Evaluate Solve 7x + 5 < 3x + 25

Answer:

see below

Step-by-step explanation:

A: Some points could be (1, 7.5), (2, 7), (3, 6.5), (4, 6), (5, 5.5) and (6, 5) because the y-coordinates all represent the heights of the candle after the x hours.

B: This is a function because no input has multiple outputs.

C: It would still be a function because no input would have multiple outputs.

Answer:

Have a great day!!

Step-by-step explanation:

Part A: my rate of change was first y= - 5x + 8 the reason i put a negative sign beforehand is that when the candle melts its height it's decreasing 

(0,8),(1,7.5)(2,7)(3,6.5)(4,6)(5, 5.5)

Part B: This is a function because there is one different output for each different input

Part C: yes, it still would be a function because the numbers haven't changed and are exactly the same and it still has one input for each output.

(0,8), (1,75), (2,7), (3,6.5), (4,6), (5,5.5)

Answer:

The rational number representing the average change in the volume of water each day is:

[tex]\frac{0.875 liters}{1 day}[/tex]

Step-by-step explanation:

Rational numbers are those that can be represented as the quotient of two integers. That is, rational numbers can be represented by a fraction [tex]\frac{a}{b}[/tex], where a is the numerator and b is the denominator that must be other than zero. To express the set of these numbers, mathematicians use a capital Q.

In this case we know that Finn's pool leaked a total 3.5 L in 4 days, so the rate can be written as:

[tex]\frac{3.5 liters}{4 days}[/tex]

Now you must make this division or quotient, where the denominator will be 1 because you must know the number of liters drained per day:

[tex]\frac{3.5 liters}{4 days}=\frac{0.875 liters}{1 day}[/tex]

So the rational number representing the average change in the volume of water each day is:

[tex]\frac{0.875 liters}{1 day}[/tex]

Answer: c( 320 gallons/34 miles or d( 320 miles/34 gallons

hope it helps..

Answer:

[tex]79213229.3 ft^3[/tex]

Step-by-step explanation:

The great pyramids pf Egypt are square based pyramids.

The volume of a square based pyramid is:

[tex]V = a^2h/3[/tex]

where a = length of square base

h = height of pyramid

The pyramid has a square base measured as 754 feet and a height of 418 feet. Its volume is:

[tex]V = 754^2 * 418 / 3\\\\V = 79213229.3 ft^3[/tex]

Answer:

(a-b)^3 = [tex]\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3[/tex]

Step-by-step explanation:

(a-b)^3 = (a-b)(a-b)(a-b)

According to the perfect cube formula (a-b)^3 = [tex]\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3[/tex]

And there you have it! The perfect cube formula already solved your equation!

Answer:

B.

Step-by-step explanation:

They all are alternating interior angles so they'll be congruent.

Answer:

B. Alternating interior angles are congruent

Step-by-step explanation:

The angles that are in the statements are all interior angles. When compared to each other, they lie on opposite sides of the transversal.

Answer:

The effect of 4 on the graph of y = sin(x) + 4 is that it shifts the graph by 4 units up.

The effect of 4 on the graph of y = sin(4x) is that its period would be 1/4th of 2π, i.e it completes one oscillation every π/2 units.

Step-by-step explanation:

The graph of y = sin(x) is a wave that keeps oscillating between -1 and 1, and repeats its shape every 2π units. The maximum value of the graph is 1 unit with a range of [-1, 1]

The graph of y = sin(x) is referred to as a periodic function because it repeats itself infinitely.

The effect of 4 on the graph of y = sin(x) + 4 is that it shifts the graph by 4 units up.

The effect of 4 on the graph of y = sin(4x) is that its period would be 1/4th of 2π, i.e it completes one oscillation every π/2 units.

Answer:

Step-by-step explanation:

x^3 - 5x2 - 8x + 48 = 0

You haven't supplied a list . To confirm which value is the correct one substitute the values for x and see if the result is 0.

Since the last term is  48 you could try some of the factors of 48 :  1, -1, 2, -2, 3 -3  and so on.

Answer:

70°

Step-by-step explanation:

RSTU is a kite,

Sum of 4 internal angles= 360°

m∠U=m∠S=80

m∠T= 360° - (130°+80°+80°)= 70°

Answer:

4x - 3y = 0

Step-by-step explanation:

The angle between the radius and the tangent at P is right

The equation of a line in slope- intercept form is

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

Rearrange 4y + 3x = 25 into this form

Subtract 3x from both sides

4y = - 3x + 25 ( divide all terms by 4 )

y = - [tex]\frac{3}{4}[/tex] x + [tex]\frac{25}{4}[/tex] ← in slope- intercept form

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

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{3}{4} }[/tex] = [tex]\frac{4}{3}[/tex] , thus

y = [tex]\frac{4}{3}[/tex] x + c ← is the partial equation

To find c substitute P(3, 4) into the partial equation

4 = 4 + c ⇒ c = 4 - 4 = 0

y = [tex]\frac{4}{3}[/tex] x ← equation of radius in slope- intercept form

Multiply through by 3

3y = 4x ( subtract 3y from both sides )

4x - 3y = 0 ← equation of radius in standard form

Answer:

2.

Step-by-step explanation:

To find the number of trailing zeroes, given n!, we take n and divide it by increasing powers of 5. For example, the number of trailing zeroes in 50! = 50/5 = 10, 50/25 = 2, 10 + 2 = 12 trailing zeroes.

In this case, 10/5 = 2, and since we cannot get an integer from dividing 10 and 25, we are left with this answer.

I hope this helps!

Answer: Attached graph in the explanation.

Step-by-step explanation:

Hi, to answer this question we have to graph points in a Cartesian coordinate graph.

The horizontal axis is called the x-axis, and the vertical axis is the y-axis.

To graph a point, first we have to locate its position on the x-axis, and then find its location on the y-axis, and finally plot where these meet.

For example, to plot the point (2, 3), we have to find the positive 2 on the x-axis and the positive 3 on the y-axis.

Finally when we have plotted all the points, we simply link all the points to form a line.

Answer:

4π

Step-by-step explanation:

find the circumference first

2π r

2π 8=16π

then find the arc length

16π  * 1/4

4π

Answer:

85

Step-by-step explanation:

The sum of the angles of a triangle are 180 degrees

A + B+ C = 180

A +72+ 23 = 180

Combine like terms

A + 95  = 180

Subtract  95  from each side

A +95-95 = 180-95

A =85

Answer:

-12

Step-by-step explanation:

[tex]7\dfrac{1}{2}\div\left( 4\dfrac{1}{2}-5\dfrac{1}{8} \right)=\\\\7\dfrac{1}{2}\div -\dfrac{5}{8}=\\\\\dfrac{15}{2}\times -\dfrac{8}{5}=\\\\-\dfrac{15\times 8}{2\times 5}=\\\\-12[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

First problem:  3x + 8 ≥ y  

Second problem:  Represent the number of cupcakes with n and that of balloons by m.  Then ($2/cupcake)(n) + ($1.25/balloon)(m) ≥ $25

Answer:

Independent variable is tickets.

Dependent variable is cost(dollars).

Step-by-step explanation:

Dependent variable depends on independent variable.

In this question, the total amount deoend on number of ticket bought. As number of tickets increases, the total cost will also increase.

Answer:

Streamers are $2.50 each

Balloons are $1.50 each

Step-by-step explanation:

Make a system of equations

3s + 15b = 30

2s + 4b = 11

Solve by elimination: multiply the top equation by 2 and the bottom equation by -3.

6s + 30b = 60

-6s -12b = -33

18b = 27

b = 1.5

Plug in 1.5 as b to find s

3s + 15(1.5) = 30

3s +22.5 = 30

3s = 7.5

s = 2.5

The streamers are $2.50 and the balloons are $1.50

Answer:

2[tex]\frac{1}{2}[/tex] litres or 2.5 litres

Step-by-step explanation:

From the question, 9 fruit juice bottles contain 4[tex]\frac{1}{2}[/tex] litres of fruit juice. Therefore, to find how many litres of fruit juice would be contained in 5 fruit juice bottles, you multiply 5 by 4[tex]\frac{1}{2}[/tex] litres and you divide the product by 9.

i.e. Let the quantity of the fruit juice for 5 bottles be x.

9 juice bottles ===> 4[tex]\frac{1}{2}[/tex] litres

5 juice bottles ===> x

∴x = [tex]\frac{5 * 4\frac{1}{2} }{9} litres[/tex]

x = [tex]\frac{5 * 4.5}{9} litres[/tex]

x = [tex]\frac{22.5}{9} litres[/tex]

x = 2.5 litres or 2[tex]\frac{1}{2}[/tex] litres

Hope this helps!!!

The linear equation of the corresponding table is y = 4x+3 which is correct option(D).

The slope of a linear function is defined as the angle of the line. It is denoted by m.

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Consider two points on a  linear function —Point 1 and Point 2. Point 1 has coordinates (x₁, y₁) and Point 2 has coordinates (x₂, y₂)

We need two of those points to come up with the equation of the corresponding line.

Solution in y-intercept form  y = mx+b

We can calculate the slope of the line using any 2 of the given points: I pick (0,3) and (3,15).

The formula for determining the slope of the line through 2 points (x₁,y₁) and (x₂,y₂) as m=(y₂-y₁)/(x₂-x₁)

By plugging in the corresponding values,

m = (15-3)/(3-0) = 12/3 = 4

Since the value of y when x is zero, i.e. the point (0,3) of the table, then the value of b is 3.

Now, Substitute the values in y = mx+b,  

y = 4x+3

Hence, the linear equation of the corresponding table is y = 4x+3.

Learn more about linear function here:

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Answer:

x = -7

Step-by-step explanation:

4(2x + 14) = 0

Divide each side by 4

2x+14 = 0

Subtract 14 from each side

2x+14-14 = 0-14

2x= -14

Divide each side by 2

2x/2 = -14/2

x = -7

Answer:

C, -7

Step-by-step explanation:

Use distributive property to get: 8x +56 = 0

Isolate x to get: 8x = -56

Then divide each side by 8: x= -7

The answer is C

Answer:

It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.

Step-by-step explanation:

Points:

Slope-intercept form:

slope is:

denominator of the fraction is zero, we can't divide by zero, so this line has no slope

----------

It has a slope of zero because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the numerator of a fraction cannot be zero.

It has a slope of zero because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.

It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the numerator of a fraction cannot be zero.

It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.

Answer:

D;

Step-by-step explanation:

It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.

Answer:

[tex]\fbox{\begin{minipage}{3em}x = 6\end{minipage}}[/tex]

Step-by-step explanation:

Given:

Equation: [tex]3x - 3 = 27 - 2x[/tex]

Solve for:

[tex]x[/tex]

Solution:

Step 1: Select relevant approach:

Let's move all the components containing x to the left side and other components to the right side (notice the change of sign of each one from + to - or - to +), then calculate [tex]x[/tex]

Step 2: Perform the calculation:

      [tex]3x -3 = 27 - 2x[/tex]

Moving components:

<=> [tex]3x + 2x = 27 + 3[/tex]

Adding up components:

<=> [tex]5x = 30[/tex]

Dividing both sides by 5 (coefficient of component containing [tex]x[/tex]:

<=> [tex]\frac{5}{5} x = \frac{30}{5}[/tex]

Simplifying to work out [tex]x[/tex]:

<=>[tex]x = 6[/tex]

Hope this helps!

:)

Answer:

x = 6

Step-by-step explanation:

3x - 3= 27 - 2x

First we put all the x terms to on side, making it 3x + 2x - 3= 27.

Remeber that when we move a term to the other side of the equals sign (=), we change its sign to be the opposite of what it currently is.

Then, we move all the numberics to the other side, so we derieve 3x + 2x = 27 +3. Again, the sign changes when we move it across.

What is left to do is add up the quantities. So 3x + 2x = 5x and 27 +3 = 30.

We are left with 5x = 30. If 5 x's is 30, how much is one? Sinply divide it to get the answer of 30 / 5 which is six!

To make sure the answer is correct substituite 6 in the equation as x and see if its accurate: 3(6) -3 = 7 - 2 (6). And it is!

So x is equal to six.

Answer:

[tex]x=8[/tex]

Step-by-step explanation:

[tex]\log _{10}\left(10x-1\right)=\log _{10}\left(9x+7\right)\\\mathrm{Apply\:log\:rule:\:\:If}\:\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\:\mathrm{then}\:f\left(x\right)=g\left(x\right)\\10x-1=9x+7\\\mathrm{Add\:}1\mathrm{\:to\:both\:sides}\\10x-1+1=9x+7+1\\\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}\\10x-9x=9x+8-9x\\\mathrm{Simplify}\\x=8\\[/tex]

The solution of the equation ㏒₅(10x - 1) = ㏒₅(9x + 7) is x = 8.

A logarithm is simply the opposite function of the exponentiation.

It is the exponent to which a number or value is raised to get some other number.

That is, if c = aˣ, then we can write it as x =logₐ c.

Given that,

㏒₅(10x - 1) = ㏒₅(9x + 7)

Let the value of both be n.

So, ㏒₅(10x - 1) = n and  ㏒₅(9x + 7) = n

By the definition of logarithms,

10x - 1 = 5ⁿ and 9x + 7 = 5ⁿ

So,

10x - 1 = 9x + 7

10x - 9x = 7 + 1

x = 8

Hence the value of x is 8.

Learn more about Logarithms here :

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The margin of error would be 1 / √n, where n is the number of students asked.

Margin of error = 1/√501 = 0.0446

Multiply by 100 to change to a percent:

0.446 x 100 = 4.46%

Rounding may be off slighly, so it looks like b would be the correct answer.

Answer:

Option C.

Step-by-step explanation:

Kurt started for the school at 07:35 and ends at 08:25.

Time taken by Kurt to reach the school

= 08:25 - 07:35

= (07 hours + 85 minutes) - (07 hours + 35 minutes) [Since 08 hours + 25 minutes = 07 hours + (60 + 25)minutes]

= 85 minutes - 35 minutes

= 50 minutes

Time taken by Drew to reach the school

= 08:30 - 07:55

= (07 hours + 90 minutes) - (07 hours + 55 minutes) [Since 08 hours + 30 minutes = 07 hours + (60 + 30)minutes]

= 90 minutes - 55 minutes

= 35 minutes

Difference in the time taken by Kurt and Drew = 50 - 35 = 15 minutes.

Therefore, Drew is 15 minutes faster than Kurt.

Option C. is the answer.

Answer:

37.5% chance

Step-by-step explanation:

well if there are 52 card in a deck and 4 aces.

the probability that it will be red is 50%. As half of the cards are red and the other half is black. the probablility it wil be an ace is 25%. so finding the middle of those would be 37.5%

Answer:

It says an ace or a red card. Red cards have a  50% chance plus 2 black ace cards 26 cards is half red plus 2 28/52 Answer Reduces to: 7/13

Step-by-step explanation:

Answer:

If sinA = sinB, that means that ∠A = ∠B. Because this is a right triangle, ∠A = 45°.

Answer:

47=4.7

1000= 100.0