TRUE or FALSE?

Two arcs of a circle are congruent if and only if their associated radii are congruent.

SSS similarity theorem states: If the corresponding sides of two triangles are proportional, then the two triangles are similar.

You have two isosceles triangle, then if

[tex]\dfrac{44}{20}=\dfrac{x}{35},\\ \\x=\dfrac{44\cdot 35}{20}=11\cdot 7=77,[/tex]

two isosceles triangles will be similar by SSS theorem.

Answer: correct choice is C.

The value of x that will make the triangles similar by SSS similarity theorem is;

x = 77.

We are told that the 2 triangles are similar by SSS theorem.

Now, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Thus, in our 2 given triangles ,applying the SSS postulate gives;

x/35 = 44/20

Applying the multiplication property of equality, let us multiply both sides by 35 to get;

x = (44 * 35)/20

x = 77

Thus, in conclusion the value of x that will make the triangles similar by SSS similarity theorem is 77.

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Answer:

Hence, the length of the radius of a circle with center at origin is 17 units.

Step-by-step explanation:

" We know that radius of  a circle is any line segment joining center to any point on the circle ".

We have to find the length of the radius of a circle with a center at the origin i.e. (0,0) and a point on the circle at 8 + 15i i.e. at (8,15).

( Since any complex number of the form z=x+iy has a point in the coordinate plane as:  (x,y) ).

Hence , we have to find the distance between the point (0,0) and (8,15).

The distance between two points (a,b) and (c,d) is given by:

[tex]\sqrt{(a-c)^2+(b-d)^2}[/tex]

Here (a,b)=(0,0) and (c,d)=(8,15)

Hence distance between (0,0) and (8,15) is:

[tex]\sqrt{(0-8)^2+(0-15)^2\\} \\=\sqrt{(8)^2+(15)^2\\} \\=\sqrt{64+225}\\ \\=\sqrt{289}\\ \\=17[/tex]

Hence, the length of the radius of a circle with center at origin is 17 units.

Answer: 17

Step-by-step explanation: the length of the radius of a circle with center at origin is 17 units.

The value of the expression for the given value of t is 44

From the question, we are to evaluate the given expression for t = 12

The given expression is

42 + t/6

To evaluate the given expression for t = 12, we will substitute 12 for t in the expression,

That is,

42 + t/6 becomes

42 + 12/6

NOTE: 12/6 = 2

Then, we get

42 + 2

= 44

Hence, the value of the expression for the given value of t is 44.

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Answer:

The slope- intercept form this situation is given by y = 0.75x + 3 .

Step-by-step explanation:

The slope- intercept is given by

y = mx + c

Where m is the slope, c is the y intercept .

As given

When visiting Baltimore, MD needs  taxi to get from your hotel to the National Aquarium.

The taxi company charges a flat fee of $3.00 for using the taxi and $0.75 per mile.

Let us assume that the total amount charge by the taxi be y .

Let us assume that the number of miles travelled by the taxi be x.

Than

Total amount charge by taxi = Amount charge by the taxi per miles + Flat free charge .

y = 0.75x + 3

(Here m = 0.75 and c = 3)

Therefore the slope- intercept form this situation is given by y = 0.75x + 3 .

The equation that models this situation is y = 0.75x + 3.

To write an equation in slope-intercept form that models the situation of renting a taxi in Baltimore, MD, you can use the following equation:

Total Cost (C) = (Cost per Mile) * (Number of Miles) + (Flat Fee)

In this case, the cost per mile is $0.75, and the flat fee is $3.00. So, the equation becomes:

C = 0.75x + 3.00

Here, C represents the total cost of the taxi ride, and x represents the number of miles traveled. This equation is in slope-intercept form (y = mx + b), where:

"C" is the dependent variable (y),

"x" is the independent variable (the number of miles traveled),

0.75 is the slope (m), which represents the cost per mile, and

3.00 is the y-intercept (b), which represents the flat fee.

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Answer with explanation:

1.⇒ The given equation is

  5x-2y=3

For one solution ,you should write linear equation in such a way

ax+by=c, such that

  [tex]\frac{5}{a}\neq \frac{-2}{b}\neq \frac{3}{c}[/tex]

So, the linear equation will be

→3x+4y=8

You can write many more by yourself.

2.⇒Exactly two solutions

The two lines intersect at only one point.So,there are no such lines which has two point of Intersection.

3.⇒No solutions

It means the two lines will never intersect.

 For no solution ,you should write equation of line in such a way

ax+by=c, such that

  [tex]\frac{5}{a}=\frac{-2}{b}\neq \frac{3}{c}[/tex]

So, the linear equation will be

→10x -4y=15

You can write many more by yourself.

4.⇒Infinitely many solutions

For Infinite number of solution ,you should write linear equation in such a way

ax+by=c, such that

  [tex]\frac{5}{a}=\frac{-2}{b}=\frac{3}{c}[/tex]

→10x-4y=6

Answer:

The time it takes to download 7 songs is 49 seconds.

Step-by-step explanation:

It is about a division problem.

The first step is to determine how long it takes to download just one song. You must divide the total seconds by the total songs downloaded. The result would be the time required to download just one song.

[tex]\frac{35\, seconds}{5\, songs}=7\frac{seconds}{song}[/tex]

The previous value indicates that the download time is 7 seconds per song.

The second step is to determine how long it takes to download 7 songs. With the previous value in mind, you must multiply the time it takes to download one song by the 7 songs that Dariya wants to download, to obtain the total time it takes to download the 7 songs.

[tex]\frac{7\, seconds}{1\, song}\times 7\, songs=49\, seconds[/tex]

Thus, the time it takes to download 7 songs is 49 seconds.

The answer would be 75 brother

Tom weighed 122 pounds at the end of the year.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Tom weighed 110 pounds at the beginning of the year.

Pounds gained in June = 13

Pounds lost in August = 5

Pounds gained in November = 4

Now,

Total pounds at the end of the year.

= 110 + 13 - 5 + 4

= 110 + 17 - 5

= 110 + 12

= 122 pounds

Thus,

122 pounds at the end of the year.

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Answer:

20 miles 1/2

Step-by-step explanation:

I did the steps my teacher taught me

Final answer:

To find the whale's average speed per hour, divide the total distance of 184 miles by the time of 6 hours, resulting in an average speed of approximately 30.67 miles per hour.

Explanation:

The question asks for the speed of a whale per hour based on a certain distance traveled over a period of time. To calculate the speed of the whale, we can use the formula:

Speed = Distance ÷ Time

In this case, the whale traveled 184 miles in 6 hours. Using the formula, we divide 184 miles by 6 hours:

Speed = 184 miles ÷ 6 hours = 30.67 miles per hour

So, the whale swam at an average speed of about 30.67 miles per hour.

Answer:

Its a perfect cube.

Step-by-step explanation:

Final answer:

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent and can only be used after proving triangles are congruent. It helps in confirming that corresponding parts of congruent triangles are congruent.

Explanation:

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. It can only be used after you prove triangles are congruent. When two triangles are proven congruent, CPCTC allows you to show that corresponding parts like angles and sides are congruent as well.

​x² - 5x - 24 = 0

First, we have to solve the quadratic equation and find the two values of x that fit the equation.​

[tex]x = \frac{5+- \sqrt{5^{2} + 4*1*24 } }{2*1} = \frac{5+- \sqrt{25 + 96} }{2} = \frac{5+- \sqrt{121} }{2} = \frac{5+-11}{2} [/tex]​

There are two values of x that fit:​

x₁ = (5+11)/2 = 16/2 = 8​

x₂ = (5-11)/2 = -6/2 = -3​

Now I can restate the original equation in terms of a product of factors, with this product being equal to zero:​

(x - x₁) * (x - x₂) = 0​

ANSWER ​(x-8) * (x+3) = 0

Now I can solve each factor by setting each one equal to zero and solving the resulting linear equations:​

x - 8 = 0 or x + 3 = 0​

x = 8 or x = -3​

We can check that these two values are the solution to the original quadratic equation.​

x² - 5x - 24 = 0​

​First value

​8² -5*8 -24 = 0

64 - 40 -24 = 0​

0 = 0 ¡Checked!​

Second value​

(-3)² -5(-3) -24 = 0​

9 + 15 -24 = 0​

0 = 0 ¡Checked!​

​Hope this helps!

​[tex]\textit{\textbf{Spymore}}[/tex]​​​

Answer:

(x+3)(x-8)=0

Step-by-step explanation:

Answer: Hello there!

in the bag we have:

5 blue balls, 4 red balls, and 3 orange balls.

This adds up to 5 + 4 + 3 = 12 balls in total.

If we took a ball at random, the probability tath this ball is blue is equal to the quotient between the number of blue balls and the total number of balls.

this is P = 5/12 = 0.4166

now we need to round it to the tenths place, this is the first number after the decimal point, in this case, a 4.

To round it we need to see the number that is after if it is 5 or bigger we round up, if is smaller than 5 we round down. In this case, is a 1, means that we need to round down

p = 0.4

If a ball is picked from the bag at random, the probability that the ball taken was a blue ball, is equal to p = 0.4

Answer:  the correct option is (C) x - 1.

Step-by-step explanation:  We are given to select the correct binomial that is a factor of the following trinomial :

[tex]T=4x^2+20x-24~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To select the factor, we need to factorize expression (i). To factorize, we need two integers with sum 20 and product -96.

From (i), we have

[tex]T\\\\=4x^2+20x-24\\\\=4x^2+24x-4x-24\\\\=4x(x+6)-4(x+6)\\\\=(x+6)(4x-4)\\\\=4(x+6)(x-1).[/tex]

So, the factors of the given trinomial are 4, (x + 6) and (x - 1).

Since 4 and ( x + 6) are not in the options, so (x - 1),  is the correct binomial.

Thus, (C) is the correct option.

Answer:

Step-by-step explanation:

B

f(x) = -1/5(3)ˣ⁻¹ formula can  be used to describe the sequence.

The given sequence is -3, 3/5, -3/25, 3/125, -3/625

We can observe that each term alternates between negative and positive.

Additionally, the denominator of each term is increasing by a power of 5, while the numerator alternates between -3 and 3.

The formula f(x) = -1/5(3)ˣ⁻¹, fits this pattern.

By plugging in the values of x = 1, 2, 3, 4, and so on, the formula generates the corresponding terms of the sequence:

f(1) = -1/5(3)¹⁻¹= -3/5

f(2) = -1/5(3)²⁻¹ = 3/25

f(3) = -1/5(3)³⁻¹ = -3/125

f(4) = -1/5(3)⁴⁻¹ = 3/625

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