(a)A tram moved downward 21meters in 7 seconds at a constant rate. What was the change in the tram's elevation each second?

(b)In a lab, a substance was heated by 4 Celisse each hour for 40hours. What was the total change in temperature?

Answer:

15, 16 and 17

Step-by-step explanation:

Consecutive numbers mean numbers that are separated by 1 from each other. For example 5, 6 and 7 are three consecutive numbers and 5 is the smallest

Let the smallest number be x
Then the next consecutive number is x + 1  
The next one after that is x + 2

Sum = x + x + 1 + x + 2 = x + x + x + 1 + 2 = 3x + 3

We are told that this sum is 33 more than the smallest number x

So 3x+3 = x + 33 Subtract x from both sides
3x - x + 3 = x + 33 -x
==>  2x + 3 = 33

Subtract 3 from both sides
==> 2x + 3 - 3 = 33 -3
==> 2x = 30
Divide both sides by 2

==> 2x/2 = 30/2
==> x = 15

So the smallest number is 15 and the three numbers are 15, 16 and 17

Verify by adding 15+16 +17 = 48
15 + 33 = 48 so consistent

A: The three consecutive numbers are 15, 16, 17.

Explanation:

Let x, y, z be the numbers.

x + y + z = x + 33

y = x + 1

z = x + 2

We will solve this system of equations using the substitution method.

x + x + 1 + x + 2 = x + 33

x + x + x - x = 33 - 1 - 2

2x = 30

x = 15

y = 15 + 1 = 16

z = 15 + 2 = 17

Solving for x + y + z = x + 33:

15 + 16 + 17 = 15 + 33

48 = 48

A: 15, 16, 17.

The square root of 58 is around 7.6

The entire number is, 7.61577310586...

false is the answer of that Q

Answer:

Mary drew 66 buildings and Tess drew 33 buildings.

Step-by-step explanation:

Let's label the number of buildings drawn by Mary as x and the number of buildings drawn by Tess as y.

We know there are 99 buildings drawn. This means

99=x+y

We also know that Mary drew twice as many buildings as Tess. We can represent this as

x=2y

Now, let's substitute x for 2y, since that would put us in common terms

99=2y+y

Add common variables together and you get

99=3y

Solve for y by dividing 99 by 3

y=33

We now know that Tess drew 33 buildings, as well as y=33. Substitute y in the equation for how many buildings Mary drew:

x=2(33)

Now we know that Mary drew 66 buildings.

To check our work,

99=x+y

99=66+33

99=99

Answer:

The only answer is 46.3. I'm not sure whether or not you mixed up one of the decimals, but this is the only answer out of the others.

I hope this helps.

The number 6.945 × 10¹⁰ is 463 times more than 1.5 × 10⁸. As a result, option A is right and the other choices are false.

A fraction is a number that, when stated mathematically, designates a component of a whole. A fraction is a portion or division of any whole, which could be any number, a specific sum, or an actual object.

The horizontal bar known as the fractional bar divides the numerator and denominator of every fraction into these two halves.

There are several types of fractions, some of them are :

According to the question,

(6.945 × 10¹⁰) / (1.5 × 10⁸)

= 463

Hence, it is concluded that 6.945 × 10¹⁰ is 463 times more than 1.5 × 10⁸.

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Answer:

126

Step-by-step explanation:

A number is divisible by 3 if its sum of digits is divisible by 3 (you can do it over and over again until it's one digit!).

A number is divisible by 2 if its last digit is 0, 2, 4, 6 or 8.

A number is divisible by 6 if it is divisible by 2 and by 3.

A number is divisible by 9 if its sum of digits is divisible by 9 (you can do it over and over again until it's one digit!).

So we need a number with last digit 0, 2, 4, 6, or 8 (because it's divisible by 6 hence by 2) and with a sum of digits divisible by 9 (because if it's divisible by 9 it's also divisible by 3).

130 is not divisible by 9, so the first digits must be 12X.

to get a number divisible by 9, we need to add a digit D so that 1+2+D is divisible by 9.

9 - 1 - 2 = 6

126 is divisible by 9 because it's sum of digits is 9. It's also divisible by 6, because it is divisible by 3 and its last digit is 6.

Answer:

B. Not a function; does not pass the vertical line test
C. Is a function; does pass vertical line test

Domain of B: -3 to 1
Range of B: -1 to 4.5

Domain of C: -3 to 6
Range of C: -4 to 2

Step-by-step explanation:

What is vertical line test?
Vertical line test is when you draw vertical lines (up and down) on the line. If two points are on one line, that means it is not a function. B has a lot of lines that have the same X so that is why it is not a function.

What is domain and range? Domain is the x values and Range is the Y values. So you will want to put the numbers between where the y starts and stop.

The speed of the faster cyclist is 30 mph.

Two cyclists, distance = 90 miles.

let the speed of one cyclist is = x and

let the speed of the other cyclist = 2x

time after which both the cyclists will meet = 3 hours.

Since they are travelling towards each other the effective speed = 2x ₊ x

= 3x

we know that time = distance/speed

3 = 90/3x

3x = 30

x = 10 mph speed of one cyclist.

speed of the other cyclist will be 3x = 3 × 10 = 30 mph

The speed of the fastest cyclist is 30 mph.

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Answer:

He can buy 2 full sets

Step-by-step explanation:

$25 divided by $9 per set is 2.8 sets.  Assuming sets are only sold as whole packages that would be 2 full sets.

Answer:

A

Step-by-step explanation:

12.5% is 4 of 32. Devide 4 by 32 you get the 0125

Answer:

A 12.5%

Step-by-step explanation:

let p be the percentage that 4 represents.

[tex]32\longrightarrow 100 \%\\4 \longrightarrow \text{p} \%[/tex]

Then

[tex]p=\frac{4}{32} \times 100[/tex]

  [tex]= 0.125 \times 100[/tex]

  [tex]=12.5[/tex]

Answer:

x = -2

Step-by-step explanation:

-12 = 1/2(6x - 12)  Multiply everything inside the parentheses by 1/2

-12 =1/2(6x) - (1/2)(12)

-12 = 3x - 6  Add 6 to both sides of the equation

-6 = 3x  Divide both sides by 3

-2 = x

Check:

Plug -2 in for x and see if statement is true

-12 = 1/2(6x - 12)

-12 = 1/2[(6)(-2) - 12]  Simplify inside the brackets

-12 = 1/2(-12 -12)

-12 = 1/2 (-24)

-12 = -12

The Projection of "a" along "b" is [tex]\sqrt{20}[/tex] and the Projection of "b" on "a" is [tex]\frac{20}{\sqrt{29} }[/tex]

Given that a = 2i-3j +4k and b = 2i+4k

To find Projection,

Projection of "x" on "Y"=(X vector).(Y unit vecot)

Projection of "a" along "b" =  (a vector).(b unit vector)

Projection of "a" along "b" = ( 2i-3j +4k).([tex]\frac{2i+4k}{\sqrt{29} }[/tex])

Projection of "a" along "b" =[tex]\frac{4+16}{\sqrt{20} }[/tex]

Projection of "a" along "b" =[tex]\frac{20}{\sqrt{20} }[/tex]

Projection of "a" along "b" =[tex]\sqrt{20}[/tex]

Projection of "b" along "a" =  (b vector).(a unit vector)

Projection of "b" along "a" = ( 2i+4k).([tex]\frac{2i-3j +4k}{\sqrt{29} }[/tex])

Projection of "b" along "a" = [tex]\frac{20}{\sqrt{29} }[/tex]

Therefore,The Projection of "a" along "b" is [tex]\sqrt{20}[/tex] and the Projection of "b" on "a" is [tex]\frac{20}{\sqrt{29} }[/tex]

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By using a linear equation, we can see that after the 19 day the population will be less than 1000 mold spores.

We know that the population decays at a rate of 30 spores per day, and we have an initial population of 1560 mold spores.

Then, the population of spores after x days is given by the linear equation:

P(x) = 1560 - 30*x

The population will be exactly 1000 spores when:

P(x) = 1000 =  1560 - 30*x

We need to solve that for x.

30x = 1560 - 1000 = 560

x = 560/30 = 18.67

So after 18.67 days the population is 1000, this means that after the 19 day the population will be less than 1000 mold spores.

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The mixed number as an improper fraction is 37/8

The diameter is give as:

Diameter = 4 5/8

Next we convert the above number to an improper fraction

The numerator is calculated as

Numerator = 8 * 4 + 5

This gives

Numerator = 37

Hence, the mixed number as an improper fraction is 37/8

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Answer:

3.4

Explanation and Check part below

Hope this helps :)

Step-by-step explanation:

Steps

1. Isolate the variable subtract 4.25 since it's positive.

4.25 - 1.25x = 0

- 4.25 - 4.25

- 1.25x = - 4.25

2. Divide by - 1.25 in both sides of equation.

- 1.25x = - 4.25

--------- ---------- <------- fraction bar/ divide

-1.25 -1.25

x = 3.4

Check:

4.25 - 1.25 (3.4) = 0

4.25 - 4.25 = 0

0 = 0

True statement.

Answer:

that's like 77% off if im reading this right

Step-by-step explanation:

Answer:

Given as at the end of the proof flowchart we are only left with one unknown m∠3, the logical conclusion is that we're proving that m∠3 = 180° - 54° = 126°

Answer:

X represents 32

Step-by-step explanation:

Bc x plus 30 = 62 - 30 equals 32 0-0

Answer:

1st=5, 2nd=10, 3rd=25

Step-by-step explanation:

We can make an equation to figure out the lengths of all 3 peices:

1st piece is represented as x

2nd piece is twice as long as the first, so 2x will represent that.

3rd piece is 5 times as long as the first, so 5x will represent that

together that is x+2x+5x=40

you can then simplify that to be 8x=40

40/8=5 so x=5

You then plug 5 in as x to figure out the lengths of the other pieces

1st=

5

2nd=2(5)

10

3rd=5(5)

25

:D

Answer:

a

Step-by-step explanation:

the answer is a

Answer:

C

Step-by-step explanation:

The expression come -70

given;

In mathematics, multiplication can be represented by using the symbol × or the symbol ·. Moreover, multiplication can be also represented just by leaving the numbers or values side by side without any symbol. For example, the expression 5x + y implies 5 should be multiplied by x. In this context, the expression  indicates -73 + 3

it means ; the number 73 substract from 3 and we get - 70.

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When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a mathematical expression.

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Answer:

the answer is 16 feet

Step-by-step explanation:

Answer: 12.9

Step-by-step explanation:

5 x 3 x 2= 30

5 x 3= 15

15 x 2= 30

D= M/V -> Try to remember the DMV

387 / 30= 12.9

30 x 10= 300

30 x 2= 60

30 x 1= 30

30 x .9= 27

10 + 2 + .9= 12.9

300 + 60 + 27= 387

The coordinates of the point on the directed line segment is (-2, 4)

The points are given as

(-5, 8) and (-1, -8)

The ratio is given as

m : n = 3 : 1

The coordinates of the point are calculated as

Point = 1/(m + n) * (mx2 + nx1, my2 + ny1)

So, we have

Point = 1/(3+ 1) * (3 * -1 + 1 * -5, 3 * -8 + 1 * 8)

Evaluate

Point = 1/4 * (-8, 16)

So, we have

Point = (-2, 4)

Hence, the coordinates of the point on the directed line segment is (-2, 4)

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There are 5548 students majoring in computer science.

This problem is related to percentage we have to calculate the number of students with the percentage given. After multiplying the percent given to the total number of students we will get the required number of students.

Given that the total number of students in the university class is =7600

Also 73% of students are majoring in computer science.

Number of students majoring in computer science is = (73/100) of 7600

                                                                                   = 73×76

                                                                                   = 5548 students

So, the total number of students majoring in computer science is 5548.

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1) The angular speed is approximately 12.566 radians per second.  

2) The linear speed of a point on the edge of the disk is 1.257 meters per second.

1) Herein we have a disk that spins at constant angular speed (ω), in radians per second, whose magnitude is found dimensional analysis and unit conversions:

ω = 120 rev / min × (2π rad / 1 rev) × (1 min / 60 s)

ω ≈ 12.566 rad / s

The angular speed is approximately 12.566 radians per second.  

2) The linear speed (v), in meters per second, on the edge of the disk is described by the following formula:

v = R · ω  

Where R is the radius of the spinning disk, in meters.

If we know that R = 0.1 m and ω ≈ 12.566 rad / s, then the linear speed is:

v = (0.1 m) · (12.566 rad / s)

v = 1.257 m / s

The linear speed of a point on the edge of the disk is 1.257 meters per second.

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Find the critical points of [tex]f_1[/tex] and [tex]f_2[/tex].

By the fundamental theorem of calculus,

[tex]{f_1}'(x) = \displaystyle \prod_{j=1}^{21} (x-j)^j = (x-1) (x-2)^2 (x-3)^3 \cdots (x-21)^{21}[/tex]

and [tex]{f_1}'=0[/tex] for [tex]x\in\{1,2,3,\ldots,21\}[/tex]. The stationary points at odd values have odd multiplicity, while the even ones have even multiplicity. At the points of odd multiplicity, [tex]{f_1}'[/tex] passes through the [tex]x[/tex]-axis and the sign of [tex]{f_1}'[/tex] changes, while at the points of even multiplicity, [tex]{f_1}'[/tex] is tangent the to [tex]x[/tex]-axis. We also have

[tex]\displaystyle \lim_{x\to-\infty} {f_1}'(x) = (-1)^{1+3+5+\cdots+21} \infty = (-1)^{11^2} \infty = -\infty[/tex]

[tex]\displaystyle \lim_{x\to\infty} {f_1}'(x) = \infty[/tex]

so the plot of [tex]{f_1}'[/tex] looks more or less like the attached curve. (Not drawn to scale)

Wherever the sign of [tex]{f_1}'[/tex] changes from negative to positive, as it does in the case of [tex]x\in\{1,5,9,13,17,21\}[/tex], there is a local minimum, so [tex]m_1 = 6[/tex]. Similarly, wherever the sign changes from negative to positive, as it does when [tex]x\in\{3,7,11,15,19\}[/tex], there is a local maximum, so [tex]n_1 = 5[/tex].

Repeat for [tex]f_2[/tex].

[tex]{f_2}'(x) = 4900 (x-1)^{49} - 29400 (x-1)^{48} = 4900 (x-1)^{48} (x-7)[/tex]

has roots at [tex]x=1[/tex] and [tex]x=7[/tex], but only the latter is a critical point due to odd multiplicity. A rough sketch of the plot of [tex]{f_2}'[/tex] is also attached. The sign of [tex]{f_2}'[/tex] changes from negative to positive at [tex]x=7[/tex], so [tex]m_2 = 1[/tex] and [tex]n_2=0[/tex].

We conclude that

Q.9) [tex]2m_1+3n_1+m_1n_1 = \boxed{57}[/tex]

Q.10) [tex]6m_2+4n_2+8m_2n_2 = \boxed{6}[/tex]

Answer:

x = (- [tex]\frac{13}{2}[/tex], 0)
y = (0,26)

Step-by-step explanation:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.