Train A and Train B leave the station at 2 P.M. The graph below shows the distance covered by the two trains. Compare the speeds of the two trains.

Answer:

i. g = 70°

ii. x = 85°

Step-by-step explanation:

Given:

Let first we name the triangle

i. ) Δ PQR , m∠ PRQ = 40°

ii. ) Δ ABC is a right angle at B and a line B- D-C

       m∠ DAC = 25°

       m∠ ACD = 60°

       m∠ BDA = x°

To Find:

i. g = ?

ii. x = ?

Solution:

i.

In Δ PQR , PR ≅ QR ...........{Given]

∴ Δ PQR is an Isosceles Triangle.

c.........{ Base angles of Isosceles triangle are equal }

∴ m∠ PQR = m∠ RPQ = g

Now sum of all the angles in a triangle is 180°

∴ m∠ PQR + m∠ RPQ + m∠ PRQ = 180°....{Angle sum property of Triangle}

[tex]g + g + 40 = 180\\2g=180-40\\2g=140\\g=\frac{140}{2} \\g=70\°[/tex]

∴ g = 70°

ii.

We know sum of all the angles in a triangle is 180°

In Δ DAC

m∠ DAC + m∠ ACD + m∠ ADC = 180°.....{Angle sum property of Triangle}

[tex]25+60+ \angle ADC = 180\\[/tex]

[tex]\angle ADC = 180-85\\\angle ADC =95\\[/tex]

Now By Linear Pair Angle Property

m∠ ADB + m∠ ADC = 180° ........{Linear Pair Angle Property}

[tex]x+95=180\\x=180-95\\x=85[/tex]

∴ x = 85°

Answer:

Step-by-step explanation:

Variables:

let x be the number of minutes

let y be the total number of pages read

Use the form y = mx + b

"b" is irrelevant in this context because the initial value is 0 (they have not read it before or it is not given)

m is the rate, how fast they can read, how many pages each minute

Alejandro:

28 = 1x   <=Simplify because any number multiplied by 1 is itself.

28 = x

Carly:

12 = 2x

Answer:

B. $336.09

Step-by-step explanation:

Monthly payment = $876.09

Interest rate = 4.8%

Convert the annual interest rate to monthly rate = 4.8% / 12

Monthly rate = 0.4% or 0.004

Amount going towards interest payment = 0.004* loan amount

Interest = 0.004 * 135,000

Interest = $540

Therefore, from the monthly payment of $876.09 , $540 goes towards paying interest and the balance is the note reduction;

Note reduction = $876.09 - $540 = $336.09

Answer:

336.09

Step-by-step explanation:

this is the right anwser

Answer:

7

Step-by-step explanation:

3(7)=21-5=16

Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (6, 0)

m = [tex]\frac{0-6}{6-0}[/tex] = [tex]\frac{-6}{6}[/tex] = - 1

Note the line crosses the y- axis at (0, 6 ) ⇒ c = 6

y = - x + 6 or y = 6 - x ⇒ B

Answer:

62 is 50% of 31

Step-by-step explanation:

For example: 50% of 62 = 31; Example 2: Calculate a percentage based on 2 numbers. For example: 31/62 = 50%

Answer:

31

To calculate a percentage of some number, change the percentage into a decimal, and the word "of" into multiplication

Answer:

247/30

Step-by-step explanation:

19 7/5-6 1/3-5 5/6

19 7/5=102/5

6 1/3=19/3

5 5/6=35/6

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

102/5-19/3-35/6

612/30-190/30-175/30=247/30

Answer:

8 7/30

Step-by-step explanation:

Answer:

6a+2-5a

ascending

2+a

descending

a+2

Answer:

The graph in the attached figure

Step-by-step explanation:

Graph the solution of the inequality

[tex]t\leq -4[/tex]

we know that

The solution is the interval ---> (-∞,-4]

All real numbers less than or equal to -4

In a number line the solution is the shaded area at left of t=-4 (closed circle, because the number -4 is included in the solution))

using a graphing tool

The graph in the attached figure

Answer:

27

Step-by-step explanation:

-8 * -2 = 16

16 + 11 = 27

Answer:

28

Step-by-step explanation:

24-7-4=13

13+15=28

Answer:

(1,c) (2,b) (3,A)

Step-by-step explanation:

May be right or worng i just read thought it better.

Answer:

43+44+45

Step-by-step explanation:

X + X + 1 + X + 2 = 132

3X + 3 = 132

3X + 3 - 3 = 132 - 3

3X = 129

3X/3 = 129/3

X = 43

consecutive means numbers after

What is the minimum cuts  needed to cut a circle into 8  equal parts ?

A : 4 cuts

Answer:

Step-by-step explanation:

When we have a circle, each cut (supposing the curst are in the exact middle) which give use two haves. So, if we cut one time, we'll have two equal parts, if we cut a second time, we'll have 4 equal parts, a third time, we'll get us 6 equal parts, and if we cut a fourth time, we'll have 8 equal parts.

So, whenever we have this kind of problem dividing circles, we just say that each cut in the exact middle equals two equal haves, so if we have 4 cuts, we just multiply them by 2, 4(2)=8. Therefore, we have 8 equal parts.

Answer:

54

Step-by-step explanation:

8*7-12/6=56-2=54

Answer:

56-2=54

Step-by-step explanation:

8×7 - 12÷6 =56 - 2= 54

Final answer:

The system of linear inequalities for Kayla's fruit purchase is x + y ≥ 15 to represent the quantity of fruit, and 0.65x + 0.78y < 20 to represent the budget constraint.

Explanation:

The student's question is asking for a system of linear inequalities that would model the situation in which Kayla wants to buy at least 15 fruits consisting of apples and oranges, without spending more than $20. Given that apples (x) are $0.65 each and oranges (y) are $0.78 each, we can set up the following inequalities:

x + y ≥ 15

0.65x + 0.78y < 20

The first inequality represents the requirement that Kayla needs to buy at least 15 pieces of fruit. The second inequality represents the constraint that she needs to spend less than $20 on her purchase.

Answer:

The scientific notation, 6.24 x 10^-4, means that the 6.24 is multiplied to 10 which is raised to exponent -4. 10^-4 has a regular number value of 0.0001. So, to find the answer you should multiply 6.24 by 0.0001 which gives an answer of 0.000624.20

Step-by-step explanation:

Answer:

x=17/150

Step-by-step explanation:

11x-4/50=70/60

11x-2/25=7/6

11x=7/6+2/25

11x=187/150

x=(187/150)/11

x=(187/150)(1/11)

x=187/1650

simplify,

x=17/150

Answer:

x=17/150

Step-by-step explanation:

an equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon

The only type of polygon that must be regular if it is equiangular is a regular polygon.

Here, we have,

we know that,

A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges.

an equiangular polygon is a polygon whose vertex angles are equal.

If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon.

Hence, The only type of polygon that must be regular if it is equiangular is a regular polygon.

To learn more on polygon click:

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Answer:

[tex]\displaystyle 15 > n[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{6n}{6} < \frac{90}{6} → n < 15[/tex]

Whenever you divide\multiply by a negative, you reverse the inequality symbol.

** The above answer is written in reverse, which is the exact same result.

≥, ≤ → Solid Circle [●]

>, < → Blank Circle [○]

I am joyous to assist you anytime.

Answer:

20/3

Step-by-step explanation:

5/(3/4)=(5/1)(4/3)=20/3

This is a mathematics problem involving the calculation of the slope of a line graph. The machine produces 20 soda bottles per minute as concluded from the given coordinates (4,80) and (7,140).

The subject of this question falls under Mathematics, specifically the topic of linear relationships or functions. The task is to calculate the rate at which soda bottles are made per minute using the given coordinates of the graph, (4,80) and (7,140).

First, we need to calculate the slope of the line represented by these points since the slope corresponds to the number of soda bottles produced per minute. In a linear relationship, the slope of the line can be found using the formula: slope = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, (x1, y1) is (4,80) and (x2, y2) is (7,140). Plugging these values into the slope formula, we get: slope = (140 - 80) / (7 - 4) = 60 / 3 = 20.

So, the machine produces 20 soda bottles per minute.

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Answer:

Step-by-step explanation:

∡ECD = 90°

∡DCA= 90°

∡BCA=90°

∡BCE =90°

⇔ ABC=DCE

Answer:

Yes

Step-by-step explanation:

312/3=104

Answer:

Cost of a 3 minute call is 50 cents at a rate of 16.67 cents per minute.

Step-by-step explanation:

We are given the following in the question:

Plan A

A rate of 8 cents per minute.

Plan B

A 50​-cent minimum charge per completed​ call.

We have to find the​ cost, in cents per​ minute, for a 3​-minute call.

Cost according to plan A:

[tex]\text{Cost per minute}\times \text{Call length in minutes}\\= 8 \times 3\\=24 \text{cents}[/tex]

Cost according to plan B:

50 cents for a 3 minute call

Rate =

[tex]\displaystyle\frac{\text{Total cost}}{\text{Duration of call}} = \frac{50}{3} = 16.67 \text{ cents per minute}[/tex]

The company chooses the plan with greater cost, thus, it chooses plan B.

Thus, cost of a 3 minute call is 50 cents at a rate of 16.67 cents per minute.

Answer:

4x(2x+3)

Step-by-step explanation:

The answer is 4x(2x+3)

Thus, a product that normally costs $20 with a 75 percent discount will cost you $5.00, and you saved $15.00. You can also calculate how much you save by simply moving the period in 75.00 percent two spaces to the left, and then multiply the result by $20 as follows: $20 x .75 = $15.00 savings.

Answer: $35

Step-by-step explanation:

20(75%)=15+20= $35

Answer:

0

Step-by-step explanation:

14+ (-4) +6+(-16) = _

10+6+(-16) =

16+(-16) = 0

Answer:

0

Step-by-step explanation:

14 + (-4) + 6 + (-16) =  

10 + 6 + (-16) =  

16 + (-16) =

0