2 ^ (x + 3) * 3 ^ (x + 4) = 18

Answer:

Step-by-step explanation:

6.5

I don't see the picture. Can you send it in the message.

The surface area of the triangular prism is 136 square units

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

The surface area of the triangular prism is the sum of the areas of the above shapes

So, we have

Surface area = 2 * area of rectangle 1 + 1 * area of rectangle 2 + 2 * area of triangle 1

Substitute the known values in the above equation, so, we have the following representation

Surface area = 2 * 7 * 5 + 1 * 7 * 6 + 2 * 0.5 * 4 * 6

Evaluate

Surface area = 136

Hence, the surface area is 136 square units

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The average rate of change of the function at the interval 0 ≤ x ≤ 4 is 11.25

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

x  0   1   2   3  4   5

y 3   6  12   24 48 96

The interval is given as

0 ≤ x ≤ 4

On the table, we have

x = 0 and y = 3

x = 4 and y = 48

This means that

f(0) = 3 and f(4) = 48

The average rate of change is then calculated as

Average rate of change = [f(4) - f(0)]/[4 - 0]

Substitute the known values in the above equation, so, we have the following representation

Average rate of change = [48 - 3]/[4 - 0]

Evaluate

Average rate of change = 11.25

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Answer:

Solve the equation for [tex]{y}[/tex].

[tex]y=\frac{5x}{2}[/tex]

Choose any value for [tex]{x}[/tex] that is in the domain to plug into the equation.

Choose [tex]{0}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex]{(0,0)}[/tex]

Choose [tex]{1}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex](1,\frac{5}{2})[/tex]

Choose [tex]{2}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex]{(2,5)}[/tex]

These are three possible solutions to the equation.

[tex]{(0,0),}[/tex] [tex](1,\frac{5}{2} )[/tex], [tex]{(2,5)}[/tex]

44 is the proportion of the botched dressing will be olive oil.

Given, Miguel is mixing up a salad dressing. regardless of the number of servings,

the recipe requires that 58 of the finished dressing mix be olive oil, 14 vinegar, and the remainder an even mixture of salt, pepper and sugar. if he accidentally doubles the vinegar and forgets the sugar altogether,

we have to find the proportion of the botched dressing that will be olive oil.

first we will find the amount of the even mixture of salt, pepper and sugar.

as, olive oil + vinegar + even mixture of salt, pepper and sugar = 100

58 + 14 + mixture of salt, pepper and sugar = 100

mixture of salt, pepper and sugar = 100 - 72

mixture of salt, pepper and sugar = 28

if he mixed doubles of the vinegar i.e. 28 then olive oil be,

x + 28 + 28 = 100

x = 100 - 56

x = 44

Hence, 44 is the proportion of the botched dressing will be olive oil.

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Answer:

it's c trust me I had the same problem

Answer:

2/3 or 0.667

Step-by-step explanation:

5/9 ÷ 5/6

5/9 * 6/5

1/3 * 2/1 (after cancelling off)

= 2/3

The algebraic expression for "The room capacity does not exceed 250" is D. c≤250

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

It should be noted that "the room capacity does not exceed 250" simply means it should be less than or equal to 250. This will be c≤250.

In conclusion, the correct option is D.

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Answer:

The value of x is (-5)

Step-by-step explanation:

9x + 2 = 10x + 7

9x - 9x + 2 - 7 = 10x - 9x + 7 - 7

(-5) = x

x = (-5)

Thus, The value of x is (-5)

Answer:

180 ft^3

Step-by-step explanation:

volume of the pyramid = (1/3)(area of base) (height)

v= 1/3×(10×12÷2)×(9)

= 180 ft^3

Answer:

answer on the picture.....

Luka will require 24 cups of water to make lemonades as calculated from the data given.

The quantity of sugar which he use is twice the amount of lemon which he us ,

= 2 x 3 = 6

and ,

as we know the amount of water is 4 times as much as lemon juice

Therefore, amount of water

= 4 * 6

= 24

A quantity in a Maths equation is a number or variable plus any algebraic combination of additional quantities. In an equation like x + 6 = 15, four values are represented.

A quantity can be described as the amount of something or how much of it there is. Quantity can also be used to refer to the size of something (its magnitude), whether in terms of numbers, units of measurement, or just relative size.

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Answer:

D

Step-by-step explanation:

when we have the zeroes, we can build the polynomial by multiplying factors that will turn the functional value to 0 at exactly these points.

f(x) = (x - 3)(x + 6)(x - 1)

we don't need to do the full multiplications to see that the constant term of the polynomial is the result of the multiplication of all 3 constant terms of the factors :

-3 × +6 × -1 = +18

and therefore, D is the correct answer (as it is the only answer option with +18 as constant term).

Answer:

Step-by-step explanation:

it is c

The complete equation in the slope-intercept form is y = 4x-1.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

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

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

So, the equation is,

y - y₁ = m (x - x₁)

And the standard form of the slope-intercept form:

y = mx+b,

where m is the slope and b is the y-intercept.

From the question, we have

m = 4 and coordinates of b is (0, -1).

So, the equation is,

y + 1 = 4 (x - 0)

y +1 = 4x

y = 4x-1

Therefore, the equation is y = 4x-1.

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Answer:

[tex]\displaystyle \frac{9}{4}[/tex]

Step-by-step explanation:

[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} )[/tex]

The second term of this sum is an Infinite Geometric Progression
To find the sum of an Infinite Geometric Progression,

- Find the first term ( 1/5 ) of the progression and call it a
- Find the common ratio, (divide any term by it's predecessor. i.e [tex]\displaystyle \frac{\frac{1}{5^2} }{\frac{1}{5} } = \frac{5}{5^2} = \frac{1}{5}[/tex]) and call it r

Finding the sum of given Geometric Progression:
Sum of Infinite GP: [tex]\displaystyle \frac{a}{1-r}[/tex]

Plugging our values in this equation, we get:
Sum of Geometric Progression = [tex]\displaystyle \frac{\frac{1}{5} }{1 - \frac{1}{5} } = \frac{\frac{1}{5} }{\frac{5 - 1}{5} } = \frac{1}{4}[/tex]

Adding to find the actual answer:
[tex]\displaystyle (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = \frac{1}{4}[/tex]
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = 2 + \frac{1}{4}[/tex]
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = \frac{9}{4}[/tex]

We can conclude that the number of possible schedules for next semester could she make is 7920.

In more mathematical terms, the factorial of a number (n!) is equal to

n(n-1). For example, if you want to calculate the factorial for four, you would write: 4! = 4 x 3 x 2 x 1 = 24.

Given that,

The student needs 11 more classes to graduate.

And, possible schedules for next semester could she make if she plans to take 4 classes

Based on the given expression, the calculation is as follows:

The combination formula is given to be:

[tex]n_{C} _{r} =\frac{n!}{r!(n-r)!}[/tex]

= [tex]11_{C} _{4}[/tex] ! * 4 !

= [tex]\frac{11 !}{4!(11-4)!}[/tex]  * 4 !

= [tex]\frac{11!}{4!7!}[/tex] * 4 !

= [tex]\frac{11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1*7*6*5*4*3*2*1}[/tex] * 4 !

We can cancel the coefficients,

= [tex]\frac{11*10*9*8}{4*3*2*1}[/tex] * 4 !

= [tex]\frac{7920}{24}[/tex] * 4 !

= 330* 4 !

= 330 * 4*3*2*1

= 7920

Therefore,

We can conclude that the number of possible schedules for next semester could she make is 7920.

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$2,060.00 is the entire amount accrued from simple interest on a principal of $2,000.00 at a rate of 3% per year for 1 years, including principal and interest.

Ayden deposits $2000 into a savings account with an annual interest rate of 3%.

To calculate simple interest, multiply the daily interest rate by the principle and the number of days between payments. Consumers that make on-time or early monthly loan payments benefit from simple interest.

A = $2,060.00

I = A - P = $60.00

A is equal to P(1 + rt).

First, convert R percent to r a decimal; for example, R/100 is 3%/100, or 0.03 per year.

A = 2000(1 + (0.03 × 1)) = 2060 \sA = $2,060.00

$2,060.00 is the entire amount accrued from simple interest on a principal of $2,000.00 at a rate of 3% per year for 1 years, including principal and interest.

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The given exponential function represents the growth in the function. The percentage of growth (increase) is 1%.

An exponential growth function is a function where the quantity increases slowly and after some time, it increases rapidly.

It is represented by the formula,

y = a(1 + r)ˣ

Here the term 'a' is the initial amount of the quantity, the term 'r' is the rate of increase and the term 'x' is the period.

The given exponential function is y = 10(1.01)ˣ

Here we can write the function as

y = 10(1.01)ˣ

⇒ y = 10(1 + 0.01)ˣ

Since 1.01 > 1, it is an exponential growth function.

So, when comparing with the formula, we get the rate of increase,

r = 0.01

Converting it into fractions, we get 1/100

Then, the percentage rate of increase is 1%.

Therefore, the given exponential function grows with a rate of 1% increase.

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Answer: Tiffany

Step-by-step explanation: Ramon Ratio 8:2 can be reduced to 1 cup of sugar every 4 cups of water. Tiffany Ration is 9:3 which is reduced to 1 cup of sugar every 3 cups of water.

The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website will be;

⇒ 0.9375

The term probability refers to the likelihood of an event occurring

Given that;

The probability that a visitor is offered a coupon (p) = 50%

Now,

Since, The probability that a visitor is offered a coupon (p) = 50%

Hence, The probability that he gets coupon all 4 days is,

⇒ p (4) = p⁴

⇒ p (4) = (50%)⁴

⇒ p (4) = 0.0625

Hence, By using the complement rule, the probability that he is not offered a coupon at least one day is,

⇒ p' = 1 - 0.0625

⇒ p' = 0.9375

Thus, The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website = 0.9375

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The statement "cross-tabulation can only be used for two variables; each variable must have well-defined labels " is false

The cross tabulation is defined as the tool that is used in statistics to categorical data. We can also says that  that present the results of the entire group of respondents

The given statement is "cross-tabulation can only be used for two variables; each variable must have well-defined labels "

The cross tabulation method can be used to represent two or more variables. The cross tabulation table has x axis as one variable and y axis as another variables

The cross tabulation can be used for two or more variables

Therefore, the the given statement is false

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The given two consecutive positive integers are 9 and 10.

It is a whole number that can be positive, negative, or zero.

Let consider x and x+1 as two consecutive positive integers.

Given that,

[tex]x^{2} -21=6(x+1)[/tex]

[tex]x^{2} -6x-27=0[/tex]

It can be written in fractional form like,

(x-9)(x+3)=0

so the values of x are 9 and -3.

Here, only positive integers are considered.

Hence 9 and 10 are the two consecutive positive integers.

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Answer:

100/63

Step-by-step explanation:

6 2/3 ÷4 1/5

20/3÷21/5

20/3×5/21

1 37/63 or 100/63 or 1.587301587

so the answer is one (whole number) thirty seven over sixty three

The operations between functions are:

a) h(f(3)) = 5

b) (f×g)(4) = -8

c) f(  g(h(0))) -1

The first thing we want to find is a composition, we want to find:

h(f(3))

That means that we need to evaluate h(x) in f(3), look at the graph and you can see that f(3) = -4

Replacing that we get:

h(f(3)) = h(-4)

And on the graph, we can see that h(-4) = 5

then h(f(3)) = 5

b) Now we have the product:

(f×g)(4) = f(4)*g(4)

Again, looking at the graph:

f(4) = -4

g(4) = 2

Then:

(f×g)(4) = f(4)*f(4)

(f×g)(4) = -4*2

(f×g)(4) = -8

c) Finally we have other composition:

f(  g(h(0)))

So we have 2 compositions, first we find:

h(0) = 5

f(  g(h(0))) = f(g(5))

Then:

g(5) = 0

f(  g(5)) = f(0)

Finally, look at the graph and you can see that f(0) = -1

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The cubic polynomial with zeros (3,0), (-6,0) and (1,0) is given as follows:

D. x³ + 2x² - 21x + 18.

We are given the zeros of the polynomial, which then can be obtained using the Factor Theorem.

The zeros of the polynomial are given as follows:

x = 3, x = -6, x = 1.

Then, applying the Factor Theorem, considering a leading coefficient of 1, the polynomial is given as the product of it's linear factors as follows:

(x - 3)(x + 6)(x - 1)

(x² + 3x - 18)(x - 1)

x³ + 2x² - 21x + 18.

Meaning that option D is correct.

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A gap of 2.03 years has a value such that 60% of age disparities are smaller than it.

If the age is expressed as a ratio, such as p:q, then qx and px are taken into account as the age. If you assume that you are x years old now, then n times that number is (xn) years. If you're assuming that x is the current age, then 1/n of that number will equal (x/n) years.

calculation

Let's say there is an age difference of x and y,

in which case the answer to question 28 should be 2.03 years:

(x-y)*60/100.

A gap of 2.03 years has a value such that 60% of age disparities are smaller than it.

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The conclusion is that the angle which measures 120° is not Acute angle.

The construction of an angle is a type of geometric shape made by connecting two rays at their termini. Three letters that make up the form of the angle can alternatively be used to symbolise the angle, with the middle letter indicating the location of the angle (i.e.its vertex). Greek characters such θ, α, β, etc. are frequently used to denote angles.

In geometry, there are mainly six different kinds of angles. All angles have the following names and characteristics:

Angle B measures 120°.

Here the angle is more than 90° so the angle is not acute.

The conclusion is that the angle which measures 120° is not Acute angle.

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Answer:

97.8263768112

Step-by-step explanation:

Geometric Mean is denoted as 'x'

x = √(110×87)

x = √9570

∴ x = 97.8263768112

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A triangle with coordinates (1,1) (4,2) (3,5) is translated three units down and five units to the left. New coordinates will be (-4,-2), (-1,-1),(-2, 2).

A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.

Given

A triangle with coordinates (1,1) (4,2) (3,5)

The value of a coordinate is impacted by translations left or right but not by translations up or down or left or right.

We multiply all of the numbers by 3 since we are translating the entire triangle down three units.

Additionally, we are converting the entire triangle to left-to-right units of five, thus we will multiply all values by 5.

A = (1 - 5, 1 - 3)

B = (4 - 5, 2 -3)

C = (3 - 5, 5 - 3)

New coordinates will be:

A = (-4,-2)

B = (-1,-1)

C = (-2, 2)

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