The correct answers are:

1. 2y=1.5x-2 ; and 4. -4y+3x=-2.

Explanation:

Using the first equation, we have the system

[tex]\left \{ {{3x-4y=2} \atop {2y=1.5x-2}} \right.[/tex]

The second equation can be written in standard form just as the first one.  To do this, we will subtract 1.5x from each side:

2y = 1.5x-2

2y-1.5x = 1.5x-2-1.5x

-1.5x+2y = -2

This makes our system

[tex]\left \{ {{3x-4y=2} \atop {-1.5x+2y=-2}} \right.[/tex]

To solve this, we will make the coefficients of x the same; we do this by multiplying the bottom equation by 2:

2(-1.5x+2y=-2)

-3x+4y=-4

This gives us the system

[tex]\left \{ {{3x-4y=2} \atop {-3x+4y=-4}} \right.[/tex]

We solve this by adding the two equations:

[tex]\left \{ {{3x-4y=2} \atop {+(-3x+4y=-4)}} \right. \\\\\\0+0 = -4\\0=-4[/tex]

There is no solution to this.

For the second system, we will follow the same process, subtract 1.5x from each side of the second equation:

2y=1.5x-1

2y-1.5x = 1.5x-1-1.5x

-1.5x+2y = -1

To make the coefficients of x the same, multiply the second equation by 2:

2(-1.5x+2y=-1)

-3x+4y=-2

We will add the two equations to solve:

[tex]\left \{ {{3x-4y=2} \atop {+(-3x+4y=-2)}} \right. \\0+0=0\\0=0[/tex]

This means that the equations are of the same line and there are infinite solutions.

For the third system, the coefficients are already the same.  We will cancel by subtracting the bottom equation from the top:

[tex]\left \{ {{3x-4y=2} \atop {-(3x+4y=2)}} \right. \\\\-4y-4y=2-2\\-8y=0\\\frac{-8y}{-8}=\frac{0}{-8}\\y=0[/tex]

Since we have a value for y, this has a solution.

For the last system, we will rearrange the second equation with the x term in front:

3x-4y=-2

Now we will subtract this from the first equation:

[tex]\left \{ {{3x-4y=2} \atop {-(3x-4y=-2)}} \right. \\-4y--4y=2--2\\0=4[/tex]

This has no solution.

Final answer:

The height of the cone is equal to the slant height plus 1.

Explanation:

To find the height of the cone, we can use the formula for the surface area of a cone: S = πr^2 + πrl, where r is the radius of the base and l is the slant height. Since the problem states that the surface area is equal to the volume, we can set S equal to V and solve for h, the height of the cone.

Here's the step-by-step calculation:

S = V

πr² + πrl = V

πr² + πrl = πr²h

πr² + πrl - πr²h = 0

Combine like terms: πr²(1 - h) + πrl = 0

Divide both sides by πr to solve for h: 1 - h + l = 0

Subtract l from both sides: 1 - h = -l

Subtract 1 from both sides: -h = -l - 1

Multiply both sides by -1 to solve for h: h = l + 1

So, the height of the cone is h = l + 1.

Answer:

Step-by-step explanation:

1) Make all the fractions have the same denominator.

- To do that you need to find the LCM (least common denominator) of 4, 9, and 7.

(look at image 1)

-Then apply the number you multiply the original denominator by to the original numerator

(look at image 2)

-Add the fractions together

(look at image 3)

Final answer:

The notation f'(x) represents the derivative of the function f with respect to x, signifying the rate of change of the function or the slope of the tangent to its curve at a specific point.

Explanation:

The notation f prime of x, often written as f'(x), represents the derivative of the function f with respect to x. This concept is a fundamental part of calculus, which deals with the rate at which quantities change. The derivative f'(x) is the instant rate of change of the function f(x) at a particular value of x, or the slope of the tangent line to the curve f(x) at that point.

For example, if f(x) = x2, then the derivative f'(x) would equal 2x, as the rate of change of x2 with respect to x is 2x. This means that for every unit increase in x, the value of x2 increases by an amount corresponding to 2x.

The derivative can also be understood in the context of physics, where it might represent things like velocity, which is the derivative of position with respect to time. Regardless of the context, f'(x) is about understanding how a function changes at a specific point.

Answer:

The y-coordinate of the solution is approximately 7.2.

Explanation:

To solve the system of equations:

1. [tex]\( 5x + 2y = 7 \)[/tex]

2. [tex]\( -2x + 6 = 9 \)[/tex]

We'll start by solving the second equation for [tex]\( x \):[/tex]

[tex]\[ -2x + 6 = 9 \][/tex]

Subtract 6 from both sides:

[tex]\[ -2x = 9 - 6 \][/tex]

[tex]\[ -2x = 3 \][/tex]

Divide both sides by -2:

[tex]\[ x = -\frac{3}{2} \][/tex]

Now that we have the value of [tex]\( x \)[/tex], we can substitute it into the first equation to find [tex]\( y \):[/tex]

[tex]\[ 5x + 2y = 7 \][/tex]

[tex]\[ 5(-\frac{3}{2}) + 2y = 7 \][/tex]

[tex]\[ -\frac{15}{2} + 2y = 7 \][/tex]

Add [tex]\( \frac{15}{2} \)[/tex] to both sides:

[tex]\[ 2y = 7 + \frac{15}{2} \][/tex]

[tex]\[ 2y = \frac{14}{2} + \frac{15}{2} \][/tex]

[tex]\[ 2y = \frac{29}{2} \][/tex]

Divide both sides by 2:

[tex]\[ y = \frac{29}{4} \][/tex]

Now, let's convert the fraction into a decimal rounded to the nearest tenth:

[tex]\[ y \approx 7.2 \][/tex]

I hope that helps!

24 -18 = 6

24/6 =4

18/6 =3

6 bundles with 4 balls and 3 clubs each

The phrase 'three times a number plus 16' translates to '3x + 16' in mathematical terms, where 'x' represents any number.

The phrase 'three times a number plus 16' can be converted into an algebraic expression. In mathematical terms, 'a number' is usually represented by the letter 'x'. 'Three times a number' can be written as '3x'. 'Plus' is represented by the '+', so 'three times a number plus 16' is written as '3x + 16'.

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Food, clothing, and medical are variable expenses because they occur regularly but can change from month to month.

The Porters’ food, clothing, and medical expenses are variable expenses.

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The given difference of two numbers which we have to estimate is

  920,026-535,722

Actual Difference=384,304

→Estimation Using Ones

 920,030-535,720=384,310

→Estimation Using Tens

 920,000-535,700=384,300

Estimation using Tens is Closer to Actual Difference.

So, Answer=384,300

Consider the Set A = {X | X is an even whole number between 0 and 2 } = [tex]\Phi[/tex].

Since, whole numbers are the set of numbers starting from zero upto infinity.

Even numbers are the numbers which are exactly divisible by '2'.

So, we have to find the even whole number between 0 and 2.

Since, only '1' is a whole number between 0 and 2 which is not an even number as '1' is not divisible by '2'.

Therefore, there is no even whole number between 0 and 2.

So, this set is empty.

Therefore, A = { X | X is an even whole number between 0 and 2} =  [tex]\Phi[/tex]

Answer:

The correct option is:   $1.45 + $0.55x ≤ $35 ;  x ≤ 61 miles

Step-by-step explanation:

Suppose, the number of miles Ariel can travel [tex]=x[/tex]

The cab charges $1.45 for the flat fee and $0.55 for each mile. So, the total charges for [tex]x[/tex] miles [tex]=\$1.45+\$0.55x[/tex]

Given that, she has $35 to spend. That means, the total charges must be less than or equal to $35.

So, the inequality will be:   [tex]\$1.45+\$0.55x\leq \$35[/tex]

Solving the above inequality....

[tex]1.45+0.55x\leq 35\\ \\ 0.55x\leq 35-1.45\\ \\ 0.55x\leq 33.55\\ \\ x\leq \frac{33.55}{0.55}\\ \\ x\leq 61[/tex]

So, the number of miles Ariel can travel is 61 miles.

The other person is correct i just did the test

To find the value of k when x^2+kx+7 is equivalent to (x+1)(x+h), we expand (x+1)(x+h), compare coefficients, and deduce that k is 8.

If h and k are constants and x^2+kx+7 is equivalent to (x+1)(x+h), we are looking for the value of k. To find k, we expand the right-hand side and then compare coefficients.

Expanding (x+1)(x+h) gives us x^2+hx+x+h, which simplifies to x^2+(h+1)x+h.

Comparing this to x^2+kx+7, we can see that k must be equal to h+1.

Since there is no h term in x^2+kx+7, we infer that h must be equal to 7. Consequently, k=h+1 which leads us to k=7+1.

Therefore, the value of k is 8.

0.075 m is 7.5 centimeters.

A unit conversion expresses the same property as a different unit of measurement.

Given that, convert 0.075 m into cm

We know that, 1 meter = 100 centimeters

0.075 meter = [(100) × 0.075] centimeter

0.075 meter = (100 × 0.075) centimeter

= (100 × 75/1000) centimeter

= (7500/1000) centimeter

= (75/10) centimeter

= 7.5 centimeter.

Hence, 0.075 m is 7.5 centimeters.

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