Use the properties of logarithms
Rewrite the following in the form log(c).
5log(2)

Answer:

TUNNEL:

f(x) = -2/4.9  [tex]x^{2}[/tex]  + 9.8

TRUCK:

Width (m) < 9.8

Height (m) <  -2/4.9 ( [tex]Width^{2}[/tex] /4 - [tex]4.9^{2}[/tex] )

Step-by-step explanation:

Please see attachment

If the maximum height of the tunnel is the same as its maximum width, 9.8 meters, The quadratic model to represent the tunnel will be f(x)= (-2/4.9)x²+9.8.

Any function of the form[tex]\rm f(x) =ax^2+bx+c[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.

It is given that, If the maximum height of the tunnel is the same as its maximum width, 9.8 meters.

We have to determine a quadratic model to represent the tunnel.

The quadratic function is formed as,

f(x) =K(x-x₁)(x-x₂)

x₁=width/2

x₁=9.8/2 = 4.9

x₂= -x₁ = -4.9

Substitute the obtained value as,

f(x) = K(x-4.9)(x-(-4.9))

f(x) =K(x²-4.9²)

f(0)=9.8

The value of K is obtained as a result,

K=-2×4.9/(4.9)²

K= -2/4.9

Substitute the value of K as,

f(x) = -2/4.9(x²-4.9²)

f(x) = (-2/4.9)x²+2×4.9

f(x)= (-2/4.9)x²+9.8

Thus, if the maximum height of the tunnel is the same as its maximum width, 9.8 meters, The quadratic model to represent the tunnel will be f(x)= (-2/4.9)x²+9.8.

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Answer:

x=2

Step-by-step explanation:

qt =tn

4x+6=5x+4

5x-4x=6-4

x=2

Answer:

11:54pm

Step-by-step explanation:

Key details in the Question:

- Starting at 11:00 pm a bus makes a stop every 27 minutes.

- starting at 11:00pm a taxi makes a stop every 18 minutes.

The task is to find the time in which both the bus and taxi would make a stop.

Since the taxi has the shorter duration for a stop, we would use it as the basis for our calculations.

During the first taxi stop - 11:18pm

The Bus has not yet made its stop.

During the second taxi stop - 11:36pm

The Bus has made it's first stop (11:27pm) but is currently on the road.

During the third taxi stop - 11:54pm

The Bus would also be making it's second stop

Answer:

at the top of the mountain or hill

Step-by-step explanation:

potential energy is stored energy so therefore the higjestpoint will have the most potential energy.

The skier begins at an elevated position, thus possessing a large quantity of potential energy (i.e., energy of vertical position).

The energy an object has as a result of motion is known as kinetic energy. A force must be applied to an object in order to accelerate it. We must put in effort in order to apply a force. After the work is finished, energy is transferred to the item, which then moves at a new, constant speed.

The skier has a lot of potential energy because they are starting from an elevated position (i.e., energy of vertical position).

If the skier is starting from rest, all of their mechanical energy is potential energy.

and, Potential energy is lost and kinetic energy, or the energy of motion, is acquired as the skier starts the ascent down the hill.

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Answer:

p<8

Step-by-step explanation:

We multiply both sides by -1 to get

But remember, when you do that you reverse it, so we turn > into a <

2p<16

we divide both sides by 2

p<8

Hope this helps :)

Answer:

p < 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

-2p > -16

Step 2: Solve for p

Here we see that any number p smaller than 8 would work as a solution to the inequality.

Work Shown:

[tex]y = \frac{1}{9}x+5\\\\9y = x+45\\\\9y-45 = x\\\\-45 = x-9y\\\\x-9y = -45\\\\[/tex]

The last equation is in the form Ax+By = C where A = 1, B = -9, C = -45

In the second step, I multiplied each term by 9 to clear out the fraction.

Answer:

point s at (0,5)   point t at (5,3)  point u at (4,1)

Step-by-step explanation:

happy life

Answer:

13

Step-by-step explanation:

1+2×6=13

boy!!!!!!!!!!!!!!

Answer:

0.6g

Step-by-step explanation:

Derek has 4.8 pounds of potting soil

He shares it equally into 8 pots

Therefore the amount in each pots can be calculated as follows

= 4.8/8

= 0.6

Hence there are 0.6g in each pots

Answer:0.6

Step-by-step explanation:

Step-by-step explanation:

[tex]A = {cos}^{ - 1} 0.5 \\ \: \: A= 60[/tex]

Answer:

B) x + 4y = 7

Step-by-step explanation:

Hope this helps. Pls give brainliest.

Answer:

The correct options are;

a) Is

b) Passes through the middle of the plotted scatter data points on the graph

b) Is not

e Does not pass through the middle of the plotted scatter data points on the graph

Step-by-step explanation:

Whereby the graph with the line of best fit on the left was drawn by Sylvia and the graph with the line of best fit on the right was drawn by Patrick, we have;

The line of best fit is a line that gives the relationship of the data points within a graph to each other, such that the line of best fit provides an approximation of the data on a graph

The line of best fit is the line that passes through the mid region of all the scatter points within a graph, and closeness of the data points on the scatter plot to the line of best fit, the higher the level of correlation between the line of best fit and the data.

Therefore, we have;

Sylva's line is a line of best fit because her line passes through the middle of the plotted scatter data points on the graph. Patrick's line is not a line of best fit as his line does not pass through the middle of the plotted scatter data points on the graph.

Answer: Sylvia’s line  is  a line of best fit because her line  is close to most of the data points . Patrick’s line  is not  a line of best fit as his line  is not close enough to all the data points .

a. The equation that both services would cost the same is

0.25x + 5 = 0.35x + 2.

b. The weight of Mr. Molinary's package is 30 ounces.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, AAA Packages Plus sends packages overnight for $5 plus $0.25 per ounce.

United Packages charges $2 plus $0.35 per ounce.

Assuming the no. of ounces to be x.

∴ 0.25x + 5 = 0.35x + 2.

0.25x - 0.35x = 2 - 5.

- 0.1x = - 3.

x = 3/0.1

x = 30 ounces.

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Answer:

 (0 -  (9 • (a^666))) -  (22•3ab^6)

 (0 -  32a^666) -  (22•3ab^6)

  -12ab^6 - 9a^666  =   -3a • (4b^6 + 3a^665)

Final result :

 -3a • (4b^6 + 3a^665)

Step-by-step explanation:

Answer:

◽Angle 14 and Angle 12

◽Angle 10 and Angle 8

Step-by-step explanation:

Vertical angles are opposite to each other on a pair of intersecting lines.

◽Angle 1 and Angle 4

These angles are not on the same two intersecting lines.

◽Angle 14 and Angle 12

These angles are on the same two intersecting lines. They are also opposite to each other.

◽Angle 7 and Angle 8

These angles are on the same intersecting lines, but they are not opposite to each other.

◽Angle 10 and Angle 8

They are on the same pair on lines, and opposite to each other.

◽Angle 3 and Angle 5

They are not on the same pair of intersecting lines.

◽Angle 8 and Angle 12

These angles are not on the same pair on intersecting lines. (However, they are also equal because they are corresponding, on the insides of an "F" pattern).

The pairs of angles are congruent because they are vertical angles that will be ∠14 & ∠12, ∠11 & ∠13, ∠10 & ∠8, and ∠7 & ∠9. Then the correct option is A.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

By the vertical angle property, then we have

∠14 = ∠12

∠10 = ∠8

∠7 = ∠9

∠11 = ∠13

The pairs of angles are congruent because they are vertical angles that will be ∠14 & ∠12, ∠11 & ∠13, ∠10 & ∠8, and ∠7 & ∠9. Then the correct option is A.

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The missing diagram is given below.

Answer:

4i + j

Step-by-step explanation:

I think you meant g instead of 8.

Given:

u = 4i + 9j

g = -8j

u + g

(4i + 9j)  + (-8j)

4i + j

Answer:

A

Step-by-step explanation:

miles over hours

40 over 1

120 over 3

Answer:

c = d/a - b

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define

a(c + b) = d

Step 2: Solve for c

Answer:

54 - 3d

Step-by-step explanation:

In order to find the cost of 3 DVDs we would simply need to multiply the expression given by 3. In order to do so we must use the distributive property and distribute the 3 to both the initial price of the dvd and the discount price, like so...

3(18 - d)  ... in order to distribute we multiply 3 by 18 and then by d seperately

(3 * 18) - (3 * d)

54 - 3d

That would leave us the expression 54 - 3d

Answer:

-31 feet

Step-by-step explanation:

so, -25 is the start point.

he goes anither -13 feet, so hes at -38.

he rises 7 feet, so hes at -31 feet.

Answer:

$960

Step-by-step explanation:

30^2 is 900

30x2 is 60

900+60 is 960.

Hope this helps plz hit the crown :D

Answer:

1.00 cm Is the greatest level of precision possible for the measurement of the width of the spin of the book

Answer:

False

Step-by-step explanation:

Additions and subtractions are done in the order they appear from left to right.

Answer:

Step-by-step explanation:

The angle of incidence and reflection is 45°

The angle between them is 90°

they lie on the same plane, and angle of incidence = angle of reflection

the sum of all the angles is 180°

let angle of incidence and reflection be x

therefore,

90 + 2x = 180

x = 45°

Answer:

huh

Step-by-step explanation:

Step-by-step explanation:

The answer has to be 4.

4×4=16

4+4+4×4=16

The values of x = 5 and pq = 86.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

Operators which let do a basic mathematical calculation

+ Addition operation: Adds values on either side of the operator.

For example 12 + 2 = 14

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 12 -2 = 10

* Multiplication operation: Multiplies values on either side of the operator

For example 12*2 = 24

Given that m is the midpoint of pq,

pm= 9x+3 and mq= 11x-17

⇒ 9x + 3 = 11x - 7

⇒ 3 = 11x - 9x -7

Rearrange the likewise terms and apply the arithmetic operations,

⇒ 3 = 2x - 7

⇒ 10=2x

⇒ x = 10/2

Divided by 2

⇒ x = 5

⇒ pq = 20x-14

⇒ pq = 20*5-14

⇒ pq = 86

Hence, the value of pq is 86.

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Answer:

Step-by-step explanation:

Let's consider an exponential function as,

f(x) = 2ˣ

Now we prepare the input-output value table to get the ordered pairs to be plotted.

f(x)     0.25     0.5          1             2            4           8

x         -2         -1            0            1             2           3    

By plotting these points we get the graph as attached.

Therefore, second option in the last attachment will be the correct option.