Pedro has been given two segments and the measure of an angle between them. He is trying to construct a congruent triangle. This is what he has done so far. What step has he just completed? A) Copy the angle. B) Copy the first line segment. C) Construct the segment between the endpoints of the two copied line segments. D) Copy the second line segment with one endpoint at the same endpoint of the first line segment.

2000 times 0.60 = 1200 doctors

3/5=0.6

x= 2000* 3/5

x=2000*0.6

x=1200

so... 1200 doctors use brand X aspirin.

Using Rise/Run, the answer would be y= -3/4x + 3.

y = - [tex]\frac{3}{4}[/tex] x + 3

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-interceot )

to calculate m use the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (4, 0 ) ← 2 points on line

m = [tex]\frac{0-3}{4-0}[/tex] = - [tex]\frac{3}{4}[/tex]

the line crosses the y- axis at (0, 3 ) → c = 3

y = - [tex]\frac{3}{4}[/tex] x + 3 ← in slope-intercept form

The equation that represents the total amount of money Layla has saved, s, after m months is s = 150m + 650.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Layla is saving up money for a trip. She already has $650 saved and plans to save an additional $150 each month for the trip.

The equation will be written as:-

S = 150m + 650

Here, 650 is how much she already saved and 150 is how much per month.

Therefore, the equation that represents the total amount of money Layla has saved, s, after m months is s = 150m + 650.

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Answer:

$21,000

Step-by-step explanation:

The cost of car=$ 28,000

A car is depreciated by 25%

Now, the price of car=$28000(1-)[tex]\frac{25}{100}[/tex]

The price of the car= $28000([tex]\frac{100-25}{100}[/tex])

The price of the car= $28000([tex]\frac{75}{100}[/tex])

The price of the car= $280×75

The price of the car= $21,000

The car worth today $21,000

Hence the correct answer is $ 21,000

The value for X, the measure of angle MKL, is not specifically given in the question. Since angle JKL is a straight angle of 180 degrees, X can be any value up to 180 degrees.

In mathematics, a straight angle is defined as an angle of 180 degrees. In the scenario described with angle JKL, it is mentioned that this is a straight angle. Given that angle MKL is a part of the straight angle, its degree measure X is a component of those 180 degrees. The specific value of X is not given in the question, and it can be any number less than or equal to 180, provided the other part of the angle KJM is equal to 180- X.

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The measure of angle MKL is 60 degrees.

Finding the Measure of Angle MKL

To determine the value of X in this problem, we first need to understand that a straight angle measures 180 degrees. The problem states that angle JKL is a straight angle, so:

Angle JKL = 180 degrees

Next, we have the measure of angle JKM given as 120 degrees. Since angle JKL is made up of angle JKM and angle MKL, we can set up the following equation to find the measure of angle MKL, which is X:

Angle JKM + Angle MKL = Angle JKL

Substituting the known values:

120 degrees + X = 180 degrees

To find X, subtract 120 degrees from both sides:

X = 180 degrees - 120 degrees = 60 degrees

Therefore, the measure of angle MKL is 60 degrees.

y- coordinate 0f A' = 2

note that the coordinates of A(1, 2 ) and the centre of dilatation (4, 2) both have the same y- coordinate 2

This means they are both on the horizontal line y = 2

and so the y- coordinate of A' will also be 2

26.25 hours = 26 hours 15 minutes

substitute y = 40 into the equation and solve for x

- 4x + 120 = 15 ( subtract 120 from both sides )

- 4x = - 105 ( divide both sides by - 4 )

x = 26.25 hours = 26 hours 15 minutes

400/16= 25

answer: it's a 16 to 25 ratio

one worker covers 25 dogs

25 : 1

the ratio of dogs : employees = 400 : 16

to simplify the ratio divide both parts by 16

400 : 16 = 25 : 1 ← in simplest form

the answer is b and d!

The examples of the Law of Detachment are:

1. If it snows tomorrow, then my dentist appointment will be canceled.

If my dentist appointment is canceled, then I will clean under my bed. Therefore, if it snows tomorrow, then I will clean under my bed.

3. If an object is a square, then it is a rhombus. If it is a rhombus, then it is a quadrilateral. Therefore, if an object is a square, then it is a quadrilateral.

It states that if a conditional statement (if-then statement) is known to be true and its hypothesis (the "if" part) is true, then the conclusion (the "then" part) can be validly inferred as true.

The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then the conclusion must also be true. In both the first and third examples, the statements follow this pattern.

So, the examples of the Law of Detachment are:

If my dentist appointment is canceled, then I will clean under my bed. Therefore, if it snows tomorrow, then I will clean under my bed.

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The Pythagorean theorem is used for finding the distance between two points. You can consider the line from the origin to (12, 5) to be the hypotenuse of a right triangle with sides 12 and 5 (parallel to the x- and y-axes, respectively). Then the relation between these and the hypotenuse length is

... d² = 12² + 5² = 144 + 25 = 169

... d = √169 = 13

The point (12, 5) is 13 units from the origin.

Okay...... so for this problem you need to use the Pythagorean Theorem. So...

12^2 + 5^2

144+25

169

this = square root of 13

so.... The point (12,5) is 13 units from  the origin.

Look for the adjacent letters A.F or F.A in the names of the pair of angles.

The appropriate choice is ...

... BAF and FAD

Answer:

BAF and FAD

Step-by-step explanation:

In order for an angle to have A.F as a side, it must have the letters A.F or FA in its name.

In DAF, the angle is made of rays AD and A.F.  In DAB, the angle is made up of rays AD and AB.  This is not the correct pair.

In EAF, the angle is made of rays AE and A.F.  In CAE, the angle is made up of rays AC and AE.  This is not the correct pair.

In BAF, the angle is made of rays AB and A.F.  In EAD, the angle is made up of rays AE and AD.  This is not the correct pair.

In BAF, the angle is made up of rays AB and A.F.  In FAD, the angle is made up of rays A.F and AD.  This is the correct pair.

( 4.625, - 3.75 )

the midpoint of (x₁, y₁ ) and (x₂, y₂ ) is

[[tex]\frac{1}{2}[/tex](x₁ + x₂ ), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]

here (x₁, y₁ ) = (5.5, - 4.75 ) and (x₂, y₂ ) = (3.75, - 2.75 )

[ [tex]\frac{1}{2}[/tex](5.5 + 3.75 ), [tex]\frac{1}{2}[/tex](- 4.75 - 2.75 ) ]

= (4.625, - 3.75 ) ← midpoint of HX

I believe so.  :) correct me if i'm wrong.

(1, 3 )

to determine if the given points are a solution to the equation

They must lie on the given line to be a solution

the only one that is on the line is (1, 3 ) and is therefore the only solution

B

since both equations express y in terms of x we can equate the right sides

2x + 7 = 25 - x ( add x to both sides )

3x + 7 = 25 ( subtract 7 from both sides )

3x = 18 ( divide both sides by 3 )

x = 6

substitute x = 6 into either of the 2 equations for y

y = 2x + 7 = ( 2 × 6 ) + 7 = 12 + 7 = 19

solution is (6, 19 )

A

the equation of a line in ' slope-intercept form ' is

y = mx + c ( m is the slope and c the y-intercept )

y = 5x + 3 is in this form with slope m = 5

function Q has equation y = 2x + 4

the slope of function P is 3 more than function Q

I had a test and this was one of the questions and the answer it said was (3x1/3) x 42 so you dont have to figure it out. hope this helps anyone who needs it. :)

Answer:

The correct answer is:

New students laughing at Steve

10 × 10 = 100

Add all the students laughing at Steve

10 + 100 = 110

Add Steve

110 + 1 = 111

There were 111 students in total laughing.

Step-by-step explanation:

Answer:

111

Step-by-step explanation:

-103  

if he lost the same weight each week that means -412 (the weight he lost) ÷ 4 (number of weeks) = -103 (amount of weight lost in one week)

Answer: -1 1/8

Step-by-step explanation: When you have a problem like this, you have to divide.

So you turn the improper fraction into a mixed number which (4 1/2 turns into 9/2) and then you do KCF (Keep Change Flip). So you keep the 9/8, change division into multiplication, and since we are going to put the four over a 1 like this 4/1, we need to change it into 1/4. Then you multiply across. 9x1=9 and 2x4=8 so it would be 9/8. But it's an improper fraction right? So you do long division, and you get -1 1/8.

Answer:

Given: A Δ ABC in which , AB ≅ BC, BE − median of ΔABC, m∠ABE = 40°30'

To Find: ∠ABC, ∠ CE B,∠A E B

Solution: In Δ ABC , BE is the median.

So, AE= EC

Now, In Δ A E B and Δ CE B

AE = EC [ BE is median]

BE is common.

AB=BC [given]

Δ A E B ≅Δ CE B { SSS Congruency]⇒S→side

So, ∠ABE=∠C BE  [ C PCT]

∴ ∠ABC=2×∠ABE=2×40°30'=81°

∠B EA =∠C E B [ C P CT]

Also,∠B A C = ∠BC A=k° [As AB =BC , if opposite sides are equal , then angle opposite to them are equal]

∠A+ ∠B+∠C=180°[ angle sum property of triangle]

k°+81°+k°=180°

2 k°=180°-81°

2 k°=99°

k°=99°/2

k°=49°30'[1°=60']

In Δ A E B, ∠ABE=40°30',∠A=49°30',∠A E B=?

∠ABE+∠A+∠A E B=180°[ angle sum property of triangle]

40°30'+49°30'+∠A E B=180°

90°+∠A E B=180°

∠A E B=180°-90°

∠A E B=90°

As, ∠B EA =∠C E B

So,∠C E B= 90°

So, BE is perpendicular bisector.

The measure of the angle ∠ABC and ∠BCA are both 69°45'. and ∠FEC measures 99°.

∠ABE and ∠BEC are opposite angles formed by the intersecting lines AB and BE, and BC and BE respectively.

Therefore, they are congruent.

The sum of the interior angles of a triangle is always 180°. So, we can find ∠ABE by subtracting ∠BEC from 180°.

Since m∠ABE = 40°30', we have:

∠BEC = ∠ABE = 40°30'

Since AB ≅ BC, the two sides are congruent.

This means that ∠ABC and ∠BCA are also congruent angles. Let's call their measure x.

Using the fact that the sum of the angles in a triangle is 180°, we can set up an equation:

∠ABC + ∠BCA + ∠BAC = 180°

Since ∠BCA = ∠ABC = x, we can substitute these values in:

x + x + 40°30' = 180°

Adding the like terms:

2x + 40°30' = 180°

Subtracting 40°30' from both sides:

2x = 180° - 40°30'

2x = 139°30'

Dividing both sides by 2:

x = 69°45'

So, ∠ABC and ∠BCA are both 69°45'.

To find ∠FEC, we can use the fact that the sum of the angles in a triangle is 180°. Since ∠BEC = ∠ABE = 40°30', we can find ∠FEC:

∠FEC = 180° - ∠BEC - ∠BCE

Substituting the values we know:

∠FEC = 180° - 40°30' - 40°30'

Simplifying:

∠FEC = 180° - 81°

∠FEC = 99°

Therefore, ∠FEC measures 99°.

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Answer:

y = 0.75x+20

Step-by-step explanation:

Given that there is an admission ticket fixed and extra cost of 0.75 per ticket for the rides.

This means even if there is no ride used, enterer has to pay a fixed amount for admission.

Let us find out this admission cost from the given information

If y is the total cost and x no of rides

a) x is the no of rides and y the total cost

b) y = 0.75x+20 is the linear equation to calculate the cost for anyone who only pays for festival admission and rides

(c)

Total cost = Admission charges +0.75 * no of ride tickets.

then y = 0.75x+C

where C is the admission fee

Kendall bought 18 tickets i.e. x= 18 and y = 33.50

33.50 = 0.75(18)+C

33.50=13.50+C

C = 33.50-13.50 = 20.00

Hence admission fee = 20

Solution: We are given data points and associated residuals:

Data Point           Residual          Absolute value(Residual)

(20,6)                     -2.00                      2.00

(15,5)                       6.75                       6.75

(5,3)                        -1.25                       1.25

(10,10)                     4.50                       4.50

From the above absolute value(Residual) column, we clearly see the data point (15,5) has the residual with greatest absolute value of 6.75.

Therefore, the data point and its associated residual is:

(15,5)  and 6.75    

Answer:

Data Point: (10,10); Residual = 4.50

Answer:

-5.27

Since when multiplying a positive and negative integer the answer will become negative

The product of -1.24 and 4.25 is -5.27, found by performing the mathematical operation of multiplication.

Given the question, you are asked to calculate the product of -1.24 and 4.25.

Which in this case, -1.24 * 4.25 equals -5.27

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Yes, you're right! The first step is rewriting the equation as

[tex] \ln(a) + \ln(b^x) = M [/tex]

Subtract [tex] \ln(a) [/tex] from both sides:

[tex] \ln(b^x) = M-\ln(a) [/tex]

Use the property [tex] \ln(a^b) = b\ln(a) [/tex] to rewrite the equation as

[tex] x\ln(b) = M-\ln(a) [/tex]

Divide both sides by [tex] \ln(b)[/tex]

[tex] x = \dfrac{M-\ln(a)}{\ln(b)} [/tex]

Alternative strategy:

Consider both sides as exponents of e:

[tex] e^{\ln(ab^x)} = e^M [/tex]

Use [tex] e^{\ln(x)} = x [/tex] to write

[tex] ab^x = e^M [/tex]

Divide both sides by a:

[tex] b^x = \dfrac{e^M}{a} [/tex]

Consider the logarithm base b of both sides:

[tex] x = \log_b\left(\dfrac{e^M}{a}\right) [/tex]

The two numbers are the same: you can check it using the rule for changing the base of logarithms

To solve ln(a*b^x) = M, apply the log properties to get ln(a) + x*ln(b) = M, isolate x to get x*ln(b) = M - ln(a), and divide by ln(b) to find x = (M - ln(a))/ln(b).

To solve the equation ln(a*b^x) = M for x, begin by applying the property that the logarithm of a product is equal to the sum of the logarithms. That is, ln(xy) = ln(x) + ln(y). Therefore, we can write:

ln(a*b^x) = ln(a) + ln(b^x)

The logarithm of a power allows us to move the exponent to the front of the log, hence:

ln(b^x) = x * ln(b)

Now, our equation becomes:

ln(a) + x * ln(b) = M

We can isolate x by subtracting ln(a) from both sides:

x * ln(b) = M - ln(a)

Finally, divide both sides of the equation by ln(b) to solve for x:

x = (M - ln(a)) / ln(b)

The rate of change of y (miles traveled) with respect to x (time in hours) is 59, the coefficient of x. The appropriate choice is ...

... C. For every hour, she will drive 59 miles.

The equation y = 59x + 13 shows that Megan's rate of change in distance traveled is 59 miles for every hour driven at cruise control, after the first 13 miles. So, the correct answer is C. For every hour, she will drive 59 miles.

The equation y = 59x + 13 represents Megan's total distance traveled after driving the first 13 miles without cruise control. The variable y stands for the total number of miles driven, and x represents the number of hours driven at a constant speed using cruise control. To identify the rate of change in the distance traveled, we look at the coefficient of x in the equation, which is 59. This coefficient indicates how many miles are added to the initial 13 miles for every hour of driving at cruise control. Therefore, for every hour, Megan will drive 59 miles after the initial 13 miles are accounted for. It is important to note that the initial 13 miles are a fixed distance and do not change with time. Thus, the correct statement describing the rate of change in the distance traveled is C. For every hour, she will drive 59 miles after the first 13 miles.

(a) [tex]a_{n}[/tex] = 4n + 8

(b) row 13 has 60 seats

(a)

the sequence of seats is an arithmetic sequence whose n th term is

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1 )d

where [tex]a_{1}[/tex] is the first term and d the common difference

here the sequence is 12, 16, ....

with [tex]a_{1}[/tex] = 12 and d = 16 - 12 = 4, thus

[tex]a_{n}[/tex] = 12 + 4( n - 1 ) = 12 + 4n - 4 = 4n + 8

(b)

calculate the number of rows n when 60 seats

solve 4n + 8 = 60 ( subtract 8 from both sides )

4n = 52 ( divide both sides by 4 )

n = 13 ← number of rows

Set up the equations:

2x+3y=80

1x + 4y = 100

solve for x and y:

1x + 4y = 100

x = 100-4y

plug into first equation

2(100-4y)+3y=80

200-8y+3y=80

y=120/5=24

x = 100-4y=100-96=4

So the charges are (x,y)=(4,24)

So the correct answer (B)

Assuming you require the measure of the angles

let x represent each equal  base angle then vertex = 7x

The sum of the angles in a triangle = 180°, hence

x + x + 7x = 180

9x = 180 ( divide both sides by 9 )

x = 20

the base angles = 20° and the vertex = 140°

The ratio of the measure of a base angle in an isosceles triangle to the measure of the vertex angle is 1:7. The measure of the base angle is 1/7 times the measure of the vertex angle.

In an isosceles triangle, the base angles are congruent, meaning they have the same measure. Let's denote the measure of the base angle as x degrees and the measure of the vertex angle as y degrees. According to the given ratio, we have the equation:

x : y = 1 : 7

To find the exact measures of the angles, we can set up the equation:

x/y = 1/7

Multiplying both sides by y, we get:

x = y/7

Therefore, the measure of the base angle is 1/7 times the measure of the vertex angle.

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Given P is T, q is F and r is F.

Let us find p ↔ q first.

↔ is called bi-conditional operator and is true when p and q both are matched.

Since here p is T and q is F, p↔q is F. ( Since p and q are not matching)

~p v r = ~T v F = F v F = F

Hence (p↔q)→(~pvr) = F → F = T     (Since conditional operator → is false if and if first proposition is T and second proposition is F, for all other values it is T)