Triangles ABC and DEF are mathematically similar.
A
9 cm
6/44
B
The area of triangle ABC is 34 cm².
Calculate the area of triangle DEF.
A
F
13.5 cm
E

=======================================================

Explanation:

Use the slope formula to find the slope of the line through A(-6,-1) and B(-5,2)

[tex](x_1,y_1) = (-6,-1) \text{ and } (x_2,y_2) = (-5,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - (-1)}{-5 - (-6)}\\\\m = \frac{2 + 1}{-5 + 6}\\\\m = \frac{3}{1}\\\\m = 3\\\\[/tex]

The slope of segment AB is 3.

-------------

Repeat these set of steps for segment CD

C = (-1,-5)

D = (0,-2)

[tex](x_1,y_1) = (-1,-5) \text{ and } (x_2,y_2) = (0,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - (-5)}{0 - (-1)}\\\\m = \frac{-2 + 5}{0 + 1}\\\\m = \frac{3}{1}\\\\m = 3\\\\[/tex]

The slope of segment CD is also 3

Parallel lines have equal slopes, but different y intercepts.

Since AB and CD have the same slope of 3, this shows AB is parallel to CD.

--------------

Now find the slope of segment BD

B = (-5,2)

D = (0,-2)

[tex](x_1,y_1) = (-5,2) \text{ and } (x_2,y_2) = (0,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - 2}{0 - (-5)}\\\\m = \frac{-2 - 2}{0 + 5}\\\\m = -\frac{4}{5}\\\\[/tex]

Segment BD has a slope of -4/5

--------------

Lastly, compute the slope of segment AC

A = (-6,-1)

C = (-1,-5)

[tex](x_1,y_1) = (-6,-1) \text{ and } (x_2,y_2) = (-1,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - (-1)}{-1 - (-6)}\\\\m = \frac{-5 + 1}{-1 + 6}\\\\m = -\frac{4}{5}\\\\[/tex]

Segment AC has a slope of -4/5

Both segments BD and AC have the same slope of -4/5.

Therefore, segments BD and AC are parallel

----------------

We have two pairs of opposite parallel sides. Ultimately figure ABDC is a parallelogram

See the diagram below.  

The mean of the remaining temperature will be 1.7°C

Since the mean of her six recorded temperatures was 2.1 °C, the total temperature will be:

= 6 × 2.1

= 12.6°

Since the temperature on one of the days was 4.1 °C, the mean of the remaining temperature will be:

= (12.6 - 4.1)/5

= 8.5 / 5

= 1.7

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Answer:

x = 134°

Step-by-step explanation:

The angle labelled [tex]x^{\circ}[/tex] and the 46° add up to 180° as they are co-interior angles.

∴ [tex]x^{\circ} + 46^{\circ} = 180^{\circ}[/tex]

⇒ [tex]x^{\circ} = 180^{\circ} - 46^{\circ}[/tex]            [Subtracting 46° from both sides]

⇒ [tex]x = 134^{\circ}[/tex]

Therefore [tex]x[/tex] is equal to 134°.

Area of base:

3 * 9 = 27

So, 243 is the answer.

Answer:

x=3

Step-by-step explanation:

8x-3x=27-12

5x=15

x=15/5=3

x=3

Answer:

x=3

Step-by-step explanation:

8x + 12 = 3x + 27

Subtract 3x from both sides.

5x+12=27

Subtract 12 from both sides.

5x=15

Divide 5 from both sides.

x=3

Hope this helps!

Please mark as brainliest if correct!

There must be pivot columns in the matrix. "A has a pivot place in every row" and "A's columns span an R5" seem to be logically equivalent.

When a matrix has been in row-echelon form, the first nonzero entry in each row is referred to as a pivot, as well as the columns wherein pivots appear are referred to as pivot columns.

The matrix must contain pivot columns. "A has a pivot position in each row" & "A's columns span an R5" appear rationally equivalent.

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The correct question is-

Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span R⁵​? ​Why?

Answer:

let's say (5x + 2) = y

then that means 118° + y = 180°(angle in a straight line)

therefore y =180 - 118= 62°

since y = 5x + 2

and y= 62°

therefore 5x + 2 = 62°

5x = 62- 2= 60°

therefore 5x = 60°

this means that x = 60 ÷5 = 12°

The 8th term of the sequence 310 is closest to the term 300.

An arithmetic progression is a series of numbers that have a set common difference in between two consecutive numbers (A.P.).

Each term in an arithmetic sequence increases or decreases by adding or subtracting a constant term.

a = 30 for the first term

d = 40, common difference

We solve in what term is closest to 300 in this manner;

300 / 40 = 7.5

Thus, find the 7th and 8th term.

7th is solved by verifying for;

a₇ = a + ( n - 1 ) d

a₇ = 30 + ( 7 - 1 ) 40

a₇ = 30 + 240

a₇ = 270

The 8th term to certify the closest;

a₈ = T7 + d

a₈ = T7 + 40

a₈ = 270 + 40

a₈ = 310

As a result, the 8th term is the closest, with a value of 310.

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The complete question is-

The numbers in this sequence increase by 40 each time 30, 70, 110,The sequence is continued with the same rule. Which number in the sequence will be closest to 300?

Answer:

Statement is true

Step-by-step explanation:

  3m

----------  >  3;  m = 8

    6

  3(8)

----------  >  3

    6

  24

----------  >  3

    6

24 ÷ 6 = 4

4 > 3

or

  3m

----------  >  3;  m = 8

    6

  3m

----------  >  3 (6)

    6 (6)

3m > 18

÷3     ÷3

m > 6

8 > 6

Either way, the statement is true. I have no idea why it would be no. I'm sorry if I wasn't of any help.

Measure of angle 4 i.e. m∠4 = 50°

The measurement of angle is the degree of that angle or we can also say that the angles are always measured in degree. In geometry, the complete one revolution of four quadrants is of 360 degrees (360°) and divided into total of 360 parts where each part of this represents a degree.

As stated above there are total 360 parts in one revolution thus thus we can find value of particular angle by subtracting the angle from 360 or 180 for a straight line.

In the question,

Let given angle is ∠8.

Given, ∠8 = 50°

Now, according to vertical angle property

∠5 = ∠8

therefore, ∠5 = 50°

Also, ∠5 = ∠4 (alternate interior angles)

Thus, m∠4 = 50°

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The complete question is :

Find measures of numbered angle.

a. ∠2

b. ∠3

c. ∠4

By solving a linear equation we can see that:

Here we have two consecutive even integers, we can write these as x and x + 2

We know that half of the smaller of the two is equal to 2 more than the larger one, this can be writen as:

x/2 = (x + 2) + 2

Now we can solve that linear equation for x:

x/2 = x + 2 + 2

x/2 = x + 4

-4 = x - x/2

-4 = x/2

-4*2  = x = -8

The smaller number is -8

The larger number is -8 + 2 = -6

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The isosceles triangle's base can be positioned along the x-axis. Because QR is b units long, you can position point R along the x-axis and calculate the coordinates (b, 0).

An isosceles triangle is a triangle with at least two equal-length sides in geometry. It is sometimes specified as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter version including the equilateral triangle as a special case.

By putting Q at the origin, the isosceles triangle's base can be positioned along the x-axis. Because QR is b units long, you can position point R along the x-axis and calculate the coordinates (b, 0). Because the vertex of the isosceles triangle, point T, is directly above the midpoint of the base, its x-value is half the length of QR and its coordinates are (b/2, c).

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Answer:

4x + 7

Step-by-step explanation:

8x + 9 - 4x - 2 ← collect like terms

= (8x - 4x) + (9 - 2)

= 4x + 7

If an artist uses gold leaf foil in his work and he wants to cover a piece of canvas that is 22.5 by 34 inches with this foil and the foil costs $4.15 per square inch, then the money the artist spent on gold leaf foil for this project is equal to $3174.75

The money spent on gold leaf foil for the project can be calculated by the multiplication of the area or square inch of the foil needed to cover the piece of canvas with the price per square inch.

The area or square inches can be calculated by multiplying the length in inches by the width in inches.

Area = 22.5 × 34

Area = 765 square inches

Now, money spent on gold leaf foil can be calculated by multiplication of the area of the need with the price per square inch.

Area × price per square inch

765 ×  4.15 = $3174.75

Hence the money the artist spent on gold leaf foil is calculated to be $3174.75

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Answer:

y= 15

Step-by-step explanation:

well I did first was I took eight and added seven because we're trying to find out what why is and whatever why is y - 7 is 8 so I added eight and seven together to get 15 and then I subtracted something and got me beat again .

Answer:

If we divide 5 by any other integer, then the remainder will be a non-zero positive integer.

Step-by-step explanation:

The given sequence is not geometric.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: [tex]\frac{1}{2}, \frac{1}{4},\frac{1}{6},\frac{1}{8},...[/tex]

Here, [tex]\frac{\frac{1}{4}}{\frac{1}{2}}\neq \frac{\frac{1}{6}}{\frac{1}{4}}\neq \frac{\frac{1}{8}}{\frac{1}{6}}[/tex]

That is, the given sequence doesn't follow the only required condition for a sequence to be geometric.

Hence, The given sequence is not geometric.

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Thus the tax rate is 1.5% and the 1.5% tax value of $135,000 is $2025.

We are given that;

A homeowner whose house was assessed at $120,000 pays $1,800 in taxes.

At the same rate, we need to find out what the tax value on a house assessed at $135,000.

The rate is always in percentage. Thus;

Tax value = 5% of 100

= 5/100 x 100

= $5

We have,

House cost = $120,000

Tax amount = $1800.

Let the rate be R%

Now;

R/100 * 120,000 = 1800

R * 1200 = 1800

R = 1800/1200

R = 18/12 = 1.5

R = 1.5%

The tax rate is 1.5%

The 1.5% tax value of $135,000 = 1.5 / 100 * 135,000

= 15/1000 x 135,000

= 15 x 135

= $2025

The tax value is $2025.

Thus the tax rate is 1.5% and the 1.5% tax value of $135,000 is $2025.

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From the given graph, we have that:

A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality, in the case of a direct relationship, as follows:

y = kx

In the case of an inverse relationship, we have that:

y = k/x.

k is the constant of proportionality for both cases.

For this problem, the function goes through point (2,10), that is, when x = 2, y = 10, meaning that we can find the constant k as follows:

2k = 10

k = 10/2

k = 5.

The constant of the relationship on the graph is of 5.

For the relationship, we have that:

Hence:

The point (7,35) in the proportional relationship graphed in this problem means that 35 gallons of water were used in 7 minutes.

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Question:

Which part of the story begins the development of a character? (5 points)

Exposition

Climax

Falling action

Resolution

Answer: It is (3,5) other one is 5. I did two of them lol.

Answer:

1000.6  (The 6 is a repeating so make sure to put a line over it)

Step-by-step explanation:

175+210+180+195+208+196

1164/6

1000.6 ( Put line over 6 is repeating decimal )

Answer:

add the like terms if there's no like the answer will be 3x+2y-3z=-1

Answer:

7 degrees

Step-by-step explanation:

Start with the temperature of -7 deg at 6:00 a.m.

The temperature increases 14 degrees in the next 6 hours.

6 hours after 6:00 a.m. is noon.

We are asked the temperature at noon.

At noon, the temperature is 14 degrees higher than -7 deg.

We add the increase, 14 deg, to the starting temperature, -7 deg.

-7 deg + 14 deg = 7 deg

Answer: 7 degrees

Super Gym employees sold 8,823 gym memberships this year, 70% more than the 5,190 gym memberships last year.

In mathematics, a percentage, usually denoted by %, is a number or ratio that represents a fraction of 100.

If the problem states that the gym's employees sold 70% (70 percent) more memberships than last year, and it's employees sold 5,190 gym memberships last year, then

memberships this year = 70% more than last year

memberships this year = 70%(5,190) + 5,190

memberships this year = 3,633 + 5,190

memberships this year = 8,823

Hence, the gym's employees sold 8,823 memberships this year.

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Algebraic expression (C) p - 125 represents the reduced price.

So, if p is the mountain bike's original price.

Therefore, algebraic expression (C) p - 125 represents the reduced price.

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  The value of the geometric mean of the numbers 40 and 15 is.

Gm ( 40, 15) = 10√6

   The geometric mean is defined as a type of measure that is calculated as the root of a product between a set of numbers, it can be expressed as follows:

Gm (a,b) = √ab

  Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b

  We substitute and solve for the square root

Gm (40, 15) = √40×15

Gm (40, 15) = √600

Gm (40, 15) = √6×100

Gm ( 40, 15) = 10√6

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Two isosceles triangles are not necessarily similar triangles.

Similar triangles are triangles that have congruent corresponding angles and proportional corresponding sides.

Analyzing each statements:

F. two right triangles with one angle measuring 30°

- these two triangles have angles measuring 90°, 30°, and 60°

- they both have equal angle measurements

∴ they are similar triangles

G. two right triangles with one angle measuring 45°

- these two triangles have angles measuring 90°, 45°, and 45°

- they both have equal angle measurements

∴ they are similar triangles

H. two isosceles triangles

- isosceles triangles are triangles that have two sides of equal lengths

- two isosceles triangles are similar if the angle of one is congruent to the corresponding angle of the other

∴ they are not necessarily similar, unless stated that their corresponding angles are equal

J. two equilateral triangles

- all equilateral triangles of any side lengths are considered similar triangles as each of its corresponding sides are proportional

∴ they are similar triangles

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The approximate circumference of the safety circle is 5026.54825 meters.

To find the circumference:

So,

Therefore, the approximate circumference of the safety circle is 5026.54825 meters.

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True, this sentence is true .

The set of all possible outcomes is the sample space.

In statistics, what does a probability mean?

True, this sentence is true .

The set of all possible outcomes is the sample space.

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