When Nathan went to bed, the outside temperature was 28°F. When he woke up the next morning, the temperature had decreased to -13°F. By how many degrees did the temperature change during the overnight hours?

Answer:

40 days

Step-by-step explanation:

If in one day and night the worm goes 1m then it will take 40 days to go 40m

40 days will it take the worm to crawl out of the hole

Given:

A worm is at the bottom of a 40m hole. It can crawl upwards at a rate of 4m in a day, but at night, it slips back 3m.

Worm is at the bottom of a 40m wall.

Worm crawls up the distance = 4m per day

and slips down the distance = 3m per day

Everyday it crawls up by the distance = 4 - 1 = 1m

Time taken to crawl up to the height 40m = 4 days [ Since it crawls up 1 m per day

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Answer:

B and D

Step-by-step explanation:

=> All of the sides are unequal so it's a scalene triangle.

=> It have a 90 degrees angle, so it is a Right Angled Triangle.

Answer:

B. Scalene

D. Right

Step-by-step explanation:

The triangle is a scalene triangle, because all the three sides have different lengths.

The triangle is a right triangle, because it has an angle of 90 degrees.

Answer:

x = 1, y = -2

Step-by-step explanation:

- 2x + 10y = -22 _______(1)

-2x - 4y = 6 _______(2)

From (1),

10y + 22 = 2x

x = (10y + 22) / 2

x = 5y + 11 .______(3)

Substitute (3) into (2),

-2 ( 5y + 11) -4y = 6

-10y - 22 - 4y = 6

-14y = 6 + 22

-14y = 28

y = 28/ -14

y =-2

Substitute y = -2 into (3).

x = 5y + 11

x = 5(-2) + 11

x = -10 + 11

x = 1

Therefore, the solution is x = 1, y = -2.

Answer:

(2,6)

Step-by-step explanation:

x+2y = 14

y = x+4

Substitute x+4 into the first equation for y

x+2(x+4) = 14

Distribute

x+2x+8 = 14

3x+8 = 14

Subtract 8 from each side

3x+8-8 = 14-8

3x = 6

Divide by 3

3x/3 = 6/3

x = 2

Now solve for y

y = x+4

y =2+4

y =6

(2,6)

Answer:

D. (2, 6)

Step-by-step explanation:

Put y as x+4 in the first equation and solve for x.

x + 2(x + 4) = 14

x + 2x + 8 = 14

3x = 14 - 8

3x = 6

x = 2

Put x as 2 in the second equation and solve for y.

y = 2 + 4

y = 6

Answer:

Graph shown below.

Step-by-step explanation:

The vertex is at (0, -1).

It is a maximum.

Answer:

32 years old

Step-by-step explanation:

Please see attached picture for full solution.

Let Sunil's present age be 4x and his wife's present age be 3x.

Answer:

I don't understand you're description, but 48 x 39 is 1872.

Step-by-step explanation:

Answer:

61.6%

Step-by-step explanation:

We know that the tank contains 250 litres and that 96 litres are used. We are trying to find the percentage of the leftover quantity.

First, we need to subtract 250 from 96 litres to get the quantity that is left in the tank in litres. 250-96=154.

Then we need to find the percentage. To find a percentage we need to divide the total minus and the used amount by the total amount and then multiple the whole thing by 100. So in our case, that would be 250-96=154/250*100. Or 154/250*100.

Thus the answer is 61.6%.

Answer:

Step-by-step explanation:

Quantity left in the tank = 250 - 96 = 154 litres

Percentage = [tex]\frac{154}{250}*100\\[/tex]

                   = 0.616 * 100

                   = 61.6 %

Answer:

1 hour 26 Minutes

Step-by-step explanation:

Tanya needs 2 hours to do the job.

Pat needs 5 hours to do this same job.

Tanya's rate  [tex]=\frac{1}{2}[/tex]

Pat's rate[tex]=\frac{1}{5}[/tex]

Let the number of hours it will take both of them =x

Rate when two of them work together  [tex]=\frac{1}{x}[/tex]

Therefore:

[tex]\frac{1}{2}+\frac{1}{5}=\frac{1}{x}\\$Taking lowest common multiple$\\\frac{5+2}{10}=\frac{1}{x}\\\\\frac{7}{10}=\frac{1}{x}\\\\$Cross multiply$\\7x=10\\x=1.43$ hours[/tex]

[tex]0.43 X 60 =25.8 \approx 26$ minutes[/tex]

Therefore: 1.43 hour = 1 hour 26 Minutes

It will take both of them approximately 1 hour 26 minutes to  the job.

Answer:

No, he is wrong

Step-by-step explanation:

To find that probability, the first thing we need to know is the total number of coins present.

Mathematically, that would be 3 + 2 + 3 = 8

Since there are 8 coins, the probability of selecting a dime is number of dimes/total number of coins = 2/8 = 1/4

The probability we want to work with is that the two selections are dimes, let’s say with replacement.

That means; first selection is a dime and second selection is also a dime

Mathematically in probability, the term and means that we have to multiply our results.

So the probability that both are dimes would be 1/4 * 1/4 = 1/16

And this makes his answer wrong

Answer:

x^2+11x+30

Step-by-step explanation:

This is a parallelogram.

Area of a parallelogram can be found with:

A=bh

Plug our values in.

A=(x+6)(x+5)

FOIL-

First: x*x=x^2

Outside: x*5=5x

Inside: 6*x=6x

Last: 6*5=30

x^2+5x+6x+30

Combine like terms.

x^2+11x+30

Answer:

The second choice.

Step-by-step explanation:

Open the compass to the width of the line and draw two arcs.

These arcs should be on the same side of the original line.

You can then draw the parallel line with the straight edge just touching the top of each arc.

Parallel lines can be drawn using compass and straightedge using the concept of corresponding angle.

Two lines are called parallel when they never meet each other if they are increased on the either side of them.

When constructing parallel lines with a compass and straightedge we can follow the below mentioned steps.

1. At first we need to draw a straight line. Then take a random point on it.

2. After that, we need to take a random point above the line that is drawn. Then, we need to connect two points.

3. After that, draw two arcs using the compass. First arc is on the angle formed by two lines drawn. The next arc is on the line that connects two points.

4. Now using the compass, we can copy the angle formed on the first line on the point above the first line.

5. Now, complete the angle on the point above the first line. These two lines are parallel lines.

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Answer:

2(2/5x+2)=4x/5+4

Step-by-step explanation:

2(2/5x+2)=4x/5+4

4x/5 +4=4x/5 +4

Answer:

i)  -240[tex]a^{4}b^{3} c^{3}[/tex]

ii) -15x²y² + 3x³y²

iii)x³y³z³ - x²y³z³ + x³y²z³

iv) pq -7p+6q-42

v)9x²-33x +42

vii)  2x² - 2y² + 7x -13y - 15

Step-by-step explanation:

To find product here means to multiply the algebraic expressions together

i) (–5a²bc)×(6ab)×(8abc² )

multiply like terms together

= -240[tex]a^{4}b^{3} c^{3}[/tex]

ii) (–3x²y) ×(5y – xy)

(–3x²y)×(5y) –  (–3x²y) ×(xy)

multiply like terms together

multiplication of same sign gives +, while that of opposite sign gives -

= -15x²y² + 3x³y²

iii) (x²y²z²) ×(xy – yz + zx)

(x²y²z²)×(xy) – (yz)× (x²y²z²) + (zx)  ×(x²y²z²)

multiply like terms together

multiplication of same sign gives +, while that of opposite sign gives -

= x³y³z³ - x²y³z³ + x³y²z³

iv) (p+6)and (q–7)

p(q–7)  +6(q–7)

multiply like terms together

multiplication of same sign gives +, while that of opposite sign gives -

= pq -7p+6q-42

v) (2x+7)and(x² –5x+6)

multiply like terms together

multiplication of same sign gives +, while that of opposite sign gives -

= 2x² -10x+12x+7x²-35x+42

collect like terms

= 9x²-33x +42

vii) (x + y + 5) and (2x – 2y – 3)

multiply like terms together

multiplication of same sign gives +, while that of opposite sign gives -

= 2x²-2xy-3x+2xy-2y²-3y+10x-10y-15

collect like terms

= 2x² - 2y² + 7x -13y - 15

Answer: 2/8, 2/6, 2/3

Step-by-step explanation:

First, find the LCM of 3, 6, and 8, in this case 24.  Then, make the denominator of each fraction 24: 16/24, 6/24, 8/24.  Then, simply sort the fractions from least to greatest by their numerators: 6/24, 8/24, 16/24

Hope it helps <3

Answer:

$105

Step-by-step explanation:

I used a proportion to solve this:

[tex]\frac{63}{3} = \frac{x}5}[/tex]

Cross multiply:

3x = 315

Divide both sides by 3

x = 105

Answer:$105

Step-by-step explanation:

Salary for 3 hrs=$63

Salary for 5hrs= salary for one hour×5 hrs,

Salary for one hour= 63/3=$21

Salary for 5 hours= 21×5: $105

Answer:

Solution,

Let the points be A and B

A(2,8)------>(X1,y1)

B(-6,-8)------>(x2,y2)

Now,

[tex]slope = \frac{y2 - y1}{x2 - x1} \\ \: \: \: \: \: \: = \frac{ - 8 - 8}{ - 6 - 2} \\ \: \: \: = \frac{ - 16}{ - 8} \\ \: \: \: \: = 2[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

2

Step-by-step explanation:

The slope is calculated like this:

Slope = vertical difference divided by horizontal difference.

So, from the line at the top marked ( 2,8 ) to the point that is vertically on line with both marked points = 8

And the horizontal difference is the number of gaps from the point marked (-6,-8) till the point we said was in line with both points. This is 4.

SO, 8/4 = 2

Hope this helps.

Good Luck

Answer:

140 degrees

Step-by-step explanation:

im basing it off of the fact that 1 is equal to 35 and so 4 must be 4 times 35 degrees

Answer:

Step-by-step explanation:

The mode is 24 so we know that at least 2 of the 5 numbers are 24.

The mean is 20 so we know that the 5 numbers add up to 100.

The median is 21 so the third number is 21.

100-(24+24+21)= 31

Now, I am pretty certain that the last 2 numbers can be anything as long as they add up to 31 AND they are not also 21 because 24 then would no longer be the mode.

E.g. 24, 24, 21, 11 & 20

Answer:

x = -3

Step-by-step explanation:

Step 1: Simplify signs

3x + 7 = -2

Step 2: Subtract 7 on both sides

3x = -9

Step 3: Divide both sides by 3

x = -3

The answer is C.) The model is not a good fit.

Answer:

B. 1 out of 5,005

Step-by-step explanation:

Given

Number of Friends = 15

Required

Probability of selecting 6 friends

The first step is to calculate the number of ways 6 friends can be selected

The keyword in the above statement is selection;

This implies combination;

The number of ways is calculated as follows;

[tex]\left[\begin{array}{c}n&r&\end{array}\right] = \frac{n!}{(n-r)!r!}[/tex]

Where n = 15 and r = 6

[tex]\left[\begin{array}{c}n&r&\end{array}\right] = \frac{n!}{(n-r)!r!}[/tex]

becomes

[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{15!}{(15-6)!6!}[/tex]

[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{15!}{9!6!}[/tex]

[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{15 * 14 * 13 * 12 * 11 *10 * 9!}{9! *6 * 5 * 4 * 3 * 2 * 1}[/tex]

[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{15 * 14 * 13 * 12 * 11 *10}{6 * 5 * 4 * 3 * 2 * 1}[/tex]

[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{3603600}{720}[/tex]

[tex]\left[\begin{array}{c}15&6&\end{array}\right] =5005[/tex]

Hence, there are 5005 ways of selecting 6 from 15 friends

Since, there's only one way of selecting the 6 named friends

Then, the probability is 1 out of 5,005

At least 105 children must attend the event

Answer:

11.67

Step-by-step explanation:

Data given in the question

∠ADC = 42°

∠BAC = 68°

Let us assume that AC be Y

Now

In ΔACD

tan 42° = AC ÷ CD = Y ÷ x ...............................(i)

In ΔACB  

tan 68° = BC ÷ AC = 26 ÷ Y ..........................(ii)

Now take the value of Y from the equation (ii)

Y = 26 ÷ Tan 68° ...................... (iii)

Now place the value of Y in equation (i)

So,

Tan 42° = 26 ÷ tan 68° × X

X = 26 ÷  tan 68° × Tan 42° ......................(iv)

Now placing the values of tan 42° and tan 68° in equation (iv)

So,

X = 26 ÷ 0.900 × 2.475

= 11.67

The tan 42° = 0.900

And, the tan 68° = 2.475

Answer:

Since the speed can't be negative it was 60 km/h for the first stage and 80 km/h on the second stage, averaging 70 km/h for the whole course.

Step-by-step explanation:

The speed of the truck for the first stage of the route is "x" km/h, while on the second one it raises to "x + 20" km/h. The time it takes to complete each stage is shown below:

[tex]t_{stage 1} = \frac{150}{x}\\t_{stage 2} = \frac{200}{x + 20}[/tex]

The sum of these times must be equal to the total time of the trip, therefore:

[tex]t_{stage1} + t_{stage2} = 5[/tex]

[tex]\frac{150}{x} + \frac{200}{x + 20} = 5\\\frac{150*(x + 20) + 200*x}{x(x + 20)} = 5\\150*x + 3000 + 200*x = 5*x*(x + 20)\\5*x^2 + 100*x - 350*x - 3000 = 0\\5*x^2 - 250*x - 3000 = 0\\x^2 - 50*x - 600 = 0\\x_{1,2} = \frac{-(-50) \pm \sqrt{(-50)^2 - 4*1*(-600)}}{2*1}\\x_{1,2} = \frac{50\pm \sqrt{2500 + 2400}}{2}\\x_{1,2} = \frac{50\pm \sqrt{4900}}{2}\\x_{1,2} = \frac{50 \pm 70}{2}\\x_{1} = 60\\x_{2} = -10[/tex]

Since the speed can't be negative it was 60 km/h for the first stage and 80 km/h on the second stage, averaging 70 km/h for the whole course.

Answer:

D

Step-by-step explanation:

If we plug in the points to A, not all 3 of them work so A is not the answer. If we repeat this process with the other functions we see that the answer is D.

Answer:

The temperature after 10 hours is -9 ºF.

Step-by-step explanation:

This statement can be translated mathematically as follows. The temperature after 10 hours from sunrise is:

[tex]T = -10\,^{\circ}F + \left(1\,\frac{^{\circ}F}{h} \right)\cdot (7\,h)+ \left(-2\,\frac{^{\circ}F}{h} \right)\cdot (3\,h)[/tex]

[tex]T = -9\,^{\circ}F[/tex]

The temperature after 10 hours is -9 ºF.

Answer:

The answer is in the picture

Step-by-step explanation:

Answer: The length AC equals 10.25 cm (approximately)

Step-by-step explanation: Please refer to the diagram attached for further details.

The triangle has been constructed according to the dimensions provided with the top B going down to the "little square inside the triangle" which is C. This clearly identifies it as a right angled triangle. The point B meets with point C at the right angle and A is the sharp tip of the triangle, which makes point A the third angle. Hence we now have a right angled triangle with side AB measuring 11 cm, side BC measuring 4 cm and side AC is unknown.

We can now apply the Pythagoras' theorem which is stated as follows;

AC² = BC² + AB²

Where AC is the hypotenuse (longest side) and BC and AB are the other two sides. We can now substitute for the appropriate sides in this question as all the sides have been labelled differently. Hence,

BA² = BC² + CA²

11² = 4² + CA²

121 = 16 + CA²

Subtract 16 from both sides of the equation

105 = CA²

Add the square root sign to both sides of the equation

√105 = √CA²

10.2469 = CA

CA ≈ 10.25 cm

The third side AC (or CA) measures approximately 10.25 cm

Answer:   (x - 2)² + (y - 3)² = 4

Step-by-step explanation:

The equation of a circle is: (x - h)² + (y - k)² = r²    where

Given:  (h, k) = (2, 3)  and   (x, y) = (2, 1)

Input those values to find r²:

(x - h)² + (y - k)² = r²

(2 - 2)² + (1 - 3)² = r²

  0       +     4     = r²

                   4    = r²

Now input (h, k) = (2, 3) and r² = 4 into the equation of a circle:

(x - h)² + (y - k)² = r²

(x - 2)² + (y - 3)² = 4