Gio plotted the following points on the coordinate plane below. R(-3.5,0), S(2.5,1.5), T(-4.5,-2.5), U(2.-3.5), V(-4,-3.5)

9514 1404 393

Answer:

  a) left curve: f(x); right curve: g(x)

  b) the functions are inverses of each other

Step-by-step explanation:

(a) An exponential function with a base greater than 1 has increasing slope. A log function has decreasing slope. The exponential function is on the left.

__

(b) The base of the exponential is the same as the base of the logarithm, so these functions are inverses of each other. This can be seen in the fact that each is a reflection of the other in the line y=x.

The quantity of bowls of soup are left in the pot aftee serving her family is 16 cups

Convert quarts to cups:

Total quantity of soup served = Number of people in Kimberly's family × Volume of bowl

= 4 × 2

= 8 cups

Quantity of bowls of soup are left in the pot = Quantity of chicken noodle soup made - Total quantity of soup served

= 24 cups - 8 cups

= 16 cups

In conclusion, 16 cups of soup are left in the pot after serving.

Read more on quarts to cups:

https://brainly.com/question/3071800

#SPJ1

Answer:

165

Step-by-step explanation:

Answer:

y = -3x + 6

Step-by-step explanation:

1. the equation has a slope of -3 => y = -3x + b (b is the number we'll find now)

2. From the point (4,-6) => x = 4, y = -6

=> -6 = (-3)(4) +b

=> b = 6

Answer:

The answer of the question is 1/3

The value of the variable 'w' for the given equation 7 ( w + 7 )³ = 7(6³)  is equal to w = -1.

As given in the question,

Given equation is equal to :

7 ( w + 7 )³ = 7(6³)

Divide both the side of the equation by 7 we get,

⇒ 7 ( w + 7 )³ / 7 = 7(6³) /7

⇒( w + 7 )³ = (6³)  

Take cube root both the side of the equation we get,

⇒∛( w + 7 )³ = ∛(6³)  

⇒ w + 7 = 6

Now subtract 7 from both the side of the equation we get,

⇒w + 7 - 7 = 6 - 7

⇒ w = -1

Therefore, the value of the variable 'w' for the given equation is equal to w = -1.

The complete question is:

Solve this equation:

7 ( w + 7 )³ = 7(6³)

Learn more about equation here

brainly.com/question/29657983

#SPJ4

With the conversion factor from tries to seconds, the time taken to to complete the average number of random tries is 24 minutes.

Your information is incomplete. Therefore, an overview will be given based on the values. Let's assume that the number of tries for 10 amino acids is 2 minutes.

Therefore, the duration for 120 amino acids will be:

= (120/10) × 2

= 12 × 2

= 24 minutes.

Learn more about conversion factors on:

https://brainly.com/question/23718955

#SPJ1

Answer:

m ≤ 5

Step-by-step explanation:

I will begin by assuming m to be the number.

Then, the sum of m and 3 is: m + 3.

The symbol for "less than or equal to" is ≤.

So we form an inequality, like this :

m + 3 ≤ 8

To find m subtract 3 on each side:

m ≤ 5

Therefore, m ≤ 5.

Your analysis is correct. Here's a summary:

If it is sunny, then it is 80° Fahrenheit. (Original statement)

Converse: If it is 80° Fahrenheit, then it is sunny. (Valid)

If it is 80° Fahrenheit, then it is sunny. (Original statement)

Converse: If it is sunny, then it is 80° Fahrenheit. (Valid)

If it is not sunny, then it is not 80° Fahrenheit. (Original statement)

Converse: If it is not 80° Fahrenheit, then it is not sunny. (Invalid)

Counterexample: A day that is not 80° Fahrenheit and not sunny (e.g., 70° and cloudy).

If it is 80° Fahrenheit, then it is sunny. (Original statement)

Converse: If it is sunny, then it is 80° Fahrenheit. (Invalid)

Counterexample: A day that is 80° Fahrenheit and cloudy.

In cases 1 and 2, the original statements and their converses are valid because the relationship between "sunny" and "80° Fahrenheit" holds in both directions. However, in cases 3 and 4, the converses are invalid because there are counterexamples where the second part of the statement (either "not 80° Fahrenheit" or "cloudy") does not necessarily imply the first part ("not sunny" or "80° Fahrenheit").

The size sample that should be taken so that at 95% confidence the margin of error will be 2 months or less is:47.0596.

Using this formula to find the sample size

n = z² × σ² / e²

Where,
n = sample size =?

z = z-score = 1.96

σ = Standard deviation = 7 months

e = Margin of error = 2 months or less

Let plug in the formula

n = (1.96²× 7²) /2²

n = 3.8416 × 49 / 4

n =47.0596

Therefore the sample size is 47.0596.

Learn more about sample size here:https://brainly.com/question/18763395

#SPJ1

Answer:

first     second           sum

5              2                   7

7             -3                   4

-10           6                  -4

second picture

D, C, B, A

Step-by-step explanation:

Answer:

Step-by-step explanation:

First second sum

5 2 7

7 -3 4

-10 6 -4

Second question

d,c,a,b

Answer:

The binomial that completes the factorization is 3p + 4q.

Step-by-step explanation:

We can start by recognizing that the given expression has two terms, which are both perfect cubes:

27p^4 is the cube of (3p)^2, and

64pq^3 is the cube of (4q)^2.

Therefore, we can use the formula for the sum of two cubes:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

to factorize the given expression:

27p^4 + 64pq^3 = (3p)^2 + (4q)^2)(9p^2 - 12pq + 16q^2)

Now, we want to find the binomial that completes the factorization. We notice that the first factor (3p + 4q)(9p^2 - 12pq + 16q^2) is not a binomial, but a product of two binomials. So we focus on the second factor, which is a trinomial. We want to see if we can factor it further.

We can try to factor out a common factor of 3 from the first two terms and a common factor of 4 from the last two terms:

9p^2 - 12pq + 16q^2 = 3(3p^2 - 4pq) + 4(4q^2)

Now we can see that we have the difference of two squares:

3p^2 - 4pq = (p(3p - 4q))

4q^2 = (2q)^2

So we can write:

9p^2 - 12pq + 16q^2 = 3p(3p - 4q) + 4q^2

= (3p - 4q)(3p + 4q) + 4q^2

Now we can substitute this back into our original expression:

27p^4 + 64pq^3 = (3p + 4q)((3p)^2 - 3p(4q) + (4q)^2) + 4q^2

= (3p + 4q)(9p^2 - 12pq + 16q^2) + 4q^2

So the binomial that completes the factorization is 3p + 4q.

A rectangular floor with a length of 14 ft and a width of 6 ft, square tiles with an edge length of 3/4 ft, a total of 144 tiles can fit.

To determine how many square tiles can fit in a rectangular floor, we need to calculate the total number of tiles that can fit both horizontally and vertically.

Given:

Length of the rectangular floor = 14 ft

Width of the rectangular floor = 6 ft

Edge length of square tile = 3/4 ft

First, let's calculate the number of tiles that can fit horizontally:

Length of the rectangular floor / Edge length of square tile = 14 ft / (3/4 ft) = 14 ft × (4/3 ft) = 56/3 ft

Since we want a whole number of tiles, we need to round down or take the floor value:

Number of tiles horizontally = floor(56/3) = 18 tiles

Next, let's calculate the number of tiles that can fit vertically:

Width of the rectangular floor / Edge length of square tile = 6 ft / (3/4 ft) = 6 ft × (4/3 ft) = 24/3 ft

Again, we round down or take the floor value:

Number of tiles vertically = floor(24/3) = 8 tiles

To find the total number of tiles, we multiply the number of tiles horizontally by the number of tiles vertically:

Total number of tiles = Number of tiles horizontally × Number of tiles vertically = 18 tiles × 8 tiles = 144 tiles

Therefore, in a rectangular floor with a length of 14 ft and a width of 6 ft, square tiles with an edge length of 3/4 ft, a total of 144 tiles can fit.

for such more question on length

https://brainly.com/question/20339811

#SPJ8

Answer:

approximately 10 times

Step-by-step explanation:

I hope this helps!

It is expected that a vowel will be spun approximately 10 times.

Spinner is divided into 6 equal sectors labeled with the alphabets A to F

We know that, the vowels in english are A, E, I, O, U.

In between A and , there are 2 vowels, A and E.

Probabilty of getting vowel in 1 spin = \(\frac{2}{6}\) = \(\frac{1}{3}\) = 0.33

The spinner is spun 30 times.

It is expected that a vowel will be spun =  0.33 × 30 times

                                                                 = 9.9 times = 10 times (approx)

Learn more about Spinner problem here :

https://brainly.com/question/27494042

#SPJ2

The graph of the system of inequalities:

y  ≤ (1/4)*x - 2

y  ≥ −(5/4)x +2

Is in the image at the end.

Here we have the system of inequalities:

y  ≤ (1/4)*x - 2

y  ≥ −(5/4)x +2

To graph this, we just need to graph both of the linear equations, and we need to shade the region below the first line (the one with positive slope) and the region above the second line, the one with negative slope.

Then the graph of the system of inequalities is the graph you can see in the image at the end of the answer.

Learn more about system of inequalities at.

https://brainly.com/question/9774970

#SPJ1

The required value of trigonometric ratios is,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

We know that,

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Therefore,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

To learn more about triangles visit:

brainly.com/question/1058720

#SPJ1

Answer:

ssssss

Step-by-step explanation:

Answer:addidion

Step-by-step explanation:

Answer:

The answer is 1, 2, and 3 only

Step-by-step explanation:

Math

Way

The equations which have slope 1/4:

ii.  (y - 3.5) = 0.25(x - 2.75)

iii.  5x - 20y = 32

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope.

I. y = x - 5 is in slope-intercept form, so we can see that its slope is 1.

II. (y - 3.5) = 0.25(x - 2.75) can be rewritten in slope-intercept form as y = 0.25x + 2.1875. Therefore, its slope is 0.25 or 1/4.

III. 5x - 20y = 32 can be rewritten in slope-intercept form as y = (1/4)x - (4/5). Therefore, its slope is 1/4.

IV. 5x + 20y = 32 can be rewritten in slope-intercept form as y = (-1/4)x + (4/5). Therefore, its slope is -1/4.

So, only equations II, and III have a slope of 1/4.

To know more about Line check:

https://brainly.com/question/17188072

#SPJ3

The correct statement is: g(x) is translated up 5 units compared to f(x).

The correct answer is A.

The correct answer is A.

For such more questions on translated

https://brainly.com/question/12861087

#SPJ8

Step-by-step explanation:

C=2πR=πD=3.14*32=100.5 mm

With the help of Linear relationships The difference in the rate of change between the two containers is 1/5 gallon per minute.

what is Linear relationships?

A statistical word used to express a straight-line relationship between two variables is a linear relationship (or linear association). Graphs and mathematical equations of the form y = mx + b can both be used to represent linear relationships. In everyday life, linear relationships are quite prevalent.

Given:

Volume of water in each container.

To find:

Difference in the rate of change.

Solution:

Take any two points on container 1.

Let the points are (10, 2) and (20, 4).

m = (y2 - y1) / ( x2 - x1 )

   = ( 4 - 2 ) / ( 20 - 10 )

   = 2/ 10

   = 1/ 5

Rate of change for container 1 is .

Take any two points on container 2.

Let the points are (5, 2) and (10, 4).

m = (y2 - y1) / ( x2 - x1 )

   = ( 4 - 2 ) / ( 10 - 5)

   = 2 / 5

Rate of change for container 2 is 2/5

Difference = (2 /5 ) - ( 1/ 5 )

                  = 1 / 5  

Hence, The difference in the rate of change between the two containers is 1/5 gallon per minute.

To learn more about Linear relationships from the given link

https://brainly.com/question/13828699

#SPJ1

Answer:

Step-by-step explanation:

What is the solution to this equation?

6 * (x - 5) = 4x + 20

6x - 30 = 4x + 20

2x = 20 + 30

2x = 50

x = 50 : 2

x = 25

-------------------

check

6 * ( 25 - 5) = 4 * 25 + 20

6 * 20 = 100 + 20

120 = 120

the answer is good

Answer:

Step-by-step explanation:

6(x-5) 4x+20

Distribute.

6x-30 = 4x+20

Subtract 4x from each side.

6x-4x-30 = 4x-4x+20

Simplify.

2x-30=20

Add 30 to both sides.

2x-30+30 = 20+30

Simplify.

2x = 50

Divide both sides by 2

2x/2 = 50/2

Simplify

x = 25

So, x = 25!

Vector v can be written as the sum of two vector components, \(v_x = -5i\)  and \(v_y = 6j\)

To write vector v as the sum of two vector components, we need to decompose it into two vectors along different directions.

v = -5i + 6j

w = 3i + 4j

We can decompose vector v into two components, one along the x-axis and the other along the y-axis.

Let's denote the component along the x-axis as \(v_x\) and the component along the y-axis as \(v_y.\)

The x-component, \(v_x,\) represents the projection of vector v onto the x-axis and can be found using the dot product of v and the unit vector i:

\(v_x = v . i = (-5i + 6j) . i = -5i . i + 6j . i = -5\)

Similarly, the y-component, \(v_y,\) represents the projection of vector v onto the y-axis and can be found using the dot product of v and the unit vector j:

\(v_y = v . j = (-5i + 6j) . j = -5i . j + 6j . j = 6\)

Now, we can write vector v as the sum of its components:

\(v = v_x + v_y = -5i + 6j\)

So, vector v can be written as the sum of two vector components: -5i along the x-axis and 6j along the y-axis.

For similar question on components.

https://brainly.com/question/28351472  

#SPJ11

The algebric expression -1/4 + 3/5 is equal to 7/20 when simplified.

To solve the expression -1/4 + 3/5, we need to find a common denominator for the fractions and then perform the addition.

The common denominator for 4 and 5 is 20. We can rewrite the fractions with this denominator:

-1/4 = -5/20

3/5 = 12/20

Now that the fractions have the same denominator, we can add them:

-5/20 + 12/20 = (-5 + 12)/20 = 7/20

Therefore, -1/4 + 3/5 is equal to 7/20.

To further simplify the fraction, we can check if there is a common factor between the numerator and denominator. In this case, 7 and 20 have no common factors other than 1, so the fraction is already in its simplest form.

Thus, the final answer is 7/20.

For more such question on algebric expression. visit :

https://brainly.com/question/4344214

#SPJ8

From the first equation, we can rearrange to get x = 12 + y.

Substituting that into the second equation, we get y^2 = 5(12 + y - 2) = 50 + 5y.

This simplifies to y^2 - 5y - 50 = 0.

Using the quadratic formula, we can solve for y to get y = 10 or y = -5.

Therefore, two possible values of y are 10 and -5.

Step-by-step explanation:

first substitute -1 for W;

= 2.1 (-1) + 4.5

=-2.1 + 4.5

= 2.4