Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2

Answer:

the answer is c) 80

all angles of the Triangle will have a sum of 180. 80+20=100 ... 180-100= 80

Answer:

B

Step-by-step explanation:

y = - |x-4|+8  ... f(x)

==> y= -|x-1|+3   ... y = f(x+3) - 5   .. horizontal translate left 3 units and

                                                      vertical translate down 5 units

Answer:

a)  zero triangles.

b)  one triangle.

Step-by-step explanation:

In triangle ABC:

Given:

Law of Sines

\(\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

To determine if any triangles are possible, substitute the given values into the Law of Sines to find angle B:

\(\implies \sf \dfrac{\sin 51^{\circ}}{10}=\dfrac{\sin B}{28}\)

\(\implies \sf \sin B=\dfrac{28\sin 51^{\circ}}{10}\)

\(\implies \sf \sin B=2.176008...\)

As -1 ≤ sin B ≤ 1, there is no solution for angle B.

Therefore, zero triangles are possible.

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

Given:

Law of Sines

\(\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

To determine if any triangles are possible, substitute the given values into the Law of Sines to find angle A:

\(\implies \sf \dfrac{\sin A}{24}=\dfrac{\sin 30^{\circ}}{12}\)

\(\implies \sf \sin A=\dfrac{24\sin 30^{\circ}}{12}\)

\(\implies \sf \sin A=1\)

\(\implies \sf A=\sin^{-1}(1)\)

\(\implies \sf A=90^{\circ}\)

Therefore, one triangle is possible (see attachment).

Answer:

A. The hulls of the drekar were shallow and fat so the ships rode high in the water.

Step-by-step explanation:

Hope this helps :)

Answer:

f(3) = -2

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

f(3) is simply asking for the y-value when x = 3. According to the graph, when x = 3, y = -2.

Therefore, f(3) = -2

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

for more search question point  

https://brainly.com/question/28162977

#SPJ8

When creating a scatterplot, it is important to carefully consider which variable to place on the vertical and horizontal axes.

The vertical axis is commonly used to represent the response or dependent variable, while the horizontal axis is used for the explanatory or independent variable.

However, when dealing with a categorical variable, there is no inherent order or numerical relationship between the categories. Thus, it does not make sense to use either axis as a response or explanatory variable. In this case, the categorical variable should be placed on either axis based on what makes the most sense for the data being displayed.

If there is an explanatory variable and a response variable, the explanatory variable should be placed on the horizontal axis and the response variable on the vertical axis. This is because the explanatory variable is usually the variable that is being manipulated or controlled, while the response variable is the one that is being measured or observed.

Overall, the placement of variables on the axes of a scatterplot should be based on the nature of the data being displayed and the relationship between the variables being studied.

To know more about a scatterplot click here:

brainly.com/question/30017616

#SPJ4

Answer:

\(x+2y-z=5 ...(1)\\ -x-y+2z=-13...(2) \\ 2x+y-2z=14...(3) \\ \\ add \: (2) + (3) \\\boxed{x= 1} \\ 2 \times (1) + (2) \\ x + 3y = - 3 \\ 1 + 3y = - 3 \\ 3y = - 4 \\ \boxed{y = - \frac{4}{3} }\\ solve \: for \: z \\ x + 2y - z = 5 \\ 1-\frac{4}{3}(2)-z=5\\3-8-3z=15\\3z=-20\\\boxed{z = - \frac{20}{3} }\)

The value of y from x= 0 to x = 3 is: y = 5(2)⁰ = 5, y = 5(2)¹ = 10, y = 5(2)² = 20, y = 5(2)³ = 40. The most rapid rate of change is: y = 7ˣ. The constant 1.20 is greater than 1 thus, the function is exponential growth.

The formula for an exponential function is f (x) = axe, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

The given function is:

y = 5(2)ˣ

The value of y from x= 0 to x = 3 is:

y = 5(2)⁰ = 5

y = 5(2)¹ = 10

y = 5(2)² = 20

y = 5(2)³ = 40

The most rapid rate of change as x increases beyond 0 is:

y = 7ˣ

This is observed as the graph increases rapidly with change in value of x.

3. y = (1.20)ˣ

The constant 1.20 is greater than 1 thus, the function is exponential growth.

Learn more about exponential function here:

https://brainly.com/question/15352175

#SPJ1

Answer:

9:20

Step-by-step explanation:

The ratio of the surface area of similar solid is equal to the square of the ratio of their corresponding linear measures.

If the ratio of their corresponding linear measures is a:b, the surface area ratio will be (a/b)².

Therefore, (A/B )² = 9/16

square root both sides A/B = √9/√16 A/B = 3/4 A:B = 3:4

The ratio of volume of two similar solid is the ratio cube of their corresponding linear measures.

Therefore, (B/C)³ = 27/125 cube root both sides B/C = 3/5 B:C = 3:5

To make the ratio equivalent A:B:C = 9:12:20

A:C = 9:20

The polygon is a decagon, measure of one interior angle  is equal to the sum of the interior angles divided by the number of sides and measure of an interior angle  is (n - 2) * 180 and the toal  measures of the interior angles  polygon of six sides are 1080.

A polygon is a closed two-dimensional shape composed of straight line segments. The sides of a polygon are joined together to form a single shape. Polygons can be categorized into different types, such as triangles, quadrilaterals, pentagons, hexagons, and octagons. A decagon is a 10-sided polygon. It is a two-dimensional figure with ten edges and ten vertices. It is a type of polygon that has interior angles that add up to 1440 degrees. It is a regular polygon, meaning all of its sides are of equal length and its angles are equal. It is often used in architecture, design, and engineering for decoration and structural purposes. Decagons can also be found in nature, such as in some snowflakes and in the seeds of some flowers. Decagons are versatile shapes that have numerous applications and are a popular choice for both decorative and practical reasons.

To know more about polygons refer to the  link  brainly.com/question/24464711

#SPJ4

Answer:

20People

Step-by-step explanation:

Buying of a picture = $4

if the total revenue made after people bought it was $80

Total number of people who bought it

= $80/$4

=20People

A. The solution of  linear equation is (x, y) = (-3, 8).

B. The solution is (x, y) = (3/4, -1).

C. The solution is (x, y) = (-31/8, 3/8).

D. The solution is (x, y) = (55/7, -117/14).

A. 3x - y = -11 --- (1)

-x + y = 5 --- (2)

From equation (2), we can write y = x + 5, and substitute it in equation (1):

3x - (x + 5) = -11

2x = -6

x = -3

Substituting x in equation (2):

-y = -8

y = 8

Therefore, the solution of the system is (x, y) = (-3, 8).

To check the solution, we substitute the values of x and y in the original equations:

3(-3) - 8 = -11 (True)

-(-3) + 8 = 5 (True)

So, the solution is correct.

B. -2y + 3 = 4x + 2 --- (1)

6x + 4y = 1 --- (2)

From equation (1), we can write 4x + 2 = -2y + 3, and substitute it in equation (2):

6x + 4y = 1

6x - 4y = 8 (rearranging)

12x = 9

x = 3/4

Substituting x in equation (1):

-2y + 3 = 4(3/4) + 2

-2y + 3 = 5

-2y = 2

y = -1

Therefore, the solution of the system is (x, y) = (3/4, -1).

To check the solution, we substitute the values of x and y in the original equations:

-2(-1) + 3 = 4(3/4) + 2 (True)

6(3/4) + 4(-1) = 1 (True)

So, the solution is correct.

C. 32y - x = -25 --- (1)

5x = 100 + x - 8y --- (2)

From equation (2), we can write 4x = 100 - 8y, and substitute it in equation (1):

32y - x = -25

32y - (100 - 8y) = -25

40y = 75

y = 3/8

Substituting y in equation (1):

32(3/8) - x = -25

x = -31/8.

Therefore, the solution of the system is (x, y) = (-31/8, 3/8).

To check the solution, we substitute the values of x and y in the original equations:

32(3/8) - (-31/8) = -25 (True)

5(-31/8) = 100 + (-31/8) - 8(3/8) (True)

So, the solution is correct.

D. To solve the system of equations:

2y + 3x = 6 --- (1)

4x + 5y + 20 = 0 --- (2)

We can rearrange equation (2) to isolate one of the variables:

4x + 5y = -20 (subtracting 20 from both sides)

5y = -4x - 20 (subtracting 4x from both sides)

y = (-4/5)x - 4 (dividing both sides by 5)

Substituting this value of y in equation (1):

2((-4/5)x - 4) + 3x = 6

(-8/5)x - 8 + 3x = 6

(-8/5)x + 3x = 14

(-8/5 + 3)x = 14

(-8/5 + 15/5)x = 14

(7/5)x = 14

x = 10

Substituting this value of x in the equation for y:

y = (-4/5)(10) - 4

y = -12.

Therefore, the solution of the system is (x, y) = (10, -12).

To check the solution, we substitute the values of x and y in the original equations:

2(-12) + 3(10) = 6 (True)

4(10) + 5(-12) + 20 = 0 (True)

So, the solution is correct.

For similar question on linear equations.

https://brainly.com/question/2030026

#SPJ11

The correct answer is B. The sample represents a proportion of the population.

A point estimate is a single value used to estimate a population's unknown parameter. The sample proportion (denoted by p), in the context of determining the population proportion, is a widely used point estimate. The sample proportion is determined by dividing the sample's success rate by the sample size.

The sample must be representative of the population for it to be a reliable point estimate of the population proportion. To accurately reflect the proportions of various groups or categories present in the population, the sample should be chosen at random.

Learn more about population:https://brainly.com/question/30324262

#SPJ1

Solution

- We are given the following formula:

- We are told that the Initial mass is 50g, the decay rate is .0491593745, time (t) is 10 hours, and e = 2.71828.

- With the above information, we can proceed to substitute the values given into the formula and get the mass of Uranium after 10 hours.

- This is done below:

Final Answer

The answer is 30.58254g (OPTION B)

Answer:

the answer is 2 :)

have a good day !!

Step-by-step explanation:

Answer:

B. A sample of 500 adults who are asked their opinion about a recent law enacted.

Step-by-step explanation:

The population would be more accurately described by 500 regular people than politicians

Answer:

75% may also be expressed as 75/100=3/4 or as 0.75 as needed.

Let x = the number

Translate:

 "if 75% of a number is 60"       means

     (75/100)  *  x      =  60            [the word "of" usually means multiply]

     (3/4) x = 60                           [reduce or just write it this way]

        x  = 60(4/3)                       [multiply both sides by  4/3]

        x = 80

Step-by-step explanation:

Answer:

x = 41.2

Step-by-step explanation:

Assuming the dotted line at the top is parallel to the segment with length x, it follows from the alternate interior angles theorem that the interior angle of the triangle (marked in diagram) is also 27º.

Using SOH-CAH-TOA, we get that tan(27º) = 21/x, so x = 21/tan(27º), which is approximately equal to 41.2.

Answer:

  350

Step-by-step explanation:

Answer:

the funtion does not satisfies the hypothese f(a)=f(b), just because when evaluate f(0) = 1 and when evaluate f(2) = 11,

Given data:

The given slope of the line is m=3/7.

The slope of the line parallel to the given line is,

m'=m

m'=3/7

Thus, option H) is correct.

Answer:

∠ BDC = 29°

Step-by-step explanation:

the sides of a rhombus are congruent, so CD = ED and Δ EDC is therefore isosceles with base angles congruent , then

∠ BCD = ∠ BED = 61°

• the diagonals are perpendicular bisectors of each other , then

∠ CBD = 90°

the sum of the 3 angles in Δ BCD = 180°

∠ BDC + ∠ CBD + ∠ BCD = 180°

∠ BDC + 90° + 61° = 180°

∠ BDC + 151° = 180° ( subtract 151° from both sides )

∠ BDC = 29°

Answer:

a decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point. The dot in a decimal number is called a decimal point. The digits following the decimal point show a value smaller than one.

Step-by-step explanation:

Answer:

The expected value of the number of letters in the selected person's home state is 6.64.

Step-by-step explanation:

What is the expected value of the number of letters in the selected person's home state

52% have 8 letters(Missouri).

28% have 6 letters(Kansas)

20% have 4 letters(Iowa).

So

\(E = 0.52*8 + 0.28*6 + 0.2*4 = 6.64\)

The expected value of the number of letters in the selected person's home state is 6.64.

The expected value of the number of letters in the selected person's home state will be 6.64.

52% are from MISSOURI of 8 letters.

28% are from KANSAS of 6 letters.

20% are from IOWA of 4 letters.

The expected value of the number of letters in the selected person's home state is required.

Let's consider the expected value E

So, 52% of 8 + 28% of 6 + 20% of 4 = E

\(\rm 0.52\times8+0.28\times6+0.2\times4=E\\\rm E= 4.16+1.68+0.8\\\rm E=6.64\)

The expected value of the number of letters in the selected person's home state will be 6.64.

Learn more about the expected values here:

https://brainly.com/question/3913865

Answer:

z > -4/5

Step-by-step explanation:

-9 - (2z - 7) > -2z - 6 - 5z

Get rid of the parenthesis

-9 - 2z + 7 > -2z - 6 - 5z

Combine like terms:

       -2 - 2z > -7z - 6

       +2       >       +2

Add 2 to both sides.

 -2z > -7z - 4

 +7z > +7z

Add 7 to both sides.

5z > -4

Divide both sides by 5 to get z.

z > -4/5

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

More on inequalities: https://brainly.com/question/21857626

Hope this helps! :)

The remainder of the polynomial division \(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)}\) is 2y²

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

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)}\)

When the numerator is expanded, we have

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = \frac{(y - 1)(y^3 + 1) + 2y^2}{y^3 + 1}\)

Split the expanded expression

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = \frac{(y - 1)(y^3 + 1)}{y^3 + 1} + \frac{2y^2}{y^3 + 1}\)

Evaluate

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = y - 1 + \frac{2y^2}{y^3 + 1}\)

From the above, we have

Quotient = y - 1

Remainder = 2y²

Hence, the remainder of the polynomial division is 2y²

Read more about polynomial division at

https://brainly.com/question/7693326

#SPJ1

Step-by-step explanation:

For a vector-valued function

\(\mathbf f(\mathbf x)=\mathbf f(x_1,x_2,\ldots,x_n)=(f_1(x_1,x_2,\ldots,x_n),\ldots,f_m(x_1,x_2,\ldots,x_n))\)

the matrix of partial derivatives (a.k.a. the Jacobian) is the \(m\times n\) matrix in which the \((i,j)\)-th entry is the derivative of \(f_i\) with respect to \(x_j\):

\(D\mathbf f(\mathbf x)=\begin{bmatrix}\dfrac{\partial f_1}{\partial x_1}&\dfrac{\partial f_1}{\partial x_2}&\cdots&\dfrac{\partial f_1}{\partial x_n}\\\dfrac{\partial f_2}{\partial x_1}&\dfrac{\partial f_2}{\partial x_2}&\cdots&\dfrac{\partial f_2}{\partial x_n}\\\vdots&\vdots&\ddots&\vdots\\\dfrac{\partial f_m}{\partial x_1}&\dfrac{\partial f_m}{\partial x_2}&\cdots&\dfrac{\partial f_n}{\partial x_n}\end{bmatrix}\)

So we have

(a)

\(D f(x,y)=\begin{bmatrix}\dfrac{\partial(e^x)}{\partial x}&\dfrac{\partial(e^x)}{\partial y}\\\dfrac{\partial(\sin(xy))}{\partial x}&\dfrac{\partial(\sin(xy))}{\partial y}\end{bmatrix}=\begin{bmatrix}e^x&0\\y\cos(xy)&x\cos(xy)\end{bmatrix}\)

(b)

\(D f(x,y,z)=\begin{bmatrix}\dfrac{\partial(x-y)}{\partial x}&\dfrac{\partial(x-y)}{\partial y}&\dfrac{\partial(x-y)}{\partial z}\\\dfrac{\partial(y+z)}{\partial x}&\dfrac{\partial(y+z)}{\partial y}&\dfrac{\partial(y+z)}{\partial z}\end{bmatrix}=\begin{bmatrix}1&-1&0\\0&1&1\end{bmatrix}\)

(c)

\(Df(x,y)=\begin{bmatrix}y&x\\1&-1\\y&x\end{bmatrix}\)

(d)

\(Df(x,y,z)=\begin{bmatrix}1&0&1\\0&1&0\\1&-1&0\end{bmatrix}\)