Find the total surface area of the triangular prism.

Answer:

180 - 127 = 53° The supplement of 127° is 53°. 127° is already greater than 90°. Therefore, there is no complement.

Step-by-step explanation:

Answer:

No, these two numbers are not complementary. 180 - 127 = 53° The supplement of 127° is 53°. 127° is already greater than 90°. Therefore, there is no complement.

Step-by-step explanation:

The class of the equation and the cross section equation are;

The equation is a hyperboloid of two sheets

The cross sections are;

Equation at z = 0 is; y²/8 - x²/8 = 1

Equation at y = -4 is; x²/8 + z² = 1

Equation at y = 0 is; x²/8 + z² = -1

Equation at y = 4 is; x²/8 + z² = 1

Equation at x = 0 is; y²/8 - z² = 1

An equation is a mathematical statement which indicates the equivalence two expressions by joining them with the '=' sign.

The equation can be presented as follows;

y² = x² + 8·z² + 8

y² - x² - 8·z² = 8

y²/8 - x²/8 - z² = 1

The above equation is the equation of an hyperboloid of two sheets, where;

a² = 8, b² = 1, and c² = 8

Please find attached the diagram of the surface, created with an online 3D graphing tool.

The equation for the cross section at z = 0, can be obtained by plugging in z = 0, into the equation as follows;

y²/8 - x²/8 - 0 = 1

y²/8 - x²/8 = 1

The above equation is the equation of an hyperbola in the xy plane

The equation for the cross section at y = -4, can be obtained by plugging in y = -4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 4²/8 = -1

- x²/8 - z² = -1

x²/8 + z² = 1

The above is an equation of an ellipse in the xz plane

The equation for the cross section at y = 0, can be obtained by plugging in y = 0, into the equation as follows;

0²/8 - x²/8 - z² = 1

- x²/8 - z² = 1

Therefore; x²/8 + z² = -1

The equation for the cross section at y = 4, can be obtained by plugging in y = 4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 2 = -1

x²/8 + z² = 1

The above equation is the equation of an ellipse in the xz plane

The equation for the cross section at x = 0, can be obtained by plugging in x = 0, into the equation as follows;

y²/8 - 0²/8 - z² = 1

y²/8 - z² = 1

The equation is the equation of an hyperbola in the yz plane

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Answer:

(7, -2)

Step-by-step explanation:

x + 3y = 1

-3x - 3y = -15

(x-3x) + (3y-3y) = 1-15

-2x + 0 = - 14

-2x = - 14

x = 7

x + 3y = 1

7 + 3y = 1

3y = 1-7

3y = -6

y = -2

Answer:

D: (7 , -2)

Step-by-step explanation:

Multiply each equation by the value that makes the coefficients of x

opposite.

(3)⋅(x+3y)=(3)(1)

−3x−3y=−15

Simplify

3x+9y=3

−3x−3y=−15

Add the two equations together to eliminate x

from the system.

3x+9y= 3

+     −3x−3y=−15

_____________

6y=−12

Divide each term by 6 and simplify.

y=−2

Substitute the value found for y into one of the original equations, then solve for x.

x=7

The solution to the independent system of equations can be represented as a point.

(7,−2)

The result can be shown in multiple forms.

Point Form:

(7,−2)

Equation Form:

x=7, y=−2

I hope this helps!!!!!!!

Answer:

area of triangle = 1/2×base×height

=1/2×20m×6m

= 20m×6m=120square metre

Answer:

Alright the answer for y+1 has to be less than 6. So the possible answers for   "y" is 1+1<6, 2+1<6, 3+1<6, 4+1<6. All of these ways can work.

anything greater than 6 is incorrect.

Answer:

Step-by-step explanation:

Given y + 1 < 6, solve for y.  To do this, subtract 1 from both sides:

y < 5

Now, because we have the < operator instead of  ≤  we know that y can never be 5; y must be less than 5.  Draw a dashed line through y = 5 and shade the area beneath this dashed line. Every point in the shaded area is a solution to the original inequality.

Both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

In triangle JKL, if angle J is less than 90 degrees, then angle K and angle L are both acute angles.

An acute angle is defined as an angle that measures less than 90 degrees. Since angle J is given to be less than 90 degrees, it is an acute angle.

In a triangle, the sum of the interior angles is always 180 degrees. Therefore, if angle J is less than 90 degrees, the sum of angles K and L must be greater than 90 degrees in order to satisfy the condition that the angles of a triangle add up to 180 degrees.

Hence, both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

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The independent variable while calculating the volume of a rectangular prisms with equal base area and different height is the height

The input values for a specific function are represented by the independent variable (x).

During an experiment, the independent variables are kept under control. The outputs of the function are represented by the dependent variable (y). The quantities being measured are the dependent variables in an experiment.

As regard the problem, the base area is a constant, the volume calculated is the dependent variable while the height iis the independent variable.

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Answer:

the answer is x=18 bc 90-72= 18 and the othet one is x=55 bc 180-125=55

Answer:

No, 92 is not a multiple of 8

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Some multiples of 8 is 8,16,24,32,40,48,56,64,72,80,88,and 96.

Answer:

See attached file.

Step-by-step explanation:

Answer:

I dont have one

Step-by-step explanation: I just need these 50 points srry :((((((((((

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

Answer:

\(\frac{9}{14}\) = 0.642857143

Step-by-step explanation:

\(\frac{1}{7}+\frac{1}{2}\)

Least common multiple of 7 and 2 is 14. Convert \(\frac{1}{7} and \frac{1}{2}\) to fractions with denominator 14.

\(\frac{2}{14} + \frac{7}{14}\)

Since \(\frac{2}{14} + \frac{7}{14}\) have the same denominator, add them by adding their numerators.

\(\frac{2+7}{14}\)

Add 2 and 7 to get 9.

\(\frac{9}{14}\)

Answer:

2,600,038

Step-by-step explanation:

If "t" number of years the study started and "y" denote the forest cover area, then the exponential-function representing the relation between "y" and "t" is y = 1500 × \((0.9225)^{t}\).

An "Exponential-Function" is a mathematical expression in which a constant (called the base) is raised to a variable power.

In this case, we want to find an exponential function that relates the area of a forest (y) to the number of years since the start of an environmental study (t).

We know that the forest is decreasing by 7.75% each year, which means that the area of the forest after "t years" will be some percentage of its original area.

The formula for an exponential function is y = a × \(b^{t}\), where "a" = initial value and "b" = growth or decay factor.

In this case, the initial area of the forest is = 1500 km², and

The forest is decreasing by 7.75% each year.

So, the "decay-factor" is = 1 - 0.0775 = 0.9225,

The exponential function that relates the area of the forest (y) to the number of years since the start of the study (t) is:

⇒ y = 1500 × \((0.9225)^{t}\),

Therefore, the required "exponential-function" is y = 1500 × \((0.9225)^{t}\).

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Answer:

-2

Step-by-step explanation:

Answer: A

Step by step explanation:

Answer: 5 inspections in 4 hours, because if its 8 hours it would be 10 inspections

Step-by-step explanation:

Answer:

1.25

Step-by-step explanation:

10 ÷ 8 = 1.25

Answer:

51°,51°,78°

Step-by-step explanation:

The sum of angles in a triangle add up to 180°

The required coefficients are:4, -1, -11, and 7.

Coefficients refer to the numerical values that are assigned to variables in mathematical equations, models, or formulas. They indicate the relative importance or contribution of each variable in the equation. Coefficients are used to determine the relationship between variables and are often estimated through statistical analysis or optimization techniques.

In algebraic equations, coefficients are the numbers multiplied by variables. For example, in the equation 2x + 3y = 5, the coefficients are 2 and 3.

In statistical models, such as linear regression, coefficients represent the slopes or weights assigned to the predictor variables. These coefficients indicate how much the response variable is expected to change for a unit change in the corresponding predictor variable, assuming all other variables are held constant.

We need to consider the polynomial:

(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)

To combine the like terms and find the coefficients of each term, we can write the polynomial in the following form:

4mn^2n - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn

Taking the coefficients of the terms with "mn^2"4mn^2n - mn^2

Taking the coefficients of the terms with "mn"-2mn - 9mn = -11mn

Taking the coefficients of the constant terms6 + 2 - 1 = 7

Therefore, the required coefficients are:4, -1, -11, and 7.

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Answer:

.333   .89   .778

Step-by-step explanation:

1. 4 divided by 12 = .333

2. 89/100= .89

3. 7/9 = .778

Answer:

1. 0.333 repeated

2. 0.89

3. 0.777 repeated

Step-by-step explanation:

You just divide 4 by 12 or 7 by 9

Also, just a tip, if you have a number over 100 like 89/100 0.89 would be the decimal, for example 26/100 would be 0.26

Answer:

$535.25

Step-by-step explanation:

539.50 - 39.50 = 504.00

504.00 - 23.75 = 480.25

480.25 + 55.00 = 535.25

The graph of the function f(x) = 4(2/3)^x is added as an attachment

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

f(x)=4⋅(

2

3

​)

x

Express the equation properly

So, we have

f(x) = 4(2/3)^x

The above expression is a an equation of a exponential function

Next, we plot the graph using a graphing tool

To plot the graph, we enter the equation in a graphing tool and attach the display

See attachment for the graph of the function

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\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7.5\% of 12.40}}{\left( \cfrac{7.5}{100} \right)12.40}\implies 0.93\)

Answer:

$0.93

Step-by-step explanation:

1) Turn 7.5% into a decimal which is 0.075

2) Multiply :

0.075 * 12.40 = $0.93 tax on the purchase

Second Part if you need to add :

1) Add :

$12.40 + 0.93 = $13.33

The graph of the function y = 5|x - 4| is added as an attachment

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

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Answer:

\(-15\geq x\geq 5\)

Step-by-step explanation:

X is between -15 and 5, the closed dots tell us we must include both -15 and 5 in the equation

The hypotenuse in a righ triangle is always in front of the right angle,

then, c is the hypotenuse. Then, Pythagorean theorem can be written as

which gives

By applying square root to both side, we get

Therefore, the missing side (which is the hypotenuse in this case) is equal to 16.6433 units.