A car is moving at a speed of 50 km/hour. The driver takes her foot off of the accelerator and the car coasts to a stop. Why? A) No acceleration means no movement. B) Energy is no longer being transformed. C) Without an external energy source, friction stops the car. D) All the kinetic energy is converted to potential energy or energy of position.

Step-by-step explanation:

the error:

it is stated that

[tex]\frac{5x}{x+7} +\frac{7}{x} = \frac{5x}{x+7} +\frac{7(7)}{x+7}[/tex]

subtract (5x)/(x+7) from both sides

[tex]\frac{7}{x} = \frac{7(7)}{x+7}[/tex]

multiply both sides by x + 7

7(x+7) = 49x

7x + 49 = 49x

subtract 7x from both sides to isolate x and its coefficient

49 = 42x

thus, this is only true when 49 = 42x. in order for these two equations to be equal, they must always be true, so this is wrong

the solution:

we want to express 7/x as (something) / (x+7). to do this, we can multiply 7/x  by 1.

anything divided by itself = 1. thus, if we multiply both the numerator and the denominator by something that turns x into (x+7), we can do what we want to do.

(x+7)/x * x turns x into (x+7), so we multiply both the numerator and denominator by (x+7)/x to get

[tex]\frac{7}{x} = \frac{7(x+7)/x}{x+7}[/tex]

substitute this for 7/x in our original problem

[tex]\frac{5x}{x+7} +\frac{7(x+7)/x}{x+7} = \frac{5x}{x+7} +\frac{(7x+49)/x}{x+7} = \frac{5x}{x+7} +\frac{7+49/x}{x+7} = \frac{5x+7+49/x}{x+7}[/tex]

Answer:

y = x/3 +5

Step-by-step explanation:

Step1 : finding the slope

m = [tex]\frac{y2-y1}{x2-x1}[/tex]

(3,6) and (−3,4)

m = [tex]\frac{4-6}{-3-3}[/tex]

m = 1/3

Solving for the equation

y-y1 = m(x-x1) , (3,6)

y-6 = 1/3(x-3)

y = x/3 -1 +6

y = x/3 +5

Answer:

  (a) higher by 0.25%

Step-by-step explanation:

The error in the estimate is found by comparing the estimated rate to the actual rate.

__

The rate of estimated closing costs is ...

  (estimated cost)/(home cost) × 100% = 6375/170000×100% = 3.75%

The actual rate is 4.00%.

  actual - estimate = 4.00% -3.75% = 0.25%

The actual closing costs were higher than the estimate by 0.25%.

Answer:

S = $76 and P = $236

Step-by-step explanation:

Let the sodas be S and the patties P. So

4S + 6P = 840  and 5S + 5P = 800

By substitution method we will have the solution

5S + 5P = 800

5S = 800 - 5P

S = 800 - 5P

          5

We'll sustitute S with this equation

4S + 6P = 840

[tex]4(\frac{800 - 5P}{5})[/tex] + 6P = 80

4(800 - 5P) + 6P(5) = 840

3200 - 20P + 30P = 840

-20P + 30P = 840 - 3200

10P = -2360

P = -2360

        10

P = -236

Since the cost of the patty can't be negative, P = $236

Now that we know the cost of the patty, we can calculate the cost of the soda

S = 800 - 5P

          5

S = 800 - 5(236)

             5

S = 800 - 1180

             5

S = -380

        5

S = -76

Here S can't be negative, so S = $76

Answer:

44 aproximately

Step-by-step explanation:

She puts a tag on 20 of them, the next day she catches 27 and notices 3 of them have a tag so we substract 27-3=24 we add 24 to the initial number of ducks (20) and the result is 44

Step-by-step explanation:

27÷3×20=180

or

3/27=20/n =180

so the numbers of ducks in her local park is 180

Answer:

A. 90°

Step-by-step explanation:

A perpendicular on a straight line creates 2 right angles.

We know the value of a right angle is 90°.

Hence :

∠2 = 90°

Answer: 475 Add 5 more.

Step-by-step explanation:

Answer:

The lowest common multiple of 10 and 20 is twenty, and the maximum common multiple is 10

          [tex]\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]

         What is the lowest common multiple of 10 and 20?

           [tex]\rule{50}{1}\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]

           First let's list a few common multiples of 10 and 20:-

[tex]\Large\textsf{Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100...}}[/tex]

        Now, let's list some multiples of 20:-

 [tex]\Large\textit{Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160...}[/tex]

      Now let's find the Least common multiple (L.C.M.) of 10 and 20:-

[tex]\Large\textsc{The LCM is 20}[/tex]

            [tex]\rule{50}{1}\smile\smile\smile\smile\smile\smile\rule{50}{1}[/tex]

Step-by-step explanation:

[tex] = 2(x - 5) ^{2} + 4(x - 5) + 1[/tex]

Now for the first term use the formula :

[tex] {a}^{2} - 2ab + {b}^{2} [/tex]

[tex] = 2( {x}^{2} - 10x + 25) + 4(x - 5) + 1[/tex]

[tex] = 2 {x}^{2} - 20x + 50 + 4x - 20 + 1[/tex]

[tex] = 2 {x}^{2} - 20x + 4x + 50 - 20 + 1[/tex]

[tex] = 2 {x}^{2} - 16x + 31[/tex]

Answer:

612 centimeters = 612 : 10 = 61,2 decimeters

Answer:

31.9°

Step-by-step explanation:

Applying the Law of Sines,

⇒ sin75° / 22 = sin x° / 12

⇒ sin (45 + 30)° / 22 = sin x° / 12

⇒ (1/√2)(√3/2) + (1/√2)(1/2) / 22 = sin x° / 12

⇒ (1/√2)(√3 + 1 / 2) / 22 = sin x° / 12

⇒ 12 × (2.73/2.82) / 22 = sin x°

⇒ x = sin⁻¹ (0.529)

⇒ x = 31.9° (nearest tenth)

Answer: 25, 90 ,90

Step-by-step explanation:

One angle on a paralel = 155
=> x+ y + z + 155 = 360
  x + y + z = 205    ; x + y ; y + z ; x + z = 180

x + y = 180
=> Z = 205 - 180
    Z = 25  Degree
x = y = 90 degree

Mark me as Brainliest pls ! Tysm !

Explanation:

By definition, the floor is assumed to be level and that means the floor is at a 0 degree angle. The shelf must also have this same angle relative to the floor so we have the shelf and floor as parallel planes. For more info, check out the converse of the corresponding angles theorem.

Answer:

  y = 5

Step-by-step explanation:

The triangles will be congruent when corresponding sides are congruent. __

We already have ...

  KL ≅ NP . . . = 15 mm

  JL ≅ MP . . . = 22 mm

So, we need ...

  JK ≅ MN

  4y +12 = 32 . . . . substitute given values

This will be the case when ...

  4y = 20 . . . . . subtract 12

  y = 5 . . . . . . . divide by 4

The value of y that makes the triangles congruent is 5.

Answer:

864.

Step-by-step explanation:

1) the required volume can be calculated according to the formula (see also the attachment):

V=Area(BKS)*height;

2) if to see the triangle ABC (see the attachment), then m∠C=90°; m∠A=30° and m∠B=60°;

3) the length of AC=BC*cot(m∠A)=2√3*√3=6 [cm];

4) if AC=6 [cm], then BS=36-2*BC=24 [cm];

5) in the equilateral triangle BKS BS=BK=KS=24 [cm], then the Area(BKS)=BS²√3/4=144√3 [cm²];

6) if the height is 2√3 [cm] and Area(BKS)=144√3 [cm²], then

V=144√3*2√3=864 [cm³].

Answer:

14 pairs of earrings

Step-by-step explanation:

Question

Navya has 10 ¹/₂ feet of craft wire that she uses to make earrings.  If each pair of earring requires 3/4 foot of wire, how many pairs of earrings is Navya able to make.

Given:

To calculate the number of pairs of earrings Navya can make, divide the total amount of wire by the wire required to make 1 pair of earrings:

[tex]\begin{aligned}\implies \sf 10\frac{1}{2} \div \dfrac{3}{4} &= \sf \dfrac{21}{2} \div \dfrac{3}{4}\\ \\& = \sf \dfrac{21}{2} \times \dfrac{4}{3}\\ \\& = \sf \dfrac{21 \times 4}{2 \times 3}\\ \\& = \sf \dfrac{84}{6}\\ \\& = \sf 14 \end{aligned}[/tex]

Therefore, Navya can make 14 pairs of earrings.

Step-by-step explanation:

1 and 2 are negative

3 and 5 are none

4 and 6 are positive

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{-9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-9}-\stackrel{y1}{(-8)}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{(-2)}}} \implies \cfrac{-9 +8}{-3 +2}\implies \cfrac{-1}{-1}\implies 1[/tex]

Answer:

Step-by-step explanation:

(-9 + 8)/(-3 + 2)= -1/-1= 1

Answer:

84

Step-by-step explanation:

Plug in 9 for k.

5(9)(2) - 6

first: (9)(2) = 9 x 2 = 18

5(18) - 6

second: 5(18) = 5 x 18 = 90

last: 90 - 6 = ?

84

hope this helps

1 kilometer = 1000 meters

5000 meters / 1000 = 5 kilometers

5 kilometers x 2 times per day = 10 kilometers per day.

answer: D) 10 kilometers

Answer:

1/17 or 0.059

Step-by-step explanation:

7/17 + (-6/17) = 7/17 - 6/17 = 7-6/17 = 1/17

Answer:  " 5.1 " .
____________

Step-by-step explanation:
____________

To find 1 percent (i.e. " 1% " )  of:  510 ;

Note:  1 %  = (1 /100) = (1 ÷ 100) ;

Note the following about "dividing by "100" ;

  We take the number:  "510" in our case;
  and move the decimal point "2 (two) places backward" .
We move it "backward" (instead of "forward") because we are "dividing" ;

and we are moving the decimal point "2 (two)" spaces backward; since we are dividing by "100" ; which has "2 (two) zeros" .
  So:   " (510.) ÷ 100 " ;
               

      Take:  " 510." ; and move the decimal point two (2) spaces backward:
                         5.10.
                             ↩

    To get: " 5.10 " ;  which we can simplify as:
             →  " 5.1 " ; which is our answer.

Hope this is helpful to you!  Wishing you well!
____________

Answer:

TV = 8 , SV = 8[tex]\sqrt{2}[/tex]

Step-by-step explanation:

given ST = TV , then

TV = 8

using Pythagoras' identity in the right triangle

SV² = ST² + TV² = 8² + 8² = 64 + 64 = 128 ( take square root of both sides )

SV = [tex]\sqrt{128}[/tex] = [tex]\sqrt{64(2)}[/tex] = [tex]\sqrt{64}[/tex] × [tex]\sqrt{2}[/tex] = 8[tex]\sqrt{2}[/tex]

Answer:

Step-by-step explanation:

Mean: Add all the values and divide by the # of values

Median: The center of the values

Mode: The value that appears the most in the data set

Mean for data set 1: 86

Mean for data set 2: (85+89+71+85+86+91+92+96+87)/2= approximately 86.89

Median for data set 1: 72,75,78,80,88,90,95,98,98

We've sorted it from least to greatest, and the center is 88 because there is 4 values to the left of it, and 4 values to the right. It's at the very center.

Median for data set 2: 71,85,85,86,87,89,91,92,96

The center for this is 87 because it is again, at the absolute center/middle between the data.

Mode for data set 1: 98 because it appears 2 times, which is more often than other values

Mode for data set 2: 85 because it appears most often (2 times) in the data set

Hope this helps! :)

Answer:

180

Step-by-step explanation:

First, we have to find out how many boys are in the school:

900 * 0.30 = 270

Now, we know that there are 270 boys. Out of these boys we need to find out how many boys have glasses:

270 * 0.40 = 108

180 is our answer.

Answer:

88%

Step-by-step explanation:

Answer:

nonlinear because the second row isn't going up by the same number

Answer:

T = 12

Step-by-step explanation:

8t+1=97

We move all terms to the left:

8t+1-(97)=0

We add all the numbers together, and all the variables

8t-96=0

We move all terms containing t to the left, all other terms to the right

8t=96

t=96/8

t=12