On a cold February morning, the temperature of the radiator fluid in Stanley’s car is . When the engine is running, the temperature of the fluid goes up per minute. Approximately how long will it take before the radiator fluid temperature reaches ?

Answer:

x = 1/2

Step-by-step explanation:

Let's represent this in a mathematical way,

(x+1)^2 - x^2 = 2

Ok now we expand,

x^2 + 2x + 1 -x^2 = 2

rearrange,

x^2 - x^2 + 2x + 1 = 2

subtract,

2x + 1 = 2

subtract 1 from both sides,

2x + 1 - 1 = 2 - 1

2x = 1

Now divide 2 from both sides and get your answer,

x = 1/2

Answer:

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

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

[tex]2x + 1 = 2[/tex]

[tex]x = 1 \div 2[/tex]

Answer:

Perimeter = 8x - 12

Step-by-step explanation:

The perimeter of a square is:

p = 4(side length)

on this case:

p = 4(2x-3)

p = 4*2x + 4*-3

p = 8x - 12

Answer:

1. 38.3 x 10^5

2. 6.67 x 10^9

3. 4.48 x 10^4

Step-by-step explanation:

4.2 X 10 ^6 - 1.2 X 10^5 - 2.5 x 10^5

For the above question, we need to make the exponents equal

=> 42 x 10^5  -  1.2 x 10^5  -  2.5 x  10^5

SInce, all the exponents are equal, we can now add and subtract the normally.

=> (42 - 1.2 -2.5) x 10^5

=> (42 - 3.7) x 10^5

=> 38.3 x  10^5

So, the answer to the 1st question is 38.3 x 10^5

Next question:

=> 3.3 x 10^9 + 2.6 x 10^9 +7.7 x 10^8

=>  we need to make the exponents equal

=> 3.3 x 10^9 + 2.6 x 10^9 + .77 x 10^9

=> All the exponents are equal, we can now add and subtract the normally.

=> (3.3 + 2.6 + .77) x 10^9

=> 6.67 x 10^9

=> So the answer to the 2nd question is 6.67 x 10^9

Next question,

=> 8 X 10^4 - 3.4 x 10^4  - 1.2 x 10^3

=> we need to make the exponents equal

=> 8 x 10^4 - 3.4 x 10^4 - .12 x 10^4

=> All the exponents are equal, we can now add and subtract the normally.

=> (8 - 3.4 - .12) x 10^4

=> 4.48 x 10^4

=> So the answer to the 3rd question is 4.48 x 10^4

The solutions to the expressions are:

[tex]4.2 \times 10^6 - 1.2 \times 10^5 - 2.5 \times 10^5[/tex]=[tex]38.3\times 10^5[/tex]

[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 7.7 \times 10^8[/tex] = [tex]6.67\times 10^9[/tex]

[tex]8.0 \times 10^4 -3.4 \times 10^4 - 1.2 \times 10^3[/tex] = [tex]4.48 \times 10^4[/tex]

[tex]4.2 \times 10^6 - 1.2 \times 10^5 - 2.5 \times 10^5[/tex]

Combine like terms:

[tex]4.2 \times 10^6 - (1.2+2.5) \times 10^5[/tex]

[tex]4.2 \times 10^6 - 3.7 \times 10^5[/tex]

[tex]42 \times 10^5 - 3.7 \times 10^5[/tex]

[tex](42-3.7)\times 10^5[/tex]

[tex]38.3\times 10^5[/tex]

[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 7.7 \times 10^8[/tex]

Convert all terms with same power:

[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 0.77 \times 10^9[/tex]

[tex](3.3+2.6+0.77) \times 10^9[/tex]

[tex]6.67\times 10^9[/tex]

[tex]8.0 \times 10^4 -3.4 \times 10^4 - 1.2 \times 10^3[/tex]

[tex]8.0 \times 10^4 - 3.4 \times 10^4 - 0.12 \times 10^4[/tex]

[tex](8.0-3.4-0.12) \times 10^4[/tex]

[tex]4.48 \times 10^4[/tex]

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Answer:

135 cubes

Step-by-step explanation:

First, find the volume of the box with the equation V = Bh, where B is the area of the base and h is the height.

V = (2.25)(0.75)(1.25)

V = 2.109375

Next, find the volume of one cube with the side length 1/4 with V = Bh:

V = (0.25)(0.25)(0.25)

V = 0.015625

Then, divide the volume of the box by the volume of one cube:

2.109375 / 0.015625

= 135

Answer:

PEMDAS

Step-by-step explanation:

P - Parentheses (Brackets also!)

E - Exponents

M and D - Multiplication and division. Many people think multiplication has to be done first as said in "PEMDAS" but it doesn't. Do multiplication and division according to which ever one is farthest to the left (left to right).

A and S - Addition and subtraction. Same thing applies here, neither addition or subtraction has to be done first, just do them according to which one is farthest to the left when reading the expression from left to right.

Answer:

13x3= 39

Step-by-step explanation:

10x3=30

3x3=9

30+9=39

Hope it helps!

Answer:

P = 27.2c-7.2d

Step-by-step explanation:

It is given that,

The width of a rectangle is (8.3c-8.4d)

The length of a rectangle is (5.3c+4.8d)

The perimeter of a rectangle is equal to the sum of its all sides i.e.

P = 2(l+b)

P = 2(8.3c-8.4d+5.3c+4.8d)

P = 2[(8.3c+5.3c)+(4.8d-8.4d)]

P = 2(13.6c-3.6d)

⇒P = 27.2c-7.2d

Hence, the expression that represents the perimeter of the rectangle is 27.2c-7.2d.

Answer:

it's true

Step-by-step explanation:

Answer:

x+5=19

Step-by-step explanation:

i think that right let me know...:/

Answer:

x= 14

Step-by-step explanation:

a number x increased by 5, so it will be x + 5 and is in math means equals to so it becomes

x+5=19

19-5=x

14=x

Answer:

1,4,9,16

Step-by-step explanation:

those are the squares

1 = 1²

4 = 2²

9 = 3²

16 = 4²

Step-by-step explanation:

[tex] {1}^{2} = 1 \times 1 = 1 \\ {2}^{2} = 2 \times 2 = 4 \\ {3}^{2} = 3 \times 3 = 9 \\ {4}^{2} = 4 \times 4 = 16 \\[/tex]

[tex] {5}^{2} = 5 \times 5 = 25 \\ [/tex]

[tex] {10}^{2} = 10 \times 10 = 100[/tex]

[tex] {6}^{2} = 6 \times 6 = 36 \\ {7}^{2} = 7 \times 7 = 49 \\ {8}^{2} = 8 \times 8 = 64 \\ {9}^{2} = 9 \times 9 = 81 \\ [/tex]

[tex] {11}^{2} = 11 \times 11 = 121 \\ {12}^{2} = 12 \times 12 = 144 \\ {13}^{2} = 13 \times 13 = 169 \\ {14}^{2} = 14 \times 14 = 196 \\ [/tex]

[tex] {15}^{2} = 15 \times 15 = 225 \\ {16}^{2} = 16 \times 16 = 256 \\ {17}^{2} = 17\times 17 = 289 \\ {18}^{2} = 18 \times 18 = 324[/tex]

[tex] {19}^{2} = 19 \times 19 = 361 \\ {20}^{2} = 20 \times 20 = 400[/tex]

Answer:

The total volume of the solid is 1.67 cubic units.

Step-by-step explanation:

Each pyramid with a height of 2 units and a rectangular base with dimensions of 5 units × 0.25 units.

1/3 x (area of base) x height

= 1/3 x (5 x 0.25) x 2= 0.833

Therefore, the volume of each pyramid will be

= cubic units.

So, the total volume of the solid is (2 × 0.833) = 1.67 cubic units. (Answer)

Hope it helped ya!

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Tysmm

The total volume of the solid is 1.67 unit³.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given:

Each pyramid has a height of 2 units.

and the rectangular base with dimensions of 5 units × 0.25 units.

So, the Volume of each Pyramid is

= 1/3 x (area of base) x height

= 1/3 x (5 x 0.25) x 2

= 0.833

and, the total volume of the solid

= (2 × 0.833)

= 1.67 cubic units.

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Answer:

17

Step-by-step explanation:

67 minus 33 leaves 34 red bikes but divided that by half gives you 17

There are approximately 17 red bikes in the bike rack outside the school.

Algebra is the estimation of mathematical representations, while logic is the manipulation of those symbols.

We can solve this problem by setting up an equation to represent the relationship between the number of bikes in the bike rack, the number of silver bikes, and the number of red bikes.

Let's define a variable, r, to represent the number of red bikes. We know that 33 bikes are silver, so the number of bikes that are not silver is 67 - 33 = 34 bikes.

Half of the remaining bikes are red, so we can say that there are r = 34/2 = 17 red bikes.

Therefore, there are approximately 17 red bikes in the bike rack outside the school.

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Answer:

20°

Step-by-step explanation:

The measure of the inscribed angle is equal to the half of the arc it sees

Since AC is the diameter the measure of arc ABC is 180°

and since A sees arc BC and C sees the arc AB

A< + C< = 90° so angle C = 20°

Answer:

19.9 cm²

Step-by-step explanation:

The following data were obtained from the question:

Angle at the centre (θ) = 150°

Diameter (d) = 7.8 cm

Area of sector =.?

Next, we shall determine the radius.

This can be obtained as illustrated below:

Radius (r) = Diameter (d) /2

r = d/2

Diameter (d) = 7.8 cm

Radius (r) =.?

r = d/2

r = 7.8/2

r = 3.9 cm

Finally, we shall determine the area of the sector as follow:

Angle at the centre (θ) = 150°

Radius (r) = 3.9 cm

Pi (π) = 3.14

Area of sector (A) =.?

A = θ/360 × πr²

A = 150/360 × 3.14 × 3.9²

A = 15/36 × 3.14 × 15.21

A = 19.9 cm²

Therefore, the area of the sector is 19.9 cm²

Answer:

3250

Step-by-step explanation:

so for the first and 2nd show, the attendance is 2580 and 2920.

The average of both these numbers is 2750

the if the third show had 3000 people, the average attendance would only be 2875.

We need the average number to be 3000.

2750 is 250 less than 3000, so the other number must be 250 more.

3250 is how many people should go to the last show.

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

Explanation:

We have 2580 people attend the first show and 2920 attend the second. So far, that's 2580+2920 = 5500 people. Add on another x people to get 5500+x, which represents the sum of all three days attendance figures. Divide this sum by 3 to get the average attendance

average attendance = (sum of individual attendance values)/(number of days)

average attendance = (5500+x)/3

So that's why (5500+x)/3 goes in the first box. The parenthesis are important to ensure that you divide all of "5500+x" over 3. If you just wrote 5500+x/3, then the computer would think you just want to divide x only over 3.

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

We set (5500+x)/3 equal to 3000 as we want the average of the three days to be 3000

(5500+x)/3 = 3000

5500+x = 3*3000

5500+x = 9000

x = 9000-5500

x = 3500

We need 3500 people to show up on day 3 so that the average of all three days is 3000.

3500 goes in the second box.

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

Check:

The figures for the three days are 2580, 2920, and 3500

They add to 2580+2920+3500 = 9000

Which divides to 9000/3 = 3000, which is the average we're after. So the answer is confirmed.

Answer:

x = -1.29 and -2.71

Step-by-step explanation:

Use the quadratic formula, which is [tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] and [tex]x=\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

[tex]\frac{-8+\sqrt{8^2-4(2)(7)} }{2(2)}[/tex] and [tex]\frac{-8-\sqrt{8^2-4(2)(7)} }{2(2)}[/tex]

[tex]\frac{-8+\sqrt{8} }{4}[/tex] and [tex]\frac{-8-\sqrt{8} }{4}[/tex]

Further reduced down to:

[tex]\frac{-8+2\sqrt{2} }{4}[/tex] and [tex]\frac{-8-2\sqrt{2} }{4}[/tex]

In decimal form, to the hundredths place, both of these are:

-1.29 and -2.71

Answer:

The third option: x= [tex]\frac{8}{3} \pi[/tex]

Step-by-step explanation:

Arc length formula=[tex]\frac{Central Angle}{360} * 2\pi r[/tex]

Arc length = [tex]\frac{120}{360} *2\pi (4)[/tex]

=[tex]\frac{8}{3}\pi[/tex]

Answer:

Step-by-step explanation:

Number of class intervals = 7

Class width = 5

Class intervals (heights)        Frequency (Number of boys)

130 - 135                                                     3                        

136 - 140                                                     5

141 - 145                                                      3

146 - 150                                                     5

151 - 155                                                      2

156 - 160                                                     1

161 - 165                                                      1

Therefore, frequency table given above will represent the distribution of the heights and number of students.

Answer: find the answer in the explanation.

Step-by-step explanation:

To increase the time the fireworks stays in the air by 2 seconds to build up the suspense, 2 should be added to the time t.

T + 2 = t

T = t - 2

Substitute T for t in the function g(t)

The company will make this happen without changing the length of the fuse by substituting T for t which will lead to

g(t) = -16(t - 2)^2 + 224(t - 2) + 120

How will this affect the maximum height of the firework?

Initially the function is:

g(t) = -16t2 + 224t + 120

Where the time at maximum height is found by using the formula

t = -b/2a

b = 224, a = -16

Substitutes both into the formula

t = -224/2(-16)

t = -224/-32

t = 7

Substitute 7 for t in the first equation

g(t) = -16(7)^2 + 224(7) + 120

g(t) = -16(49) + 224(7) + 120

g(t) = -784 + 1568 + 120

g(t) = 904 metres

But when the time is delayed by 2 seconds in the air, the maximum height will be

g(t) = -16( 7 - 2 )^2 + 224(7 - 2) + 120

g(t) = -16(5)^5 + 224(5) + 120

g(t) = -16(25) + 224(5) + 120

g(t) = -400 + 1120 + 120

g(t) = 840

The effect will surely reduce the maximum height of the fireworks.

Answer:

5/12

Step-by-step explanation:

4√y√y / 3√y

The above equation can be simplified as follow:

4√y√y / 3√y

4√y × √y ÷ 3√y

Recall:

√a = a^1/2

m√a = a^1/m

Therefore,

4√y√y ÷ 3√y

y^1/4 × y^1/2 ÷ y^1/3

Recall:

a^m × a^n = a^(m+n)

Therefore,

y^1/4 × y^1/2 ÷ y^1/3

y^(1/4 + 1/2) ÷ y^1/3

y^3/4 ÷ y^1/3

Recall:

a^m ÷ a^n = a^(m–n)

Therefore,

y^3/4 ÷ y^1/3

y^(3/4 – 1/3)

y^5/12

Comparing the above with y^m, we have

y^5/12 = y^m

m = 5/12

Therefore, the value of m is 5/12

Answer:

1 miles/hour = 1.467·feet/second

Step-by-step explanation:

The given measurement unit are;

88 feet/second = 60 miles/hour

The number of feet per second that is equal to one mile per hour is found as follows;

88 feet/second = 60 miles/hour

To have a unit measure of one mile per hour , we divide both sides of the equation by 60 to get

(88 feet/second)/60 = (60 miles/hour)/60

Which gives;

(88/60 feet/second) = (60/60 miles/hour) = 1 miles/hour

22/15 × feet/second =  1 miles/hour

1.46667·feet/second =  1 miles/hour

Rounding to the nearest thousandth gives;

1.467·feet/second =  1 miles/hour

The number of feet per second that is in 1 mile per hour is 1.467·feet/second.

Answer:

A

Step-by-step explanation:

it is A for every output y , there is only one input x

Answer:

A

Step-by-step explanation:

Because all the x-intercepts are different. Whereas all the other ones have repeats of numbers in the x-intercepts.

[tex]1^4+1^2+1-k=0\\3-k=0\\k=3[/tex]

Answer:

k=3

Step-by-step explanation:

Hello, if p-1 is a factor of

[tex]f(p)=p^4+p^2+p-k[/tex]

it means that f(1)=0, so

1+1+1-k=0

3-k=0

k=3

thank you

Answer:

r = 1

Step-by-step explanation:

6r - 1 + 6r = 11

Adding 6r and 6r (because they're like terms) gives us:

12r - 1 = 11

Adding 1 to both sides of the equation gives us:

12r - 1 + 1 = 11 + 1

12r = 12

Dividing both sides of the equation by 12 gives us:

12r/12 = 12/12

r = 1

Answer:

2.7 hours

Step-by-step explanation:

We can use the formula

1/a + 1/b = 1/c

where a and b are the times working alone and c is the time working together

1/8 + 1/b = 1/2

Multiply each side by 8b to get rid of the fractions

8b( 1/8 + 1/b = 1/2)

b + 8 = 4b

Subtract b from each side

b+8-b = 4b-b

8 = 3b

Divide each side by 3

8/3 = 3b/3

2.666666repeating = b

Round to 1 decimal place

2.7 = b

Answer:

2.7 hr

Step-by-step explanation:

2/8 +2/x = 1

2x+16 =8

16/8

x=8/3 =2.7

Answer:

[tex]\boxed{2\pm \frac{\sqrt{2}}{2}}[/tex]

Step-by-step explanation:

[tex]2x^2-8x=-7[/tex]

[tex]\sf Add \ 7 \ on \ both \ sides}.[/tex]

[tex]2x^2-8x+7=-7+7[/tex]

[tex]2x^2-8x+7=0[/tex]

[tex]ax^2 +bx+c=0[/tex]

[tex]\sf Apply \ quadratic \ formula.[/tex]

[tex]a=2 \ \ \ b=-8 \ \ \ c = 7[/tex]

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-(-8)\pm\sqrt{(-8)^2-4(2)(7)}}{2(2)}[/tex]

[tex]x=\frac{8\pm\sqrt{64-56}}{4}[/tex]

[tex]x=\frac{8\pm\sqrt{8}}{4}[/tex]

[tex]x=\frac{8\pm2\sqrt{2}}{4}[/tex]

[tex]x=2\pm \frac{\sqrt{2}}{2}[/tex]

Answer:

1. 2cm 3cm and 4cm

yes, because 2+3>4

2. 2cm 3 cm 6 cm

no, 2+3<6

3. 90 degrees 45 degrees 45 degrees

yes, 90+45+45 = 180

4. 90 degrees 60 degrees 60 degrees?

no, 90+60+60=210!=180

Answer:

A'(5, 2), B'(5, -1), C'(6, -1), D'(6, 2)

Step-by-step explanation:

A transformation is the movement of a point from its initial position to a final position. If an object is transformed all its points are also transformed. Types of transformation are reflection, rotation, translation and dilation.

If a point O(x, y) is translated left by h unit, the new coordinate is O'(x-h, y) while if O(x, y) is translated right by h unit the new coordinate is O'(x+h, y)

If a point O(x, y) is translated up by h unit, the new coordinate is O'(x, y+h) while if O(x, y) is translated down by h unit the new coordinate is O'(x, y-h)

The location of the shape as shown in the diagram is:

A(3, 6), B(3, 3), C(4, 3), D(4, 6)

If the points are translated two yards East and four yards south, it means it is translated 2 unit right and 4 unit down i.e. (x+2, y-4). The new coordinates are:

A'(5, 2), B'(5, -1), C'(6, -1), D'(6, 2)

Answer:

ombining the expressions from parts E and F, for any given initial point (x, y), the coordinates of the new point after a translation of two yards east and four yards south are (x + 2, y + (-4)).

Step-by-step explanation:

this is more simple

Answer:

Now solve these two equations.ull get andwer

The original number will be "63".

Let,

The equation will be:

→ [tex]x=y+3[/tex]...(equation 1)

Original number will be:

→ [tex]10x+y[/tex]

then,

→ [tex]2 (10x+y)-\frac{(10y+x)}{2} = 108[/tex]

→ [tex]\frac{4(10x+y)}{1} -(10y+x) = 216[/tex]

→ [tex]40x+4y-10y-x = 216[/tex]

→ [tex]39x-6y=216[/tex]...(equation 2)

By using (equation 1) and (equation 2), we get

→ [tex]39(y+3)-6y=216[/tex]

→ [tex]39y+117-6y=216[/tex]

→                   [tex]33y=99[/tex]

→                       [tex]y = \frac{99}{33}[/tex]

→                          [tex]= 3[/tex]

Now,

[tex]x = y+3[/tex]

  [tex]=3+3[/tex]

  [tex]=6[/tex]

hence,

The original number will be:

= [tex]10x+y[/tex]

= [tex]10\times 6+3[/tex]

= [tex]60+3[/tex]

= [tex]63[/tex]

Thus the above approach is right.

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