What is the volume of this rectangular prism?

Answer:

the first option

Step-by-step explanation:

f(c)= 1/3p + 5/3

21 inch²

we splitthe two shapes, find the areas by multiplying the two sides and we add both of the answers, 15+6

Answer:

2(3) + 2(6) = 6 + 12 = 18 square feet

The unknown angle of the right angle triangle is as follows:

A right angle triangle is a triangle that has one of its angles as 90 degrees.  The sides of a right angle triangle can be named base on the position of the angles. The sides includes hypotenuse side, opposite side and adjacent side.

The sum of angles in a right angle triangle is 180 degrees.  Therefore, let's find the ∠C in the triangle ABC.

Therefore,

180 = ∠A + ∠B + ∠C

m ∠B = y + 40

m ∠C = 3y - 10

m ∠A = 90°

Hence,

180 = 3y - 10 + y + 40 + 90

180 = 4y + 120

180 - 120 = 4y

y = 60 / 4

y = 15

Hence,

m ∠C = 3(15) - 10

m ∠C = 45 - 10

m ∠C = 35 degrees

learn more on right angle triangle here: https://brainly.com/question/13737075

#SPJ1

Answer:

7/4

Step-by-step explanation:

To solve the given system of linear equations: 5z + 3 = 12, 4x + 4y + 20z = 10x + 10y + 50z = 30.

We can rewrite the equations in a more simplified form: 5z = 9 --> Equation 1, -6x - 6y + 30z = 0 --> Equation 2. Now, let's solve this system of equations: From Equation 1, we can solve for z: z = 9/5. Substituting this value of z into Equation 2, we have: -6x - 6y + 30(9/5) = 0, -6x - 6y + 54 = 0. Dividing through by -6: x + y - 9 = 0. Now we have two variables (x and y) and one equation relating them. We can express one variable in terms of the other, e.g., y = 9 - x. So, the solution to the system of equations is: x = x, y = 9 - x, z = 9/5.

In this solution, one variable (x) is arbitrary, and the other variables (y and z) are determined by it. Thus, the solution corresponds to "There are infinitely many solutions with one arbitrary parameter," which is option D.

To learn more about linear equations click here: brainly.com/question/32634451

#SPJ11

a. The value of n is 3/2

b. The value of a is 8.

c. The value of p is 125

The curve is an exponential function

An exponential function is a function of the form y = axⁿ where a and n are constants

Since y = axⁿ where a and n are constants, passes through the points (2.25, 27), (4, 64) and (6.25, p), substituting these points into the equation, we have

y = axⁿ

27 = a(2.25)ⁿ  (1)

64 = a(4)ⁿ        (2)

P = a(6.25)ⁿ     (3)

Dividing (2) by (1), we have

64/27 = a(4)ⁿ/a(2.25)ⁿ

4³/3³ = (4 ÷ 2¹/₄)ⁿ

4³/3³ = (4 ÷ ⁹/₄)ⁿ

4³/3³ = (4 ×  4/9)ⁿ

4³/3³ = (16/9)ⁿ

4³/3³ = (4²/3²)ⁿ

(4/3)³ = (4/3)²ⁿ

Equating exponents, we have

2n = 3

n = 3/2

The value of n is 3/2

Using equation (2)

64 = a(4)ⁿ        

a = 64/(4)ⁿ        

substituting n = 3/2 into the equation, we have

\(a = \frac{64}{4^{\frac{3}{2} } } \\= \frac{64}{(\sqrt{4 } )^{3} } \\= \frac{64}{2^{3} } \\= \frac{64}{8} \\= 8\)

So, the value of a is 8.

Using equation (3), we have

P = a(6.25)ⁿ     (3)

substituting the values of a and n into the equation,we have

\(P = 8(6.25)^{\frac{3}{2} } \\= 8(\sqrt{6.25}) ^{3} \\= 8(2.5}) ^{3} \\= 8(15.625})\\= 125\)

The value of p is 125

Learn more about exponential function here:

https://brainly.com/question/12940982

#SPJ1

Answer:

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a right triangle to represent the situation:

        |\

        | \

   h    |  \   9 ft

        |   \

        |    \

        |     \

        -------

        6 ft

Here, h represents the height on the wall where the ladder touches. We want to find the angle of elevation θ.

Using the right triangle, we can write:

sin(θ) = h / 9

cos(θ) = 6 / 9 = 2 / 3

We can solve for h using the Pythagorean theorem:

h^2 + 6^2 = 9^2

h^2 = 9^2 - 6^2

h = √(9^2 - 6^2)

h = √45

h = 3√5

So, sin(θ) = 3√5 / 9 = √5 / 3. We can solve for θ by taking the inverse sine:

θ = sin^-1(√5 / 3)

θ ≈ 37.5 degrees

Therefore, to the nearest tenth of a degree, the angle of elevation the ladder makes with the ground is 37.5 degrees.

Answer:

C. 7 because 7 x 7 = 49

Answer:

17t+9

Step-by-step explanation:

Answer:

perimeter = 17t +9 feet

Step-by-step explanation:

width W = 7t - 1.5

length L = 1.5t + 6

Perimeter = 2W + 2L

substitute expressions for W & L:  2(7t - 1.5) + 2(1.5t + 6)

expand:  14t - 3 + 3t + 12

collect like terms:  14t + 3t - 3 + 12

combine like terms: 17t +9

** can't give an exact value for the perimeter as don't have a value for t **

Answer:

x = 3

Step-by-step explanation:

Is x an exponent?

\( y = 3^x \)

\( 27 = 3^x \)

\( 3^3 = 3^x \)

\( x = 3 \)

The correct option is A. It can be solved by the concept of ratio and proportion.

What is ratio?

It is the way of representation of a quantity relative to the other quantity. Its symbol is :. For example size of 2 relative to 5 is represented by 2:5 or 2/5.

Total number of applicantas = 9

Accepted applicants             = 2

Not accepted applicants      = 9-2 = 7

Take the ratio of accepted to the not accepted applicants = 2/7

Now, if new not accepted applicants are x then accepted applicants are 360. To keep the ratio constant, the following equation must be satisfied:

\(\frac{2}{7}=\frac{360}{x}\\x=\frac{7}{2}\times 360\\x=1260\)

Hence, the correct option is A. It can be solved by the concept of ratio and proportion.

Learn more about the ratio and proportion from the followin link:

https://brainly.com/question/19994681

#SPJ1

Considering that y is between x and z, we have that:

We consider that y is between x and z, hence the length of the segment is given by:

xz = xy + yz

The separate lengths are given as follows:

Hence:

4k + 38 = 3k - 2 + 7k + 4.

4k + 38 = 10k + 2

6k = 36

k = 6.

Hence the length of yz is given by:

yz = 7k + 4 = 7(6) + 4 = 42 + 4 = 46 units.

A similar problem, in which the length of a line segment is found, is given by https://brainly.com/question/24778489

#SPJ1

There are 127 subsets of {1,2,3,4,5,6,7} that do not contain two consecutive integers, including the empty set.

Each number in the set {1,2,3,4,5,6,7} can either be included or not included in a subset.

So, the number of subsets of this set is:

However, we need to exclude the subsets that contain two consecutive numbers, such as {2,3} or {5,6}. This can be achieved by considering each number as the starting point of a subset and appending it with a number of non-consecutive numbers that can follow.

For example, if 1 is the starting point, the next numbers can only be 3, 4, 5, 6, or 7. Hence, the number of subsets starting from 1 is 5.

By repeating this process for each number in the set, we obtain a total of 5555551 = 127 subsets.

Learn more about subsets here: brainly.com/question/13265691

#SPJ4

Answer:

2x-2= -21

Step-by-step explanation:

Answer:

-9.5

Step-by-step explanation:

We can create an equation to represent this, where \(n\) is the missing value.

\(2n - 2 = -21\)

Now we can solve for \(n\) by isolating it on one side of the equation.

Add 2 to both sides:

\(2n - 2 + 2 = -21+2\\\\2n = -19\)

Divide both sides by 2:

\(2n\div2 = -19\div2\\\\n = -9.5\)

Hope this helped!

Answer:

$35

Step-by-step explanation:

25 x 1.4 = 35

The business cycle is a recurring pattern of economic expansion and contraction that occurs in economies over time. Each business cycle typically consists of four phases: expansion, peak, contraction, and trough.

The peak is the highest point of economic activity within a business cycle. It marks the end of the expansion phase and the beginning of the contraction phase. During this phase, economic indicators, such as GDP, employment, and consumer spending, reach their highest levels.

The peak is indeed a part of the business cycle. It represents the phase of maximum economic activity and is characterized by various indicators reaching their highest points. This phase is followed by the contraction phase, where economic activity slows down. Therefore, the peak is a crucial element in understanding and analyzing business cycles.

To learn more about business cycles

Click here brainly.in/question/8552279

#SPJ11

Answer:

The unit rate is 3:1: Demi solves 3 questions every minute.

Step-by-step explanation:

A simple way to find this is to device the questions by the time taken.

30 ÷ 10 = 3

Answer:

2

Step-by-step explanation:

1 + 1 = 2

also is this question a joke ?

A. can be used to test joint hypotheses.

In statistical analysis, F-statistics are used to compare the fit of two nested models, typically to test joint hypotheses. Maximum likelihood estimators are a popular method for estimating the parameters of a statistical model by maximizing the likelihood function. They are widely used in various fields due to their desirable properties, such as being consistent and asymptotically efficient.

When F-statistics are computed using maximum likelihood estimators, they can still be employed to test joint hypotheses. This involves comparing the difference in the log-likelihoods between two nested models, one being a restricted model and the other being an unrestricted model. The test statistic, in this case, follows an F distribution under the null hypothesis, which states that the restrictions imposed on the model are valid.

Learn more about non-linear models here: brainly.com/question/29470083

#SPJ11

Answer:

A realistic budget is hard to come by. All budgets tell you what you should include in your monthly plan, but what about unexpected expenses? Here are some ideas for making a realistic budget, and sticking to it.

daid1784 avatar

Well, the dozens of apps, spreadsheets, and other methods just don’t account for real life and all the expenses we don’t think of. There are plenty of expenses we have that aren’t monthly that take up more of our money than we planned.

Step-by-step explanation:

\(2\frac{2}{3}(x)=1/3\\x=(1/3)/2\frac{2}{3}\\x=\frac{1}{8}\)

Step-by-step explanation:

point slope formula: y-y1=m(x-x1)

m= y2-y1/x2-x1

input numbers

so slope:

m=(9--8)/(-7--8)

(-)×(-)=+

(+)×(-)=(-)

so m=17/1

m=17

now point slope

y--8=17(x--8)

y+8=17x+136

to get y alone we have to use opposite operations

y and 8 are adding so we need to subtract on both sides

y+8-8=17x+136-8

y=17x+128

the vertical asymptοtes οf the functiοn are given by: x = 3 and x = -3.

Asymptοtes are lines that a curve apprοaches but dοes nοt intersect as it extends infinitely in οne οr mοre directiοns. They can be vertical, hοrizοntal, οr οblique.

Vertical asymptοtes οccur when the denοminatοr οf a ratiοnal functiοn is equal tο zerο and the numeratοr is nοt equal tο zerο. This creates a pοint οf discοntinuity in the functiοn, where the functiοn apprοaches infinity οr negative infinity as it apprοaches the vertical line.

The functiοn y = 5tan(0.1x) has vertical asymptοtes whenever the tangent functiοn is undefined, which οccurs at οdd multiples οf π/2.

the vertical asymptοtes οf y = 5tan(0.1x) are given by:

x = (2n+1)π/2*10, where n is an integer.

Fοr Explοratiοn 4.3.3, Questiοn 2, the given functiοn is:

\(y = (x^2 - 5x + 6)/(x^2 - 9)\)

Tο find the vertical asymptοtes οf this functiοn, we need tο determine where the denοminatοr becοmes zerο. This οccurs at x = 3 and x = -3.

Therefοre, the vertical asymptοtes οf the functiοn are given by: x = 3 and x = -3.

Learn more about asymptotes, by the following link.

brainly.com/question/4138300

#SPJ1

Answer:

48.5 cm

Step-by-step explanation:

Let's see the formulas for areas of the shapes

Rectangle = length * width

Square = side^2

Triangle = 1/2(base*height)

Let's calculate area of rectangle first since it's easiest

Length  = 8cm

Width = 4cm

8*4 = 32 cm

Now, let's get area of square.

3cm * 3cm = 9cm

Now, the triangle.

Because one side of the square is 3cm, all of its sides are 3cm, therefore the base of the triangle = 3cm

The height is 8-3 = 5cm

Area of triangle = 1/2(b*h) = 1/2(5*3) = 15/2= 7.5cm

Add up all the areas we got earlier...

Area of Shape = 32cm + 9cm + 7.5 cm = 48.5cm

Answer:

58

Step-by-step explanation:

True. Rational functions are defined as the division of two polynomials. These functions are limited in their scope and, as a result, have specific properties. One such property is the existence of vertical asymptotes.

Vertical asymptotes occur when the denominator of a rational function approaches zero, resulting in a discontinuity in the graph of the function, or a point at which the function can approach but never reach. This creates a divide in the graph, resulting in two halves with a vertical line at the point where the denominator equals zero. This vertical line is the vertical asymptote of the rational function. In conclusion, all rational functions have vertical asymptotes due to their limited scope and specific properties.

To learn more about rational functions:

https://brainly.com/question/26087898

#SPJ4

The given triangles ABD and CBD are congruent because their corresponding sides and angles are equal.

Congruent triangles are two triangles that have exactly the same size and shape. In other words, all corresponding sides and angles of the two triangles are equal.

There are several ways to show that two triangles are congruent, including:

Side-Side-Side (SSS) Congruence: If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

Side-Angle-Side (SAS) Congruence: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Angle-Side-Angle (ASA) Congruence: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.

In the given triangles ABD and CBD, each of their angles is 60⁰, since the triangles are equilateral, so the triangles are congruent.

Learn more about congruent triangles here: https://brainly.com/question/2938476

#SPJ1

Answer:

y = 2x + 5

Step-by-step explanation:

For this question we have to use the equation y=mx+c

m represents the gradient

c represents where the line crosses the y-axis (the y-intercept)

1) Find the gradient

To find the gradient we have to divide the change in y by change in x

In this question that means we have to divide 2 by 1

2) Find the y-intercept

We can see that the line crosses the y-axis on the point (0,5) meaning the y-intercept is 5

y = 2x + 5

Hope this helps, have a lovely day! :)

Answer:no

Step-by-step explanation: