Similar Triangles Sorting Activity 1 (be sure each pair of triangle is in the right column)


Similar Triangles


*sorting mat*


Similar Triangles


NOT Similar Triangles

Answer: The distance between the points (3, 4) and (0, 0) is 5.

Step-by-step explanation: The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem can be used to find the distance between two points in a coordinate system.

To find the distance between two points in a coordinate system, you can use the following steps:

Identify the coordinates of the two points.

Calculate the difference between the x-coordinates and the y-coordinates of the two points.

Use the Pythagorean Theorem to find the distance between the two points.

For example, to find the distance between the points (3, 4) and (0, 0), you would do the following:

Identify the coordinates of the two points: (3, 4) and (0, 0).

Calculate the difference between the x-coordinates and the y-coordinates of the two points: 3 - 0 = 3 for the x-coordinates and 4 - 0 = 4 for the y-coordinates.

Use the Pythagorean Theorem to find the distance between the two points: the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides, so the distance between the points is equal to the square root of 3^2 + 4^2 = 9 + 16 = 25 = 5.

Therefore, the distance between the points (3, 4) and (0, 0) is 5.

39 is 0.3​% of 13,000.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the number be x

So, 0.3% of x= 39

0.3/ 100 x= 39

0.3 x = 3900

x= 3900/ 0.3

x= 13000

Hence, 39 is 0.3​% of 13,000.

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m<A = 112.5

m<B = 67.5

m<C = 67.5

m<D = 112.5

Consider the provided information.

The sum of all interior angle of a polygon is: (n-2)*180

Substitute n = 8.

(8-2)*180 = 1080

Thus, the measure of each angle is:

∠B and ∠C are congruent and their sum is 135°

∠B+∠C=135°

∠B=67.5°

Hence, the m angle B and m angle C is 67.5°.

The sum of all angles of a quadrilateral is 360°.

∠A+∠D+∠B+∠C=360°

∠A+∠D=360°-135°

∠A+∠D=225°

∠A and ∠D are congruent and their sum is 225°

∠A+∠D=225°

∠A=∠D=112.5°

Hence, the m angle A and m angle D is 112.5°.

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Answer:

S , P , T

Step-by-step explanation:

collinear points are points that lie on the same line.

S , P , T lie on the same line and are therefore collinear

Answer:

SPT

Step-by-step explanation:

You also have XPY but that isn't a choice in your list. SPT goes in a straight line making it collinear

The matrix equations are solved as

a) The value of matrix X is   [tex]X = \begin{pmatrix}-2&0&4\end{pmatrix}[/tex]

b) The value of matrix X is  [tex]X=\begin{pmatrix}-5&1\end{pmatrix}[/tex]

What is multiplication of matrices?

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix

Given data ,

a)

Let the value of the matrix be X

Now , the equation is

[tex]2X = \begin{pmatrix}-4&0&8\end{pmatrix}[/tex]

Now , on simplifying the equation , we get

Divide by 2 on both sides of the equation , we get

[tex]X = \begin{pmatrix}-4&0&8\end{pmatrix} / 2[/tex]

Now , the value of matrix X is

[tex]X = \begin{pmatrix}-2&0&4\end{pmatrix}[/tex]

Therefore , the value of matrix X is   [tex]X = \begin{pmatrix}-2&0&4\end{pmatrix}[/tex]

b)

Let the value of the matrix be X

Now , the equation is

[tex]3X\:-\:\begin{pmatrix}1&7\end{pmatrix}=\begin{pmatrix}-16&-4\end{pmatrix}[/tex]

On simplifying the equation , we get

Adding  [tex]\begin{pmatrix}1&7\end{pmatrix}[/tex]  on both sides of the equation , we get

[tex]3X=\begin{pmatrix}-16&-4\end{pmatrix}+\begin{pmatrix}1&7\end{pmatrix}[/tex]

Now , the value for 3X can be calculated as adding the 2 matrices

[tex]3X=\begin{pmatrix}-15&3\end{pmatrix}[/tex]

Divide by 3 on both sides of the equation , we get

[tex]X=\frac{1}{3}\begin{pmatrix}-15&3\end{pmatrix}[/tex]

So , [tex]X=\begin{pmatrix}-5&1\end{pmatrix}[/tex]

Therefore , the value of matrix X is  [tex]X=\begin{pmatrix}-5&1\end{pmatrix}[/tex]

Hence , the matrix equations are solved as

a) The value of matrix X is   [tex]X = \begin{pmatrix}-2&0&4\end{pmatrix}[/tex]

b) The value of matrix X is  [tex]X=\begin{pmatrix}-5&1\end{pmatrix}[/tex]

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Answer:

-6x²-x-6

Step-by-step explanation:

-7x²-1+x²-x-5

-6x²-1-x-5

-6x²-x-6

Answer:

(A) x + 3y - 10

Step-by-step explanation:

This Questions tests on the concept of solving algebraic expressions.

Eg. 7x + 4y + 3y + 9x = 16x + 7y

(Note that BODMAS rule applies to algebraic expressions as well.)

Given from the question:

5x + 8 - 13y - 4x - 18 + 16y

= 5x - 4x - 13y + 16y + 8 - 18 (Regroup the terms)

= x + 3y - 10 (A)

The correct option for the given linear equation condition is D. i.e. Liza will pass Ralph after 5 hours, and they each will have travelled 325 miles.

What is a linear equation?

When the parameter in the equation has a degree of 1, the system is said to be linear. One, two, or even more variables could be present.

The collection of two or more linear equations involving the same variables is known as a system of linear equations.

From the question,

The situation is given as:

y = 60x + 25

y = 65x

The time after Liza leaves, she passes Ralph will be

or, 65x = 60x + 25

or, 5x = 25

or, x = 5 hours

Then the distance covered by both of them, then after 5 hours will be

y = 65 (5)

y = 325 miles

Hence, the correct option is D.

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Answer:

Step-by-step explanation:

To find which one is faster, it would be distance/speed.

40m/3 = 13.33 repeating

50m/4 = 12.5

You would be traveling faster at 40 miles in 3 hours since you are going at 13.33 miles per hour

To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following except The Degrees of Freedom.

Given,

To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following except _____.

Now, According to the question:

Let's know:

The Degrees of Freedom:

Degrees of freedom refers to the maximum number of logically independent values, which are values that have the freedom to vary, in the data sample. Degrees of freedom is calculated by subtracting one from the number of items within the data sample.

Hence, To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following except The Degrees of Freedom.

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Answer:

[tex]\sf P(B|A)=0.60[/tex]

Step-by-step explanation:

Given:

If events A and B are independent then:

[tex]\boxed{\begin{aligned} \sf P(A \cap B)&=\sf P(A)P(B)\\\sf P(A|B)&=\sf P(A)\\\sf P(B|A)&=\sf P(B)\end{aligned}}[/tex]

Therefore:

[tex]\implies \sf P(B|A)=P(B)=0.60[/tex]

Answer:

Step-by-step explanation:

Can You Please Send Me A Clearer Picture I Can Help

Answer:

f(x) = x^3 - 7x + 1

Step-by-step explanation:

ƒ”(x)=6x ==> ƒ”(x)=6 * (x^1)

f'(x)=6/(1+1) * x^(1+1) + C  ==> C is a constant that doesn't affect the derivative

f'(x)=6/2 * x^2 + C ==> simplify the first derivative

f'(x)=3 * x^2 + C ==> f'(x)=3(x^2) + C

f'(-3)=3((-3)^2) + C  ==> plug in -3 into the derivative equation

f'(-3)=3(9) + C ==> simplify

20=3(9) + C  ==> plug in 20 for f'(-3)

20=27+C

20-27=27-27+C ==> solve for C

C=-7

f'(x)=3(x^2) + (-7)  ==> plug in -7 for C

f'(x)=3(x^2) - 7  ==> simplify

f(x) = 3/(2+1) * x^(2+1) - 7x + C

f(x) = 3/3 * x^3 - 7x + C

f(x) = x^3 - 7x + C

f(-3) = (-3)^3 - 7(-3) + C ==> plug in -3 into f(x)

f(-3) = -27 - (-21) + C

f(-3) = -27 + 21 + C ==> simplify

f(-3) = -6 + C

-5 = -6 + C  ==> plug in -5 for f(-3)

-5 + 6 = -6 + 6 + C ==> solve for C

C = 1 ==> simplify

f(x) = x^3 - 7x + 1

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Answer:

(24x-18)-9x

hope this helps, tell me if you need to simplify it further

Match each of the expressions to the right point:

[tex]-\sqrt{18}[/tex] = c

[tex]-\frac{17}{3}[/tex] = b

[tex]-2\pi[/tex] = a

Answer:

Given below in the picture

I hope my answer helps you.

Answer: yes

Step-by-step explanation: there’s a pattern of 2, as we can see from the first equation. 5+2 is 7, so therefore the answer is yes.

Answer:

D

Step-by-step explanation:

Use a calculator to approximate [tex]\ln 28[/tex] to the nearest thousandth.

Ashley's hair grew at a rate of approximately 0.545 inches per month.

What is the rate of change?

Rate of change problems can generally be approached using the formula R = D/T, or rate of change equals the distance traveled divided by the time it takes to do so.

To find the rate at which Ashley's hair grew per month, we need to divide the total amount of hair growth by the number of months.

First, let's convert the units to a common denominator. 1 and 1/2 inches is the same as 3/2 inches, and 2 and 3/4 months is the same as 11/4 months.

Now we can divide the total amount of hair growth (3/2 inches) by the number of months (11/4 months) to get the rate at which Ashley's hair grew per month:

(3/2 inches) / (11/4 months) = (3/2) * (4/11) inches/month

= 6/11 inches/month

= approximately 0.545 inches/month

Therefore, Ashley's hair grew at a rate of approximately 0.545 inches per month.

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Applying the Pythagorean theorem, the missing side of each of the right triangle are:

i. c = 15.8 m

ii. s = 24.1 cm

iii. a = 12.8 feet

iv. t = 4.6 inches

Pythagorean theorem is one that can be used to determine the third unknown side of a right angled triangle. It is given by:

/Hyp/^2 = /Adj/^2 + /Opp/^2

The missing side of each of the right triangle can be determined as:

1. Let the value of unknown hypotenuse side by represented by c, so that:

/Hyp/^2 = /Adj/^2 + /Opp/^2

c^2  = /13/^2 + /9/^2

             = 169 + 81

             = 250

c = [tex]\sqrt{250}[/tex]

  = 15.8

c = 15.8 m

2. Let the value of unknown hypotenuse side be represented by s, so that;

/Hyp/^2 = /Adj/^2 + /Opp/^2

 s^2 = /16/^2 + /18/^2

        = 256 + 324

        = 580

s = [tex]\sqrt{580}[/tex]

  = 24.1

s = 24.1 cm

3. Let the value of unknown adjacent side be represented by a,

/Hyp/^2 = /Adj/^2 + /Opp/^2

19^2 = a^2 + /14/^2

361 = a^2 + 196

a^2 = 361 - 196

      = 165

a = [tex]\sqrt{165}[/tex]

  = 12.8

a = 12.8 ft

4. Let the unknown adjacent side be represented by a,

/Hyp/^2 = /Adj/^2 + /Opp/^2

/11/^2 = t^2 + /10/^2

121 = t^2 + 100

t^2 = 121 - 100  

      = 21

t = [tex]\sqrt{21}[/tex]

  = 4.6

t = 4.6 in

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Answer: 22

Step-by-step explanation:

f(x) = -5x + 2

Substitute the x for -4

f(-4) = -5(-4) + 2

f(-4) = 20+2

f(-4) = 22

Answer: It will be 4.433333333 as a decimal and 4 13/30 as a mixed number in simplest form

The answer for the equation is  x = 1 , y = 3.

Solve the following system: using elimination:

x + 5 y = 17 | (equation 1)

6 x - 5 y = -3 | (equation 2)

Swap equation 1 with equation 2:

6 x - 5 y = -3  (equation 1)

x + 5 y = 17  (equation 2)

Subtract 1/3 × (equation 1) from equation 2:

6 x - 5 y = -3 (equation 1)

0 x+(20 y)/3 = 20 (equation 2)

Multiply equation 2 by 3/20:

{6 x - 5 y = -9 | (equation 1)

{0 x+y = 3 | (equation 2)

Add 5 × (equation 2) to equation 1:

6 x+0 y = 6 (equation 1)

0 x+y = 3 | (equation 2)

Divide equation 1 by 6:

x+0 y = 1 | (equation 1)

0 x+y = 3 | (equation 2)

Collect results:

Answer: x = 1 , y = 3

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Answer: y=1/5x + b

Step-by-step explanation:

The slope intercept for the equation is y=mx +b

Your equation is already in the slope-intercept form!

Answer:

(2,0)

Step-by-step explanation:

5x + 9y = 10

4x -3y = 8  If I multiple this second equation all the way through by 3, then the y's would cancel out when I add the equations together.

12x -9y = 24  multiplied the second equation through by 3

5x + 9y = 10  Add the 2 equations together

17x         = 34  Divide both sides by 14

x = 2

Plug 2 in for x for either of the two original equations and solve for y

5x + 9y = 10

5(2) + 9y = 10

10 + 9y = 10  Subtract 10 from both sides

9y = 0  Divide both sides by 0

y = 0

(2,0)

Answer:

-4 = -6(r+3)

r+3 = 2/3

r = -1/2/3

Answer:

b)  The mixed number seven and three fourths inches.

Step-by-step explanation:

Given:

To find the total length of the wood, sum the length of the picture and two margins:

[tex]\implies \sf Total\;length=6\frac{3}{4}+\dfrac{1}{2}+\dfrac{1}{2}[/tex]

Two halves equal 1:

[tex]\implies \sf Total\;length= 6\frac{3}{4}+1[/tex]

When adding a mixed number to a whole number, simply add the whole numbers together:

[tex]\implies \sf Total\;length= (6+1)\frac{3}{4}[/tex]

[tex]\implies \sf Total\;length= 7\frac{3}{4}[/tex]

Therefore, the total length of the wood required is:

Answer:

The largest possible product of two positive integers whose sum is 9 is achieved when the two integers are as far apart as possible, which occurs when one integer is the largest possible integer and the other is the smallest possible integer. The largest possible integer is the one that is closest to but less than 9, which is 8, and the smallest possible integer is 1. The product of 8 and 1 is 8, so the largest possible product of two positive integers whose sum is 9 is 8.