Famous piece of artwork was up for bid at a museum auction. The minimum bid was more than $20,000. Determine which inequality represents the bid for the artwork.

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]

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?

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

Answer:

2,6

Step-by-step explanation:

internal angles of the polygon

angle a = 180 - 45 = 135°

angle b = 180 - 90 = 90°

angle c = 180 - 60 = 120°

angle d = 540 - 135 - 90 - 120 - 77 = 118°

angle e = 180 - 103 = 77 °

angle x = 180 - 118 = 62°

the polygon is not a regular polygon because the measure of its angles are different

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:

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

Houston to NY= 1608

NY to Chicago=802

Chicago to Houston=1067

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

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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3) $1,899.81

4) $1,899.26

6) $17,150

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 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:

the program I will get back to you on that date is approaching the

Step-by-step explanation:

the program I will get back to you on that date is approaching the

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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Answer:

7 cm

Explanation:

The area of a parallelogram:

From the diagram:

• Base = y cm

• Height = y cm

Thus:

The value of y is 7cm.

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.

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 two given triangles are congruent because of SAS.

In geometry, two figures or objects are congruent if their shapes and sizes match, or if one is the mirror image of the other.  Both of the bread slices have the same shape and size when stacked on top of the other. Congruent refers to having the same precise size and shape. Having the same size and shape makes two shapes congruent. The mirror image of one shape is the same as the other if the two shapes are congruent.

The given triangles are RTP and STP

P is the midpoint of RS and TP is the altitude of triangle RTS.

In the triangles RTP and STP

TP = TP (common)

∠RPT = ∠ SPT (90°)

RP = SP (median divides the side equally)

So, both triangles are congruent using SAS property.

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On solving the given equation the value of y=7/10 so this value the given equation will be true as the definition of solution of equation says ,"A solution to an equation is a number that can be plugged in for the variable to make a true number statement. "

A number that can be entered for the variable to produce a true number statement is the solution to an equation. One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. In an equation, both sides will remain equal if we add the same amount to each side. Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the given equations on a graph and locate the point(s) where they all intersect to solve a system by graphing. You can find the values of the variables you are solving for by finding the coordinate of this point.

Here,

12y - 1/2 = 9y +8/5

3y=8/5+1/2

3y=(16+5)/10

3y=21/10

y=7/10

According to the definition of an equation's solution, "A solution to an equation is a number that can be plugged in for the variable to make a true number statement," the value of y will be 7/10 when the given equation is solved.

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Answer:

49.5 minutes

Step-by-step explanation:

Amount of time that Philip took

= [tex]\frac{distance}{speed}[/tex]

= [tex]\frac{66km}{80km/h}[/tex]

= [tex]0.825h[/tex]

= [tex]49.5 min[/tex]

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 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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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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Answer: 66/2 or in simplest form, 33/1

Step-by-step explanation:

11/2 divided by 1/6

*Keep the first fraction, flip the sign to multiplication, reciprocal or flip the fraction*

= 11/2 x 6/1

=66/2

=33/1

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

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).

Answer:

Step-by-step explanation:

Answer:

y-2 = 7(x-1)