Which equation represents a line which is perpendicular to the line y = 2x - 5?

If AC = 4x - 3, DC = 2x + 9, m ∠ ECA = 15x + 2, and EC is a median of ΔAED then EC is not an altitude of ΔAED because of m ∠ ECA = 92.

In geometry, an altitude is a line that passes through two very specific points on a triangle: a triangle's vertex, or corner, and its opposite side at a right, or 90-degree, angle. The base is the opposite side. Triangles have three vertices and three opposite sides in common.

Given: AC = DC

4x - 3 = 2x + 9

4x - 2x - 3 = 2x - 2x + 9

simplifying the above equation, we get

2x - 3 = 9

2x - 3 + 3 = 9+3

2 x = 12

x = 6

Substitute the value of x in m ∠ ECA, then we get

m ∠ ECA = 15x + 2

= 15(6) + 2

m ∠ ECA = 92

EC is not an altitude of ΔAED because of m ∠ ECA = 92.

Therefore, EC is not an altitude of ΔAED.

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When a die is rolled, the probability of outcome less than 2 is 1/6.

As given in the question,

Let the possible outcomes of the given event is represented by S.

Formula used :

Probability of an event

= (Favorable outcomes) /(Total Number of possible outcomes)

When a dice is rolled, all possible outcomes are 1, 2, 3, 4, 5, 6.

Sample space, S =(1, 2, 3, 4, 5, 6)

Favorable outcomes = Only 1 is smaller than 2, remaining number is greater than 2

So, total number of favorable outcomes = 1

Probability of outcome less than 2

= (Favorable outcomes) /(Total Number of possible outcomes)

⇒ Probability = 1/6

Therefore, when a die is rolled, the probability of outcome less than 2 is 1/6.

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He will break even on the 25th month.

The cost to start the business is $20,000 and the monthly costs are $8,000.

He has been earning $8,800 every month in revenue.

Profit = Selling Price - Cost Price

Therefore,

let

x = number of month

Hence,

selling price = 8800x

cost price = 20000 + 8000(x) = 20,000 + 8000x

Therefore,

profit =  8800x - (20,000 + 8000x)

profit = 8800x - 20000 - 8000x

profit = 8800x - 8000x - 20000

profit = 800x - 20000

Hence,

The month when they will break even is as follows:

8800x = 20,000 + 8000x

20000 = 8800x - 8000x

20000 = 800x

x = 20000 / 800

x = 25

Therefore, he will break even on the 25th month.

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If two trains leave towns 978 miles apart at the same time and travel toward each other and one train travels 21 miles per hour faster than the other and if they meet in 6 hours, then the rate of the faster and slower train will be 92mph and 71 mph respectively.

To determine the rate or speed of each train, an algebraic expression can be used.

As one train travels 21 miles per hour faster than the other, consider x to be the speed of the train that travels slower. In this case, an algebraic expression can be given as,

6x + 6(x + 21) = 978

Here, (x + 21) represents the speed of the faster train

6x + 6x + 126 = 978

12x = 978 - 126

12x = 852

x = 852 ÷ 12

x = 71

x + 21 = 71 + 21 = 92

Hence, the rate of the faster train is 92 miles per hour and the rate of the slower train is 71 miles per hour.

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Answer:

2 times as much

Step-by-step explanation:

1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes

3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins

200 is twice as much as 100

The required simplified value of x and y is 32 and 84 respectively.

Given that,
To find the values of x and y. State which theorem(s) you used.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Vertical opposite angles

3x = 5x - 64
2x = 64
x = 32

Now,

5x - 64 = 5*32 - 64
            = 160 - 64

            = 96°
Now complementary angle y
y = 180 - 96°

y = 84°

Thus, the required simplified value of x and y is 32 and 84 respectively.

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Answer:

a

Step-by-step explanation: codigo binario

Answer:

Option 2

Step-by-step explanation:

2.2 x 1.25 = 2.7510-2.75=7.25

Answer:

195.86

Step-by-step explanation:

Answer: 195.86. Yw.

Step-by-step explanation: Pls add me Brainliest >3

The equation of the line 4x + 6y = 12 expressed in slope-intercept form is y = -2/3 x + 2 with a slope equal to -2/3.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula:

y = mx + b

where m is the slope of the line

b is the y- intercept

Given the equation of the line 4x + 6y = 12, which is in standard form, transform it into slope-intercept form by isolating the variable y in one side.

4x + 6y = 12

6y = -4x + 12

Dividing both sides by 6,

y = -4/6 x + 2

y = -2/3 x + 2

Hence, the equation of the line in slope-intercept form is y = -2/3 x + 2 where the slope, m, is equal to -2/3.

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Answer:

Step-by-step explanation:

[tex]\displaystyle\\-8(-\frac{10}{7})= 4(-\frac{10}{7} +5)+2(-\frac{10}{7} )\\[/tex]

[tex]\displaystyle\\Let \ -\frac{10}{7} =t\\Hence,\\(-8)(t)=(4)(t+5)+(2)(t)\\-8t=(4)(t)+(4)(5)+2t\\-8t=4t+20+2t\\-8t=6t+20\\-8t+8t=6t+20+8t\\0=14t+20\\0-20=14t+20-20\\-20=14t\\-20=(14)(-\frac{10}{7} )\\-20=-\frac{(14)(10)}{7} \\\\-20=-\frac{(7)(2)(10)}{7} \\-20=-(2)(10)\\-20\equiv-20[/tex]

The coordinates of the midpoint M of the segment AB is (-4,6).

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Point A (-8, 5)

Point B (0,7)

To determine the midpoint, plug the given points into the formula above and simplify.

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

M = ( ((-8)+0)/2, (5+7)/2 )

M = ( ( -8+0 )/2, (5+7)/2 )

M = ( ( -8 )/2, (12)/2 )

M = (-4,6)

Therefore, the coordinates of the midpoint M of the segment AB is (-4,6).

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The company catches 1,237,275.5 fishes over 10 years.

Given that, a company catches 175000 fishes in a year, the population decreases, the number of fish the company was able to catch decreased by 8% each year.

So, the population in 10 year =

The second year = 175000 × 0.92 = 161000

The third year = 161000 × 0.92 = 148120

The fourth year = 148120 × 0.92 = 136,270.4

The fifth year = 136270.4 × 0.92 = 125368.8

The sixth year = 125268.8 × 0.92 = 115339.3

The seventh year = 115339.3 × 0.92 = 106112.2

The eighth year = 106112.2 × 0.92 = 97623.2

The ninth year = 97623.2 × 0.92 = 89813.3

The tenth year = 89813.3 × 0.92 = 82628.3

The total = 175,000+161000+148120+136,270.4+125368.8+115339.3+106112.2+97623.2+89813.3+82628.3 = 1,237,275.5

Hence, the company catches 1,237,275.5 fishes over 10 years.

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The number of minutes it will take the marshal to catch up to the robber in discuss is; 210.

Let 30minutes = 0.5 hours.

Let x represent the time for which the marshal has ran.

On this note, the robber must have galloped at; (x +0.5) hours.

Hence, it follows from the task content that if they are at the same distance from the bank; we have;

14(x+0.5) = 16(x)

14x + 7 = 16x

7 = 2x

x = 7/2 = 3.5 hours.

= 3.5 × 60minutes = 210minutes.

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It is proved that ΔLMN is an isosceles triangle.

So,

Given:

To prove congruency:

Therefore,  ΔM LO ≅ ΔMNO under SSA congruency.

Therefore, it is proved that ΔLMN is an isosceles triangle.

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Answer:

The method for appearing with numbers for the 2x2 matrix whose determinant is 13 is clarified.

Step-by-step explanation:

Determinant of 2×2 matrix

If we have a 2×2 matrix A of the form;

A =

\binom{a \: \: \: b}{c \: \: \: d}(

cd

ab

)

The determinant of the matrix is;

|A| = (a.d) - (b.c)

Therefore, to appear with numbers for a, b, c, and d, we must ensure; (a.d) - (b.cdeterminantse, if a = 3, d = 15, b = 2, and v = 1.

Ultimately, |A| = (3×5) - (2×1) = 13

Answer:

A. s+7726>=12,600

Step-by-step explanation:

s is the number of steps left to reach her goal of at least 12,600 steps.

7726 is the number of steps already taken.

12,600 is her goal.

s+7726>=12,600

Hope this helps!

Please mark as brainliest if correct!

Answer:

The graph of g(x) shows exponential decay, while the graph of f(x) shows exponential growth. What you need in your answer: The graphs are reflections of each other over the y-axis. The g(x) function represents exponential decay.

The set of items that exist as part of both sets A and B exists at the intersection of the two sets.

If p(a|b) =0.40, p(b) = 0.74, and p(a) = 0.42, then P(A∩B) is 0.46.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

It exists given that the Probability of two independent event A and B exists given by P(A)  and P(B).

The intersection of event A and B is given by P( A∩B).

The group of items that are part of both sets A and B is the intersection of the two sets. A ∩ B represent the intersection. The symbol "∩" can be used to represent the intersection of sets.

The collection of all outcomes that are components of both sets A and B is known as the intersection of events A and B (abbreviated AB).

Given: P(a|b) = 0.40

P(A) = 1 - 0.40 = 0.6

P(B) = 1 - 0.74 = 0.26

P(A∪B) = P(A) + P(B) − P(A∩B)

substitute the values in the above equation, we get

0.40 = 0.6 + 0.26 - P(A∩B)

- P(A∩B) = 0.40 -  0.6 - 0.26

P(A∩B) = 0.46

Therefore, the independent events of A and B exists 0.46.

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

the fractions have like denominators so we add numerators :

[tex]\sf{\frac{3}{6} +\frac{2}{6} =\frac{3+2}{6} =\frac{5}{6}[/tex]

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

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[tex]\textcopyright ELIZA[/tex]

The sequence of the angles from lower to bigger will be ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

In a triangle, if the angle is small then the opposite side will be short, and if the angle increases then the side also increases.

The sides of the triangle are in ascending order, then we have

WY < YZ < WX < XY < XZ

Then the sequence of the angles is given as,

∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ

The sequence of the angles from least to biggest is ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.

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Answer:

they stopped at 110 for a restroom break?

I don't think I fully understand lol srry

Thomas and his grandparents are on a trip of 140-mile. From Points D and E, there is no movement of the bus, which means they halt at the point.

An orderly schematic illustration or diagram of facts or quantities is known as a graph in mathematics.

Usually, the graph's examples indicate how two or more items are related to one another.

As per the graph provided in the question,

As we can see in the graph there are covering 140 miles in a bus and the graph shows distance (in miles) and time (in hours).

From the graph we can see that between point D and E only time is increasing but the distance is constant which means they stopped at some place to halt.

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Answer:

Hello,

x=-4, y=3

Step-by-step explanation:

14*x+19*y=1 since gcd(182,247)=13

Here is a automatic calculus (using Bezout 's method)

All you have to do is to put in B1 and B2 the right numbers

The values of x and y given that 182x + 247 y = gcd(182, 247) would be x=-4 and y=3.

An equation represents equality of two or more mathematical expression.

To solve an equation, then the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).

And Solutions to an equation are values of the variables involved in that equation for which the equation is true.

We have given the equation as;

182x + 247 y = gcd(182, 247)

Then we get

14*x+19*y=1

Thus, x=-4 and y=3.

since we have given gcd(182,247)

=13

Hence, The values of x and y given that 182x + 247 y = gcd(182, 247) would be x=-4 and y=3.

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The second term of the given geometric sequence is: 6.

Given:

To find: Second term of the GP (a₂).

Finding:

Since the given sequence is a GP, the nth term will be given by: [tex]a_n=a_1(r^{n-1})[/tex], where r = common ratio of the GP.

Now, for n  = 3, [tex]a_3=3(r^{3-1})[/tex]

=> 12 = 3 (r²)

=> 4 = r²

=> r = ±2

Since the given sequence is increasing and positive, r = 2.

Thus, a₂ = a₁ (r¹)

=> a₂ = 3 (2) = 6

Hence, The second term of the given geometric sequence is: 6.

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Answer:

5 degres

Step-by-step explanation:

0-10 is -10

-10+15 is 5

Step-by-step explanation:

222-6=216

216÷4=54

so 54 students per bus

Answer:

54 students

Step-by-step explanation:

222 - 6 (students that had to travel in cars) = 216

216 / 4 (4 buses) = x

x = number of students on each bus

216 / 4 = 54

x = 54

54 students on each bus

216 students rode the bus, 6 students rode in cars

The slope of a line perpendicular to the line of x + 4y = 16 is 4.

Given the equation of line;

x + 4y = 16

First, rearrange in slope intercept form ( y = mx + b ) by solving for y

x + 4y = 16

Subtract x from both sides

x - x + 4y = 16 - x

4y = -x + 16

Divide each term by 4 and simplify

4y/4 = -x/4 + 16/4

y = -(1/4)x + 4

Using the slope intercept form ( y = mx + b ) to compare.

y = -(1/4)x + 4

Slope m = -(1/4)

Now, the equation of a perpendicular line to y = -(1/4)x + 4 must have a slope that is the negative reciprocal of the original slope.

Hence, m_perpendicular will be;

m_perpendicular = -( 1 / original slope )

m_perpendicular = -( 1 / -(1/4) )

m_perpendicular = -( -4 )

m_perpendicular = 4

Therefore, the slope of a line perpendicular to the line of x + 4y = 16 is 4.

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Hello,

[tex]f(x) = - {x}^{2} + 8[/tex]

[tex]h(x) = - {x}^{2} + 8 - 3 = - { {x}^{2} } + 5[/tex]