Please see attachment

Answer:

0.5401

Step-by-step explanation:

In Standard form

due to the negativity of the power, you move the decimal point to the left...and u move it once

Answer:

try using demos its a great app for creating and reading maps

The equivalent form of the function showing the remainder as a fraction is: h(x) = (x - 6) + 4 / (x - 4)

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The given function is:

h(x) = (x^2 - 2x - 4) / (x - 4)

To rewrite this function in an equivalent form showing the remainder as a fraction, we can use polynomial division.

Let's divide x^2 - 2x - 4 by x - 4:

           x - 6

   --------------------

x - 4 | x^2 - 2x - 4

      - (x^2 - 4x)

      -------------

            2x - 4

            - (2x - 8)

            ---------

                   4

Therefore, we can write:

h(x) = (x^2 - 2x - 4) / (x - 4) = (x - 6) + 4 / (x - 4)

Therefore,  the equivalent form of the function showing the remainder as a fraction is: h(x) = (x - 6) + 4 / (x - 4)

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Answer:

Step-by-step explanation:

10(a)+5(c)=310

a= number of adult

c= number children

The Triangle Proportionality Theorem, also known as the Side Splitter Theorem, states that if a line is parallel to one side of a triangle, then it divides the other two sides proportionally.

Triangle Proportionality Theorem:

To prove this theorem, we begin by drawing a ΔABC with a line DE parallel to side AB. We then draw lines BD and CE, which intersect the parallel line DE at points F and G, respectively. By the properties of parallel lines, we know that ∠ADE and ∠ABD are congruent, and ∠AED and ∠ADB are congruent. Similarly, ∠CDE and ∠BDC are congruent, and ∠CED and ∠DCB are congruent.

We can then use the properties of similar triangles to show that ΔADE and ΔABC are similar, as are  ΔCDE and ΔACB. This means that the ratios of corresponding side lengths are equal:

BA/DE = CA/CE and CB/DE = AB/BD

We can then substitute CA - BA for CB in the first equation, and BD for AB in the second equation:

BA/DE = (CA - BA)/CE and CB/DE = BD/(CA - BA)

Cross-multiplying both equations, we obtain:

BA * CE = DE * (CA - BA) and CB * DE = BD * (CA - BA)

Adding the two equations, we get:

BA * CE + CB * DE = (DE + CE) * CA

Dividing both sides by CB * DE, we obtain:

BA/CB = (DE + CE)/CE * CA/DE = DE/CD

Thus, we have proven the Triangle Proportionality Theorem.

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Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) \(\times\)(x + 1/2)

(y - 6) = -1/4 \(\times\)(x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

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The graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

The functions for this problem are defined as follows:

When a function is multiplied by 2, we have that it is vertically stretched by a factor of 2.

Hence the graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

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Answer: 1/8

Step-by-step explanation:

First make the bottom half the same:

3/4*2/2=6/8

We don’t need to change the first portion since they have a common factor

7/8-6/8=1/8

Answer:

I think its 502.65 km 2

Step-by-step explanation:

(This is what I think, I might be wrong)

Answer:

502.655km

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

-18 + 2k    wherre k = 6

=> -18 + 2(6)

=> -18 + 12

=> -6

The rate of the slower car is 77km/hr

Velocity is the rate of change of displacement with time. It is measured in meter per second and it is a vector quantity.

velocity = displacement/time

displacement = velocity × time

represent the faster car by v1 and the slower car by v2

v1 = v2+16

V2 = v1-16

Total displacement = 680km

680 =( v1+V2)t

680 = (v1+V2)4

v1+v2 = 680/4

v2+16+v2 = 170

2v2 = 170-16

2v2 = 154

v2 = 154/2

v2 = 77km/hr

therefore the rate of the slower car is 77km/hr

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Answer:

∠ABC = 94°

∠BCD = 25°

∠ACB = 43°

Step-by-step explanation:

∠ABD = 133°

Since △ADC is an isosceles triangle where AD = CD, it means that ∠CBD = 133°

We know sum of angles at a point is 360°.

Thus; ∠ABC = 360 - (133 + 133)

∠ABC = 94°

Now, in △BCD, ∠B = 133° and ∠D = 22°

Sum of angles in a triangle = 180°

Thus; ∠BCD = 180 - (133 + 22)

∠BCD = 25°

Since the △ABC is also an isosceles triangle , it means that;

In △ABC, ∠A = ∠C

Thus; ∠ACB = (180 - 94)/2

∠ACB = 86/2

∠ACB = 43°

The linear approximation of f(1.07) using the tangent line is T(1.07) is 10.77, which is slightly lower than the actual value f(1.07) = 11.77.

First, we need to find the derivative of the function f(x) = x + 10x.

The derivative is given by:

f'(x) = 1 + 10

Next, we need to find the tangent line at the point (a, 6), which means we need to find the value of "a" that makes the tangent line pass through (a, 6). To do this, we use the equation of the tangent line:

y - 6 = (1 + 10)(x - a)

y = (1 + 10)(x - a) + 6

Now we need to use the value of "a" to find the value of f(a) and then use this to find the value of the linear approximation of f(1.07).

Let's assume that the value of "a" is 1.

So, f(a) = f(1) = 1 + 10(1) = 11

And the equation of the tangent line is:

y = (1 + 10)(x - 1) + 6 = 11x - 4

Now, to find the value of the linear approximation of f(1.07), we use the equation of the tangent line:

T(1.07) = 11 * 1.07 - 4 = 10.77

Finally, we compare this value with the actual value of f(1.07), which is:

f(1.07) = 1.07 + 10 * 1.07 = 11.77

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Answer:

Step-by-step explanation:

You mean. Btw it is wait huh

Answer:

y = 2x - 5

Step-by-step explanation:

\(y+3=2(x-1)\\y+3=2x-2\\y+3-3=2x-2-3\\y=2x-5\)

The solution of the function 3f(1) - 4g(-2)  is -19.

The functions can be solved as follows;

f(x) = 7x - 4

g(x) = 11 - x²

Therefore, let's solve the composite function as follows:

A composite function is generally a function that is written inside another function.

Hence,

3f(1) - 4g(-2) = ?

f(1) = 7(1) - 4 = 7 - 4 = 3

g(-2) = 11 - (-2)² = 11 - 4 = 7

Therefore,

3f(1) - 4g(-2) = 3(3) - 4(7) = 9 - 28 = -19

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Answer:

One ticket cost $10.90.

Step-by-step explanation:

The total spent was $98.50--food, drinks, admission--everything.

$44.00 was for food and drinks.

We can take the 44 away from the total.

98.50 - 44.00

= 54.50

They spent 54.50 on 5 tickets to get in. Divide to find the cost of one tickets. This assumes that all 5 tickets were the same price.

54.50 ÷ 5 = 10.90



The price of one ticket was $10.90

To make this look like algebra class...

let x = the price of one ticket

5x = the price of 5 tickets

5x + 44 = 98.50

subtract 44

5x = 54.50

divide by 5

x = 10.90

The logarithmic regression equation that models the situation is given as follows:

y = 242.9037 + 23.7097ln(x).

The estimated population in 2010 is of:

313.9 million

Which overestimates the actual amount by 5.2 million.

The prediction for when the population will be of 400 million is of:

Year of 2,744.

The logarithmic regression equation is obtained inserting the points of the data-set into a logarithmic regression calculator.

From the table given by the image at the end of the answer, the points are given as follows:

(0, 248.8), (10, 281.4), (20, 308.7), (30, 331.4), (31, 331.9).

Inserting these points into a calculator, the equation is given as follows:

y = 242.9037 + 23.7097ln(x).

2010 is 20 years after 1990, hence the estimate is given as follows:

y = 242.9037 + 23.7097 x ln(20) = 313.9 million.

The overestimate of the actual value, from the table, is of:

313.9 - 308.7 = 5.2 million.

The prediction for when the population will be of 400 million is obtained as follows:

400 = 242.9037 + 23.7097 x ln(x)

ln(x) = (400 - 242.9037)/23.7097

ln(x) = 6.6258.

x = e^(6.6258)

x = 754.

Hence during the year of 2,744.

The table is given by the image presented at the end of the answer.

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Answer:

667.302???

Step-by-step explanation:

I tried my best but I don't know if it's right though

Answer:

Step-by-step explanation:

Set up an equation:

7x + 10x + 13x = 100000 and solve for x:

30x = 100000 so

x = 3333.33

Anna gets 7(3333.33) = 23333.31

Louise gets 10(3333.33) = 33333.33

Lacey gets 13(3333.33) = 43333.29

11 miles far does the boat travel

Step-by-step explanation:

hope it helps

The total distance travelled will be 22 miles and the bearing will be 60.89° .

It is given that a boat travels from port town to north for 7.4 miles and then east for 3.6 miles and stops at destination.

We have to find out the total distance travelled and bearing from stopped position.

What are bearings ?

A bearing is the angle in degrees measured clockwise from north i.e., 30° from north.

As per the question ;

Boat travels from port town to north for 7.4 miles and then east for 3.6 miles and it then stops at destination.

So ;

a)

Total distance travelled from port town to destination is ;

= 7.4 miles + 3.6 miles

= 11 miles

And

If boat's captain turns back to town , then total distance will be ;

= 11 + 11

= 22 miles

b)

We know that ;

cos θ = B/H

The bearing would be ;

cos θ = \(\frac{3.6}{7.4}\)

cos θ = 0.486

θ = \(cos^{-1}\) (0.486)

θ = 60.89°

Thus , the total distance travelled will be 22 miles and the bearing will be 60.89° .

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If wheel on a scooter completes 124 revolutions and travels 22.4 meters then  diameter of the wheel is 57 mm

Each revolution of the wheel covers a distance equal to the circumference of the wheel.

The diameter of the wheel "d".

The distance covered in 124 revolutions is:

distance = 124 x circumference

= 124 x pi x d

= 124 x 3.14 x d

We know that this distance is equal to 22.4 meters, so we can set up an equation:

124 x 3.14 x d = 22.4

Simplifying and solving for d:

d = 22.4 / (124 x 3.14)

d = 0.057 meters

As we know that 1 meter is equal to thousand millimeters so multiply by 1000 to get in millimeters

d = 57 millimeters

Therefore, the diameter of the wheel is approximately 57 mm.

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Yes, Dan productivity is constant and slope is given as 3/2.

What is slope?

The slope of a line is also called its gradient or rate of change. The slope formula is the vertical change in y divided by the horizontal change in x, sometimes called rise over run. The slope formula uses two points, (x1, y1) and (x2, y2), to calculate the change in y over the change in x.

Let we take one pair of point (4,6) and (2,3) and other pair of point is (6,9) and (0,0)

The slope between  (4,6) and (2,3)  is

m = y2-y1/x2-x1

m = 3-6/2-4

=3/2

The slope between (6,9) and (0,0)

m = 0-9/0-6

=3/2

Hence, both the slopes are equal, therefore his work is constant.

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The solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11). The system has exactly one solution.

Let's solve the system of linear equations correctly.

The given system of linear equations is:

x = y + 3z = 6

x - 2y = 5

2x - 2y + 5z = 9

To determine the number of solutions, we can analyze the system using the method of elimination or substitution. Let's use the method of elimination:

From equation 1, we have:

x = y + 3z

Substituting this value of x in equation 2:

(y + 3z) - 2y = 5

y + 3z - 2y = 5

-z + 3z = 5 - y

2z = 5 - y

Now, let's substitute the value of x in equation 3:

2(y + 3z) - 2y + 5z = 9

2y + 6z - 2y + 5z = 9

11z = 9

Simplifying the equation, we find:

z = 9/11

Now, substituting this value of z back into the equation 2z = 5 - y, we get:

2(9/11) = 5 - y

18/11 = 5 - y

18/11 - 5 = -y

18/11 - 55/11 = -y

-37/11 = -y

y = 37/11

Finally, we can substitute the values of y and z into equation 1 to find the value of x:

x = y + 3z

x = 37/11 + 3(9/11)

x = 37/11 + 27/11

x = 64/11

Therefore, the solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11).

The system has exactly one solution.

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The bearing from the phone to the transmitter is approximately 31 degrees to the east of the north direction.

To determine the bearing from the phone to the transmitter, we can use trigonometry.

The bearing is typically measured clockwise from the north direction.

Given that the transmitter is 13 km west and 21 km south of the phone, we can form a right triangle with the phone as the vertex angle.

The side opposite to the vertex angle represents the north-south direction, and the side adjacent to the vertex angle represents the east-west direction.

Using the tangent function, we can calculate the angle:

tangent(angle) = (opposite side) / (adjacent side)

tangent(angle) = 21 km / 13 km

Taking the inverse tangent (arctan) of both sides, we find:

angle = arctan(21 km / 13 km)

Evaluating this using a calculator, we find the angle to be approximately 58.57 degrees.

However, since the bearing is measured clockwise from the north, we need to subtract this angle from 90 degrees (which represents the north direction) to obtain the bearing:

bearing = 90 degrees - 58.57 degrees

Calculating this, we find the bearing to be approximately 31.43 degrees.

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We know that the sum of the internal angles is equal to 180°, then we write and solve a linear equation to see that the missing angle is 94°.

Remember that for any triangle, we know that the sum of the interior angles is equal to 180°.

In this case we know that two of the angles have a measure of 62° and 24°, and if the third angle is x, then we can write the linear equation:

62° + 24° + x = 180°

To solve this we need to isolate x, we will get:

x = 180° - 24° - 62°

x = 94°

So the measure of the third interior angle is 94 degrees.

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Easy way to do this, divide 24 with 3, you will get 8. That means 8 is 1/3 of 24. To get 2/3 you just add 8+8 which equals to 16