The weight of one bag of groceries is 9 12/13 pounds. A second bag of groceries weighs 9 21/26. How many pounds more does the heavier bag weigh?

4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.

5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.

In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;

RU ║ ST

Slope of side RU = Slope of side ST

Slope of RU = (y₂ - y₁)/(x₂ - x₁)

Slope of RU = (1 + 3)/(5 + 3)

Slope of RU = 4/8

Slope of RU = 0.5.

Slope of RS = (y₂ - y₁)/(x₂ - x₁)

Slope of RS = (-9 + 3)/(-4 + 3)

Slope of RS = -6/-1

Slope of RS = 6.

Slope of ST = (y₂ - y₁)/(x₂ - x₁)

Slope of ST = (-2 - 1)/(10 - 5)

Slope of ST = -3/5

Slope of ST = -0.6.

Slope of UT = (y₂ - y₁)/(x₂ - x₁)

Slope of UT = (-2 + 9)/(10 + 4)

Slope of UT = 7/14

Slope of UT = 0.5.

Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.

Question 5.

In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance RT = √[(-2 + 3)² + (10 + 3)²]

Distance RT = √170 units.

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance US = √[(5 + 4)² + (1 + 9)²]

Distance US = √181 units.

Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.

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Answer:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    6-2*x-(3)=0  

Step by step solution :

STEP

1

:

Solving a Single Variable Equation

1.1      Solve  :    -2x+3 = 0  

Subtract  3  from both sides of the equation :  

                     -2x = -3

Multiply both sides of the equation by (-1) :  2x = 3

Divide both sides of the equation by 2:

                    x = 3/2 = 1.500

x = 3/2 = 1.500

Step-by-step explanation:

hope this helps

For the function, the x-intercept of g(x) is at (5,0).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

Given f(x) = ln(x)

and g(x) = -f(x - 4)

the function is

g(x) = -ln(x - 4)

when x = 5

g(x) = -ln(5 - 4)

g(x) = -ln1

g(x) = 0

the coordinates are (5, 0)

Hence the x-intercept is (5, 0).

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Answer:

Step-by-step explanation:

7g-6+3n+4= 7g+3n-2

The expression {P(x) + Q(x)} − {R(x) + S(x)} is a zero polynomial.

From the question, we have the following polynomial that can be used in our computation:

P(x) = 2x² (x + 3) − (7x − 10)

Q(x) = 8(x − 1) (x² + x + 1) − 3x² + 4

R(x) = (2x + 1)² - (2x² + 7)

S(x) = 2(5x³+6) + x(x - 11)

Add the expressions P(x) and Q(x)

So, we have

P(x)  + Q(x) = 2x² (x + 3) − (7x − 10) + 8(x − 1) (x² + x + 1) − 3x² + 4

Evaluate

P(x)  + Q(x) = 10x³ + 3x² - 7x + 6

Add the expressions R(x) and S(x)

So, we have

R(x) + S(x) = (2x + 1)² - (2x² + 7) + 2(5x³+6) + x(x - 11)

R(x) + S(x) = 10x³ + 3x² - 7x + 6

So, we have

P(x) + Q(x)} − {R(x) + S(x)} = 10x³ + 3x² - 7x + 6 - (10x³ + 3x² - 7x + 6)

Evaluate

P(x) + Q(x)} − {R(x) + S(x)} = 0

Hence, the expression {P(x) + Q(x)} − {R(x) + S(x)} is a zero polynomial.

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Below, you'll find a list of all the answers to the questions which are solved by using proportional relationship.

The general equation for a straight line is y=mx + c, where m represents the line's slope and expresses the rate of change of y per unit time with respect to x.

The point where the graph crosses the y-axis is called the y-intercept, or c.

Direct proportionality is also represented by y = mx. We can express m as follows: m = y/x

OR

y₁/x₁ = y₂/x₂

In our cafeteria, lemonade is made using a powdered drink mix. The quantity of water required to manufacture a certain amount of powdered drink mix is proportional to the number of scoops required. For every 2 scoops of mix, 1/2 gallon of water is required, and for every 5 scoops,

1 1/4 gallons of water are required.

The proportional formula is written as y = k x.

Using the information provided, we can now write: 2 scoops require 0.5 gallon of water.

1.25 gallon of water is required for 6 scoops.

This means that k = 2/0.5

k = 2/(1/2)

k = 2 x 2

k= 4

Equations describing the relationship can be expressed as y = 4x + c.

0.5 gallon of water is now required for 2 scoops.

2=4(1/2)+c

2=2+c

c=0

Therefore, the formula will be y = 4x.

The end includes a graph for y = 4x.

12 scoops of water:

12=4x

x=3 gallons of water is needed.

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Answer:

8.1 is the answer i think

This is the same as writing y = sqrt(4(x+5)) - 1

===============================================

Explanation:

The given graph appears to be a square root function.

The marked points on the curve are:

Reflect those points over the line y = x. This will have us swap the x and y coordinates.

Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.

----------

Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).

Plug the coordinates of each point into the template y = ax^2+bx+c.

For instance, plug in x = 1 and y = -4 to get...

y = ax^2+bx+c

-4 = a*1^2+b*1+c

-4 = a+b+c

Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c

Repeat for (5,4) and you should get 4 = 25a+5b+c

We have this system of equations

Use substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.

In other words

a = 1/4, b = 1/2, c = -19/4

We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4

----------

Next we complete the square

y = (1/4)x^2+(1/2)x-19/4

y = (1/4)( x^2+2x )-19/4

y = (1/4)( x^2+2x+0 )-19/4

y = (1/4)( x^2+2x+1-1 )-19/4

y = (1/4)( (x^2+2x+1)-1 )-19/4

y = (1/4)( (x+1)^2-1 )-19/4

y = (1/4)(x+1)^2- 1/4 - 19/4

y = (1/4)(x+1)^2 + (-1-19)/4

y = (1/4)(x+1)^2 - 20/4

y = (1/4)(x+1)^2 - 5

The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.

----------

The last batch of steps is to find the inverse.

Swap x and y. Then solve for y.

y = (1/4)(x+1)^2 - 5

x = (1/4)(y+1)^2 - 5

x+5 = (1/4)(y+1)^2

(1/4)(y+1)^2 = x+5

(y+1)^2 = 4(x+5)

y+1 = sqrt(4(x+5))

y = sqrt(4(x+5)) - 1

I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.

You can also use a tool like GeoGebra to verify the answer.

Answer:

2 pencils

Step-by-step explanation:

3 - 1 = 2

Answer:

No.of pencils = 3

No.of pencils John gave Abbie = 1

How many pencils John has left = 3 -1

                                                      = 2

I was bored so added all the steps lol

Answer:

To find the radius of the water bottle, we can use the formula for the volume of a cylinder:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

Plugging in the given values, we have:

205 = 3.14 x r^2 x h

We also know that the height of the water bottle is 7.9 cm. Substituting this value, we get:

205 = 3.14 x r^2 x 7.9

Simplifying and solving for r, we get:

r^2 = 205 / (3.14 x 7.9)

r^2 = 6.75

r ≈ 2.6 cm

Therefore, the radius of the water bottle is approximately 2.6 cm.

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Answer:

12 feet

Step-by-step explanation:

1 inch= 8 feet

1/2 inch= 4 feet

1/4 inch= 2 feet

(2x2)/2= 2  (one triangle)

2x4=8 (rectangle)

2+2=4 +8=12

^2 was added 2 times cause there are 2 triangles

(you did not need a 3rd measurement cause the triangle measurements were equal)

The coordinates of the midpoints of the given line segment is:

(3.5, 1.5)

The midpoint of a line segment is simply referred to as the center of that specific line segment.

Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.

The coordinates of the endpoints of the line are:

(4,6) and (3,-3)

The formula to find the coordinates of the midpoint of the line is:

(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Thus, we have:

(x, y) = (4 + 3)/2, (6 - 3)/2

= (3.5, 1.5)

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Hello!

The distance, d, is less than 200 miles.

B. d > 200

Step-by-step explanation:

2 numbers will have an even sum.

Looking at the odd numbers between 3 and 36, there are 9 odd numbers whose digits add up to an even number.

The odd numbers between 3 and 36 are in the sequence of 3,5,7,9,11,13,15,...,35. A number can be defined as having an even sum when the sum of its digits is an even number. For single-digit numbers, all of them except 3 and 5 (which are 3 and 5 itself in sum respectively) have an even sum. For the two-digits numbers, we have to check each number individually. For instance, 11 does not have an even sum because 1+1 equals 2 which is an even number. Following this process, we find that the numbers 7, 9, 11, 13, 15, 17, 31, 33, and 35 have an even sum of digits. So, there are 9 odd numbers between 3 and 36, whose digits add up to an even number.

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To model the number of enrolled students, y, x years after the program began, we can use an exponential equation in the form:

y = ab^x

where a is the initial number of students, b is the growth factor, and x is the number of years after the program began.

We are given that the initial number of students was 245, and that the number of enrolled students after one year is 294. Therefore, we can use these values to find the growth factor b:

294 = 245b^1

b = 294/245

b = 1.2

Now that we know the growth factor, we can write the exponential equation in the form y = a(1.2)^x:

y = 245(1.2)^x

This equation can be used to model the number of enrolled students, y, x years after the program began, assuming that the advertising strategy continues to be successful and the growth rate remains constant.

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For figure {0}, the number of tiles will be equal to 2.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph as shown in the image.

The line passes through point -

(3, 8) and (4, 10)

So, the slope of the line will be -

m = (10 - 8)/(4 - 3)

m = 2

y = 2x + c

For the point (3, 8), we can write -

8 = 6 + c

c = 2

For figure {0}, the number of tiles will be equal to 2.

Therefore, for figure {0}, the number of tiles will be equal to 2.

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The solution to the inequality expression is u ≤ 42

From the question, we have the following parameters that can be used in our computation:

21≥ u/2

Rewrite properly

So, we have the following representation

21 ≥ u/2

Multiply 2 to both sides of the expression

So, we have the following representation

2 * 21 ≥ u/2 * 2

Evaluate

42 ≥ u

Rewrite both sides of the equation as

u ≤ 42

Hence, the solution to the expression is u ≤ 42

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Answer:

20 units

Step-by-step explanation:

we find the side lengths by looking at the coordinates and just counting up

Sides are 6,4,6,4

So we just add

6+4+6+4

10+10

20

Hopes this helps please mark brainliest

Answer: Your answer is 20 units, because the height is 6 units, and the length is 4 units, so we then multiply by 2 for both numbers, then add them together, having a sum of 20 units.

Hope that helps.

Answer: 1/6

Step-by-step explanation: There are 4 primes. So the probability for the first draw is 4/9. Since the card is not replaced, the second probability is 3/8. 3/8 * 4/9 is 12/72, which simplifies into 1/6.

Answer:

ln t^5s^6.

Step-by-step explanation:

5In t + 6In s

= ln t^5 + ln s^6

= ln (t^5*s^6)

= ln t^5s^6.

Answer:

Step-by-step explanation:

Perimeter add all the sides.

so let's walk around and combine like terms:

starting on the bottom moving to the left.

3x^2 + x^2= 4x^2 (there are no other squared terms)

back to the bottom moving left again:

-11x-3x+3x+x = -10x (-3x + 3x =0)

so -11x + x = -10x

now add all of the constants

-1 + 2 = 1

so your answer is

4x^2 -10x + 1

There is no change in its slope as initial and final slope is 1.

What is slope?

In arithmetic, the slope or gradient of a line may be a variety that describes each the direction and therefore the abruptness of the line.

Main body:

formula for slope with two points form is =

y -y₁ =( y₂-y₁ /x₂-x₁ )(x - x₁)

according to question ,

points are (0,0) and (3,3)

y - 0 = (3-0/3-0)(x -0)

y = 3/3 *x

y = x

hence slope of line is 1.

Now points are (0,0) and (-3,-3).

y - 0 = (-3-0/-3-0)(x -0)

y =- 3/-3 *x

y = x

hence slope of line is 1.

So there is no change in its slope.

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The point of intersection is (3,3)

What is meant by intersection?

The intersection points show where both equations have their answers. To put it another way, the intersection point is the answer to both equations. There are multiple intersecting points if there are multiple solutions that satisfy both equations.

If we plot a function, y = f(x), and its inverse, y = f1(x), we can see that the inverse function is the exact opposite of the original function with regard to y = x.

Consequently, only when y = x can both intersect as show in the fig.

Therefore A place where the lines y and x cross must be there.

Find the spot that the line y = x meets at this time.

Of course, the line y = x is satisfied at only one point, which is (3,3).

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Given: A survey of 100 high school students provided this frequency table on how students get to school:

Required: Probability that a random selected student does not drive to school.

Explanation:

Let E be the event that a random selected student does not drive to school.

Favourable outcomes: Number of students not diving to school, that is, either they take the bus or walk = 25+20+5+3+2+5 = 60

Total outcomes = Total number of students = 100.

So

Thus Probability that a random student does not drive to school is 3/5.

Final Answer: The probability is 3/5.

Answer:

46

Step-by-step explanation:

(14+x)/4 = 15

14 + x = 60

x = 46

Answer:

46

Step-by-step explanation:

Let a to d be number 1 to 4 respectively.

15 = (a + b + c + d) / 4

(a + b + c + d) = 60 ------> total sum of the 4 numbers

Since the sum of 3 numbers (assuming a to c) is 14,

Fourth number (d) = 60 - 14

= 46

That's how I would do it, hope this helps :)