Se muestran resultados de an architect builds a scale model of a building he is designing. the scale model is 1/30 of the original size of the building. The height, in inches of the scale model is 14 inches. Determine the height in inches of the building.

Answer:

\( \displaystyle\theta = {30}^{ \circ} \)

Step-by-step explanation:

we would like to solve the following equation:

\( \displaystyle\sin( \theta) = \frac{5}{10} \)

notice that, the fraction can be reduced therefore reduce fraction:

\( \displaystyle\sin( \theta) = \frac{ \cancel{5 \: }}{ \cancel{1 0} _{2} } \)

\( \displaystyle\sin( \theta) = \frac{1}{2} \)

by trigonometric value table we obtain:

\( \displaystyle\sin( \theta) = \sin( {30}^{ \circ} ) \)

get rid of sin:

\( \displaystyle\theta = {30}^{ \circ} \)

and we are done!

Answer:

\( \displaystyle\theta = {30}^{ \circ} \)

Step-by-step explanation:

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If one pound 1.2 euros then 14 pounds is 21 euros.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity

Given that 1 pound is 1.2 euros

We have to find 14 pounds in euros

To do this we just need to multiply 14 with 1.2

14×1.5

21 euros

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Answer:

∠ 1 = 155° , ∠ 2 = 25°

Step-by-step explanation:

the 2 angles are adjacent angles and sum to 180° , that is

5x + x - 6 = 180

6x - 6 = 180 ( add 6 to both sides )

6x = 186 ( divide both sides by 6 )

x = 31

then

∠ 1 = 5x = 5(31) = 155°

∠ 2 = x - 6 = 31 - 6 = 25°

The present value (PV) of the investment today is approximately $2,965.05.

To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.

The formula for the present value of an annuity is given by:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present Value

C = Cash flow per period

r = Interest rate per period

n = Number of periods

In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.

Let's plug in these values into the formula and calculate the present value (PV):

PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]

Using a calculator, we can evaluate the expression inside the brackets:

PV = $500 * [(1 - 0.376889) / 0.105]

Simplifying further:

PV = $500 * [0.623111 / 0.105]

PV = $500 * 5.930105

PV = $2,965.05

Therefore, the present value (PV) of the investment today is approximately $2,965.05.

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The result of the unknown variable x is equivalent to 7

Linear equations are equation that has a leading degree of 1. Given the expression below:

5(3x − 15) + 16 = 5x + 11

Expand the expression

5(3x) - 5(15) + 16 = 5x + 11

15x - 75 + 16 = 5x + 11

15x - 5x - 59 - 11 = 0

10x - 70 = 0

10x = 70

Divide both sides by 10

10x/10 = 70/10

x = 7

Hence the value of x makes the equation true is 7

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The six terms of the series 247 are 2, 2, 2, 2, 2, and 2.

To find the six terms of a series, we need to first understand what a series is. A series is defined as the sum of the terms of a sequence. A sequence is a set of numbers in a specific order.

Therefore, a series is a sum of terms from a sequence. There are different types of series, and they have different formulas for calculating their terms.In this case, we are required to find the six terms of the series 247. Since this is a finite series, we can use a formula to calculate the nth term of a finite series.

The formula is given as follows:Tn = a + (n - 1) dWhere Tn is the nth term of the series, a is the first term of the series, n is the number of terms in the series, and d is the common difference between the terms of the series.To find the six terms of the series 247, we need to know the value of a and d. In this case, we can see that the first term of the series is 2. Therefore, a = 2.

Since this is a constant series, we can see that the common difference between the terms is 0. Therefore, d = 0.Substituting these values in the formula, we get:T1 = a + (1 - 1) dT1 = 2 + 0T1 = 2T2 = a + (2 - 1) dT2 = 2 + 0T2 = 2T3 = a + (3 - 1) dT3 = 2 + 0T3 = 2T4 = a + (4 - 1) dT4 = 2 + 0T4 = 2T5 = a + (5 - 1) dT5 = 2 + 0T5 = 2T6 = a + (6 - 1) dT6 = 2 + 0T6 = 2.

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The values of x for the right triangles are:

a. x = 1/3

b. x = 3.0952

The vertical height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

a. (6x +2)/(9x - 2) = 8/10

8(9x - 2) = 10(6x +2) {cross multiplication}

72x - 60x = 20 - 16 {expand the and collect like terms}

12x = 4

x = 4/12

x = 1/3

b. (2x + 6)/16 = 16/21

21(2x + 6) = 256 {cross multiplication}

42x = 256 - 126 {expand the and collect like terms}

42x = 130

x = 130/42

x = 3.0952

Therefore, the values of x for the right triangles are:

a. x = 1/3

b. x = 3.0952

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The area of the circle circumscribed about the right triangle with legs 6 and 8 is approximately 78.54 square units.

To find the area of the circle circumscribed about a right triangle, we can use the fact that the diameter of the circle is equal to the hypotenuse of the right triangle. In this case, the legs of the right triangle are given as 6 and 8.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

\(c^2 = a^2 + b^2\)

where c is the length of the hypotenuse, and a and b are the lengths of the legs.

Substituting the values:

\(c^2 = 6^2 + 8^2\)

\(c^2 = 36 + 64\\ c^2 = 100\)

Taking the square root of both sides:

\(c = \sqrt{100} \\ c = 10\)

Therefore, the length of the hypotenuse is 10 units.

Since the diameter of the circumscribed circle is equal to the hypotenuse, the radius of the circle is half the length of the hypotenuse, which is 10/2 = 5 units.

Now we can calculate the area of the circle using the formula:

Area = π \(r^2\)

where r is the radius of the circle.

Area = π \(5^2\)

Area = π × 25

Area = 78.54 square units

Hence, the area of the circle circumscribed about the right triangle with legs 6 and 8 is approximately 78.54 square units.

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Answer:

I have completed the answers and attached them to the explanation.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question asks for a subtraction expression:

length is always a positive number so bigger number first here.

OB = 4-(-1)              >only moves in x direction so subtract x's

AB = 4-(-2)             >only moves in y direction so subtract y's

If the archaeologist found a fossil whose length is 489.44 inches, using the conversion table, the length in feet, to the nearest tenth, is 40.8 feet.

The conversion table refers to the tabulated standard units of measurement, showing temperature, length, area, volume, weight, and metric conversions

For instance, the conversion table shows that 12 inches equal 1 foot.

The length of the fossil = 489.44 inches

12 inches = 1 foot

489.44 inches = 40.8 feet (489.44 ÷ 12)

Thus, using the conversion table, which relies on multiplication or division operations using the conversion factors, the length in feet of the fossil is 40.8 feet.

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Both balls will strike the ground simultaneously, but the faster ball will do so farther away from the table.

The unit g stands for gravitational acceleration. At sea level, the standard value of g on earth's surface is 9.8 m/\(s^{2}\)

They will strike the ground simultaneously if the table and the ground are both flat.

It is customary to divide an object's motion into a vertical component and a horizontal component. While they are on the table, neither of the balls is moving vertically. Both balls begin to accelerate downward as soon as they leave the table due to the effects of gravity. Given that both balls experience the same acceleration from gravity, they will fall at the same rate and with the same downward velocity.

Both balls will strike the ground simultaneously, but the faster ball will do so farther away from the table.

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Answer:

should have divided it directly ........ maybe or it's just messy........ maybe

Step-by-step explanation:

..........

...........

8x + 16 = 36

8x = 36 - 16

8x = 20

x = 20 / 8

x = 2.5

Answer:

x = | 1 |

Step-by-step explanation:

how are u in college doing this???

Answer:

1

Step-by-step explanation:

(x+8)=9

x+8=9

x=9-8

x=1

A graph is a way to represent a lot of data in such a visual format. The correct option is C, he/she should use graph B.

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.

If an employee wants to request a raise, the graph he/she should use to support his or her case is graph B. Because that graph is showing all thought the company is earning good profit the salary of the employees is still reducing.

Hence, the correct option is C, he/she should use graph B.

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To solve the savings plan balance, we have to calculate the interest for 19 months. The formula for calculating interest for compound interest is given below:$$A = P \left(1 + \frac{r}{n} \right)^{nt}$$where A is the amount, P is the principal, r is the rate of interest, t is the time period and n is the number of times interest compounded in a year.

The given interest rate is 11% per annum, which will be converted into monthly rate and then used in the above formula. Therefore, the monthly rate is $r = \frac{11\%}{12} = 0.0091667$.

The monthly payment is $PMT = $250. We need to find out the amount after 19 months. Therefore, we will use the formula of annuity.

$$A = PMT \frac{(1+r)^t - 1}{r}$$where t is the number of months of the plan and PMT is the monthly payment. Putting all the values in the above equation, we get:

$$A = 250 \times \frac{(1 + 0.0091667)^{19} - 1}{0.0091667}$$$$\Rightarrow

A = 250 \times \frac{1.0091667^{19} - 1}{0.0091667}$$$$\Rightarrow

A =250 \times 14.398$$$$\Rightarrow A = 3599.99$$

Therefore, the savings plan balance after 19 months with an APR of 11% and monthly payments of $250 is $3599.99 (approx).

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Answer:

Step completed incorrectly:  2

Correct Answer: y = -4x + 22

Step-by-step explanation:

The graph is a straight line through points M(4, -1) and N(8, 0).  Point Q is located at (6, -2).

To calculate the slope of the line, substitute the points into the slope formula:

\(\textsf{Slope $(m)$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-(-1)}{8-4}=\dfrac{1}{4}\)

Therefore, the slope of MN is 1/4, so step 1 of Francisco's calculations is correct.

If two lines are perpendicular to each other, the slopes of these lines are negative reciprocals. The negative reciprocal of a number is its negative inverse.

The negative reciprocal of 1/4 is -4.

Therefore, the slope of the perpendicular line is -4.

So Francisco has made an error in his calculation in step 2 by not making the perpendicular slope negative.

Corrected work

\(\textsf{Step 1:} \quad \sf slope\;of\;MN:\; \dfrac{1}{4}\)

\(\textsf{Step 2:} \quad \sf slope\;of\;the\;line\;perpendicular:\; -4\)

\(\begin{aligned}\textsf{Step 3:} \quad y-y_1&=m(x-x_1)\;\; \sf Q(6,-2)\\y-(-2)&=-4(x-6)\end{aligned}\)

\(\textsf{Step 4:} \quad y+2=-4x+24\)

\(\textsf{Step 5:} \quad y+2-2=-4x+24-2\)

\(\textsf{Step 6:} \quad y=-4x+22\)

Therefore, step 2 has been completed incorrectly.

The correct answer is y = -4x + 22.

The solving linear equation states that the temperature of the oven is 119 after an minute.

A linear equation is just an algebraic equation of something like the form y=mx+b that only contains a constant and a first-order (linear) component, where m represents the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where y and x are now the variables.

Given:

y = 40x+79

X = number of minutes using it to bare:

When X = 1

y = 40(1)+79

y = 119

It means that the temperature of the oven is 119 after an minute.

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Answer:

f(8) = 0

Step-by-step explanation:

The definition of an x intercept is a point where the function is equal to zero.

Answer:

246.76$

Step-by-step explanation:

199 x .24 =

47.76

199 + 47.76 =

246.76

Answer:

a. rad27

Step-by-step explanation:

we can use a2+b2=c2 where c is the hypotonuse.

we plug in 3^2+b2=6^2

9+b^2=36

b^2=27

then do a rad over each to get rid of the ^2 on the b

b=rad 27

answer is rad27

Answer:

Let's start by assigning a variable to Susan's present age. Let's call it "x".

According to the problem, in seven years, Susan will be "x + 7" years old.

Three years ago, Susan was "x - 3" years old.

The problem tells us that Susan will be 2 times as old in seven years as she was 3 years ago. So we can set up the following equation:

x + 7 = 2(x - 3)

Now we can solve for x:

x + 7 = 2x - 6

x = 13

Therefore, Susan's present age is 13 years old.

Let's assume Susan's present age is "x" years. According to the information provided, "Susan will be 2 times old in seven years as she was 3 years ago."

Seven years from now, Susan's age would be x + 7, and three years ago, her age would have been x - 3. According to the given statement, her age in seven years will be two times her age three years ago:

x + 7 = 2(x - 3)

Let's solve this equation to find Susan's present age:

x + 7 = 2x - 6

Subtracting x from both sides:

7 = x - 6

Adding 6 to both sides:

13 = x

Therefore, Susan's present age is 13 years.

Answer:

(0, -6) is the y-intercept.

Answer:

12

Step-by-step explanation:

Answer:

288

Step-by-step explanation:

To solve, we need to find the area of the four triangle sides and add that to the square base's area.

Area of triangle sides: base * height * 0.5

Area of square base: base * height

Substitute the values

8 * 14 * 0.5 = 56

There are four of these sides, so the area of all the triangles is 224.

The square base is 8 * 8, or 64

Add these two values together.

64 + 224 = 288

Thus, the answer is 288

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

1. The quadratic function for the Area in terms of x: A(x) = 24x.

2. The cross-sectional area is maximized when the depth of the gutter is 0.

3. The maximum cross-sectional area is square inches 0.

To determine the depth of the gutter that maximizes its cross-sectional area and allows the greatest amount of water to flow, we need to follow a step-by-step process.

1. Write a quadratic function for the area in terms of x:

The cross-sectional area of the gutter can be represented as a rectangle with a width of 24 inches and a depth of x. Therefore, the area, A(x), is given by A(x) = 24x.

2. The cross-sectional area is maximized when the depth of the gutter is:

To find the value of x that maximizes the area, we need to find the vertex of the quadratic function. The vertex of a quadratic function in form f(x) = ax² + bx + c is given by x = -b/(2a). In our case, a = 0 (since there is no x² term), b = 24, and c = 0. Thus, the depth of the gutter that maximizes the area is x = -24/(2 * 0) = 0.

3. The maximum cross-sectional area is square inches:

Substituting the value of x = 0 into the quadratic function A(x) = 24x, we get A(0) = 24 * 0 = 0. Therefore, the maximum cross-sectional area is 0 square inches.

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Account number. A deposit slip contains the date, the name of the depositor, the depositor's account number, and the amounts being deposited as well as break down of whether the deposit is comprised of checks, cash, or if the depositor wants a specific amount of cash back from a check deposit.

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hope it helps