Find the scale factor.

Answer:5.03x10^5 and 3.2x10^6

Step-by-step explanation:

Number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10

503,000 divide by 10 until the number before decimal point digit becomes less than 10

To solve this problem the first thing we have to do is identify our variables

The time taken by Janice will be represented by a j, and the time taken by Donald by a d.

• Donald builds the picnic table in hours: , 1/d, of the picnic table per hour

• Janice builds the picnic table ,j=d-2, in hours: ,1/(d-2), of the picnic table per hour

Now we will get our equation to solve

Janice and Donald worked together for 2 hours to build a picnic table, after which Donald continued working for 1 hour without Janice to finish the job.

We factor our equation to find Donald's time

They gave us 2 values but we discarded the value of d=1 because the joint calculations would give negative calculations then

3) $1,899.81

4) $1,899.26

6) $17,150

The error is in step 2 that is 3x-3=2x+6 as in step 2 we shifted 2x to LHS side of calculation.

Error is the difference between a true value and an estimate, or approximate, representation of that value in applied mathematics. The difference between the mean of the entire population and the mean of a sample taken from that population is a frequent example in statistics. Three types of errors can occur when solving math problems: factual, procedural, and computational. Students can make a variety of math mistakes, and it's crucial to know how to avoid them and how to take lessons from them. An error is an inaccurate or incorrect action (from the Latin error, meaning "wandering"). An error is often used interchangeably with the word mistake. The term "error" in statistics describes the discrepancy between the computed value and the correct value.

Here,

5x-3=2x+6

3x-3=6

3x=9

x=3

The mistake is in step 2, which reads 3x-3=2x+6 because we shifted 2x to the LHS side of the calculation in step 1.

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Answer:

Step-by-step explanation:

first you need to make sure that the fractions you are adding and subtracting have like denominators. To do this you need to find the least common multiple between the two

1. 4/6 - 3/12= 8/12 - 3/12 Answer: 5/12

2. 5/6 - 3/4 = 10/12 - 9/12 Answer: 1/12

3. 5/9 - 2/6= 10/18 - 6/18 Answer 4/ 18 (reduces to 2/9 for simplest terms)

4. 9/12 - 11/18 = 27/36 - 22/36 Answer: 5/36

5. 4/9 - 4/10 = 40/90 - 36/90= 4/90 ( reduces to 2/45)

6. 6/7 - 5/14= 12/14-5/14 Answer 7/14 (reduces to 1/2

7. 2/5- 1/7= 14/35 - 5/35 Answer 8/35

8. 4/6 - 3/5 = 20/30 - 18/30 Answer 2/30 (1/15 simplified

Leah and Philip have same unit rate.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The table is shown for the number of pages and number of nights.

Now,

The unit rate to read the number of pages for Leah;

⇒ 45 / 3 = 15

The unit rate to read the number of pages for Rose;

⇒ 48 / 4 = 12

The unit rate to read the number of pages for Hannah;

⇒ 30 / 3 = 10

The unit rate to read the number of pages for Philip;

⇒ 150 / 10 = 15

Thus, Leah and Philip have same unit rate.

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The value of x for the ΔPRT is 7.

As its given in the question that ΔKMN ≅ ΔPRT (congruent)

MN = 20

KN = 25

KM = 15

RT = 3x - 1

Therefore,

MN = RT

KM = PR

KN = PT

So,   RT = MN

   3x - 1 = 20

        3x = 20 + 1

        3x = 21

          x = 21/7

          x = 7

Hence, x = 7.

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An order of 1 slice of cheese pizza and 3 sodas cost will be $5.25.

Two or more algebraic equations that share variables, such as x and y, are said to be simultaneous equations. Since the equations are solved simultaneously, they are known as simultaneous equations.

Given data -

Cost of 3 slices of cheese pizza and 2 sodas = $8.75

Cost of  2 slices of cheese pizza and 4 sodas = $8.50

Let x be the cost of 1 slice of cheese pizza

and y be the cost of 1 soda

According to the given data,

3x + 2y = $8.75         -------------equation 1

2x + 4y = $8.50        -------------equation 2

Equation 1 by equation 2 multiplied results in

6x + 4y = $17.5          ------------equation 3

By subtracting equation 2 from equation 3 to get the cost of 1 slice of cheese pizza, we will get

4x = $9

x = $2.25

By substituting the value of x in equation 2 so that we can get the cost of 1 soda, we will get

2*2.25 + 4y = $8.50

4.5 + 4y =  $8.50

4y = $8.50 - 4.5

4y = $4

y = $1

To get the cost of 3 sodas, multiplying the value of y by 3

Therefore the cost of 3 sodas will be $1*3 = $3

The total cost of 1 slice of cheese pizza and 3 sodas cost = $2.25 + $3

= $5.25

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The length of the arc is 1.63

In circle M with m \angle LMN= 42m∠LMN=42

The diagram shows a sector of a circle, center M

The radius of the circle is 14 units

The angle LMN = 42

We need to find the perimeter of the sector

s = r∅

Where ∅ is the angle subtended by the arc

r is the radius of the circle

s = 14 (42/360)

s = 14 (7/60)

s = 1.63

Therefore,  the  length of the arc is 1.633

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An equation for the distance between the two friends after time (t) in hours is given by: c = 50t

Given,

Two friends drive off in different directions from the same place. One heads North at 30 miles per hour, while the other heads East at 40 miles per hour.

We have to find the equation for the distance between the friends after t hours.

Here,

The distance covered by each friend should be calculated as follows:

For the first friend heading North, we have;

Distance, a = speed × time

Distance, a = 30t

For the second friend heading East, we have:

Distance, b = speed × time

Distance, b = 40t

By applying Pythagorean theorem, the distance between these two friends after an amount of time (t) is given by:

Distance, c² = a² + b²

Distance, c² = (30t)² + (40t)²

Distance, c² = 900t² + 1600t²

Distance, c² = 2500t²

Distance, c = √(25 × 100t²)

Distance, c = √25t² × √100

Distance, c = 5t x 10

Distance, c = 50t

Therefore,

The equation for the distance between the friends after t hours is c = 50t

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The slope-intercept form of a linear equation is given by the expression:

y=mx+b, so in this case you just have to solve the equation for y by inverse operations to solve equations:

x+5y=5

5y=5-x

y=5/5-x/5

y=-1/5x+1

16+14i will the required simplified value as the expression is -6(3i)(-2i)=2(3-i)(4i-2) which is a complex number having imaginary and real part.

A complex number is one with the formula a + bi, where a and b are real numbers and I is an imaginary number. Complex numbers are those that are expressed as a+ib, where a,b are real numbers and I is an imaginary number known as "iota." (√-1) is the value of i. 2+3i is a complex number, for example, where 2 is a real number (Re) and 3i is an imaginary number (Im). A complex number is one that can be expressed as a + bi, where a and b are real numbers and I is an imaginary unit, and which solves the equation i² =-1. In this expression, a represents the complex's real part and b represents its imaginary part.

Here,

-6(3i)(-2i)=2(3-i)(4i-2)

-6(-6i²)

=36i²

=-36

2(3-i)(4i-2)

=2(12i-4i²-6+2i)

=2(14i+4-6)

2(14i-2)=-36

14i-2=-18

on simplifying,

16+14i will the required simplified value.

As the expression is -6(3i)(-2i)=2(3-i)(4i-2) which is a complex number with imaginary and real parts, the required simplified value is 16+14i.

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Answer:

−6(3i)(−2i) =

✔ –36

2(3 − i)(−2 + 4i) =

✔ –4 + 28i

Step-by-step explanation:

The total pounds of rice will be 18 pounds.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, each basket contains 3 identical bags of stuffing and 6 pound bag of rice. The total pounds will be:

= 3 × 6

= 18 pounds

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Complete question

Each basket contains 3 identical bags of stuffing and 6 pound bag of rice. What is the total pounds of rice?

EXPLANATION

Since the two planes are 3400 miles apart, and their speed differs by 80 mph, we can apply the following relationship:

2660 / 4 = 665 mph

Assuming that x is the speed of the slower plane and y is the speed of the faster, we have:

(1) x + 65 = y

(2) x + y = 665 [Combined speed of both planes]

Plugging in (1) in (2):

x + (x + 65) = 665

Removing the parentheses:

x + x + 65 = 665

Adding like terms:

2x + 65 = 665

Subtracting -50 to both sides:

2x = 665 - 65

Subtracting numbers:

2x = 600

Dividing both sides by 2:

x = 300

Plugging in x=315 into (1):

300 + 65 = 365

In conclusion, the speed of both planes is:

Slower plane = 300 mph

Fastest plane = 365 mph

The △IJK is shifted 9 units toward left and then shifted 10 units toward down to get △I'J'K' by applying translation rule.

What is the translation rule?

An example of a transformation is a translation, which moves every point in a figure uniformly and in one direction. Slides are a common term used to describe translations. You can use notation or words to express a translation, such as "moved up 3 and over 5 to the left."

The coordinate of the vertices of △IJK are K(3, 7), I(1,2), J(6, 5).

The coordinate of the vertices of △I'J'K' are K(-6, -3), I(-8, -8), J(-3, -5).

The difference between x-coordinate of △IJK and △I'J'K' corresponding vertices are 3 - (-6) = 1 - (-8) = 6 - (-3) = 9

The difference between y-coordinate of △IJK and △I'J'K' corresponding vertices are 7 - (-3) = 2 - (-8) = 5 - (-5) = 10.

Thus △IJK is shifted 9 units toward left and then shifted 10 units toward down to get △I'J'K'.

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Let A be the total amount of money that Mrs. Sorenstam had before buying the school supplies. Let C be the unit price of the compass, M the unit price of the mechanical pencil and R the unit price of the ruler.

The total amount of money required for the school supplies of one student, is C+M+R. Since there are 12 students, the total amount of money required for school supplies is:

Since Mrs. Sorenstam had a total A of money and she bought the school supplies for 12 students, with 36 cents left after the transaction, then:

Since C=1.49, M=0.59 and R=0.49, then:

Then, our equation is equivalent to:

which is the equation that we may write for the first part of the problem.

For the second part, one step is to multiply 12 times 2.57, and then add the result to both sides of the equation to solve for A:

1.- Multiply 12 times 2.57:

2.- Add 30.84 to both sides of the equation:

The required solutions are m∠1 + m∠7 = 143° + 37° = 180° and 'a' is parallel to 'b' due to the same-side exterior angle.

Transversal c intersects lines a and b which is given in the question.

As per the given figure,

m∠1 + m∠7 = 143 degrees + 37 degrees = 180 degrees

m∠1 = 143° and m∠7 = 37°.

First, we can write m∠1 + m∠7 and then substitute angles with their actual degree measure:

143° + 37° = 180 degrees

The first statement will be:

m∠1 + m∠7 = 143° + 37° = 180°

Exterior indicates that both angles are on the same side, or outside, of the parallel lines.

Angles a, b, c, and d in the figure are outside of the parallel lines.

We can then state;

a and b are parallel since they both agree with the same-side exterior theorem.

As a result, 'a' and 'b' are parallel because they both satisfy the same-side exterior theorem.

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Answer:

2,6

Step-by-step explanation:

The equation r-c= p represents  the profit equation

Profit can be defined as the difference between revenue and cost i.e. revenue minus cost. The formula for profit can be written as:

p = r - c

where r is the revenue and c is the cost

Notice that the equation, r-c = p is the same as p = r-c when rearranged.

Therefore, the equation r-c=p stands for the profit equation

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Answer:

Step-by-step explanation:

Answer:

y-2 = 7(x-1)

Looking at figure A, we have a prism with a triangular base that looks like a right triangle.

Since the prism has a right triangular base, the base shape is a right triangle (shape 5).

Looking at figure B, we have a prism with a pentagonal base.

Since the prism has a pentagonal base, the base shape is a pentagon (shape 1).

Looking at figure C, we have a prism with a triangular base that looks like an equilateral triangle.

Since the prism has an equilateral triangle base, the base shape is an equilateral triangle.(shape 4).

Looking at figure D, we have a prism with a triangular base that looks like an equilateral triangle.

Since the prism has an equilateral triangle base, the base shape is an equilateral triangle.(shape 4).

The vertical change from point A to point B is 1. The horizontal change from point A to point B is 2. The rate of change in the graph is 0.5.

A graph is a diametrical representation of any function between the dependent and independent variables.

For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.

As per the given,

Point A translate to point B on a straight line.

The Coordinate of point A is (2,1).

The Coordinate of point B is (4,2).

Vertical change = 2 - 1 = 1

Horizontal change = 4 - 2 = 2

Slope = vertical change / horizontal change

Slope = 1/2 = 0.5

Hence "The vertical change from point A to point B is 1. The horizontal change from point A to point B is 2. The rate of change in the graph is 0.5".

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We have that (Some) alternate exterior angles in this graph are:

1 & 7

2 & 8

9 & 15

10 & 16

(Some) Alternate interior angles are:

3 & 5

4 & 6

12 & 14

11 & 13

Some linear pairs are:

1 & 2

9 & 10

4 & 3

12 & 11

5 & 6

13 & 14

8 & 7

16 & 15

(Some) Consecutive interior angles are:

4 & 5

3 & 6

12 & 13

11 & 14

(Some) Corresponding angles are:

1 & 5

2 & 6

9 & 13

10 & 14

(Some) Vertical angles:

1 & 3

2 & 4

9 & 11

10 & 12

5 & 7

6 & 8

13 & 15

14 & 16

Answer:

[tex]\frac{5}{14}[/tex]

Step-by-step explanation:

First, find the total number of students:

[tex]252+140=392[/tex]

Then, divide the number of students at hand by the total number:

[tex]\frac{140}{392}[/tex]

When possible, reduce the fraction to its simpliest form:

[tex]\frac{140}{392}\div\frac{28}{28}=\frac{5}{14}[/tex]

When we rotate a figure 90° around a point, we need to check the difference in x and y coordinates between the point and the center of rotation.

Then these differences will swap among themselves.

The difference in x-coordinate between A and B is 1, so now this difference will be the difference in y-coordinate.

The difference in y-coordinate between A and B is 7, so now this difference will be the difference in y-coordinate.

So the coordinates of A'' will be:

Also, the point will be in the third quadrant, so all coordinates are negative:

Therefore the answer is C.

Given data:

The diameter of the cut sphere, D=14 in.

The radius of the cut sphere is,

The cut sphere is called a hemisphere.

The surface area of a sphere is

So, the lateral surface area of a hemisphere is half the surface area of sphere. Therefore, the lateral surface area of a hemisphere is,

The hemisphere has a lateral surface and a circular surface. The area of the circular surface is,

Therefore, the total area of the hemisphere is,

The total surface area of a hemisphere is,

Therefore, the total surface area of the cut sphere is 461.8 square inches.

Answer:

40/36=20/x

X=18

Step-by-step explanation:

it solve by Proportion and proportion

Answer:

Area of the small rectangle is 9m²

y = 0.125x² - 3 is equation of parabola in vertex form

The standard form of the parabola is [tex]y = ax^{2} + bx + c[/tex]

The vertex form of parabola is [tex]y = a(x-h)^{2} + k[/tex]

where h and k are vertex of parabola.  The vertex formula is used to find vertex coordinate of parabola .

Vertex point of parabola are usually represented by (h, k).

Given that the vertex of parabola is 0, -3

(h, k) = (0, -3)

h = 0 and k = -3

substituting the values of h and k in vertex form of parabola,

[tex]y = a(x-0)^{2} -3\\y = ax^{2} - 3[/tex]

Parabola is also passing through (12,15) means it should satisfy vertex equation of parabola

[tex]15= a(-12)^{2} -3\\15+3 = 144a\\18 = 144a\\a = \frac{18}{144}\\\\a = 0.125[/tex]

Substituting value of a

Vertex form of parabola is [tex]y = 0.125x^{2} - 3[/tex]

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Question:

Find the value of 3a + 2b if a = 4 and b = (-9) .

Solution:

Let the following expression

now, if a = 4 and b = -9, and we substitute them in the previous expression, we obtain:

then, we can conclude that the correct answer is: