the conference room of a hotel measures 40 ft by 50 ft has a 12-foot ceiling what is the area of the walls​

Answer:

42 feet

Step-by-step explanation:

This is a ratio question. The ratio of the height of the lamp to its shadow is the same as the ratio of the height of the building to its shadow.

So, 15/9 = 70/x, where x is the building's shadow.

Cross mutiply and solve for x.

15x = 630

x=42

Using the concept of similar triangles, we set up a proportion comparing the heights and shadow lengths of the lamp and building. After solving the proportion 15/9 = 70/x, we find that the shadow cast by the 70-foot tall building is 42 feet long.

To find the length of the shadow cast by the building, we can use the concept of similar triangles. The lamp and its shadow form one triangle, and the building and its shadow form a second triangle. These two triangles are similar because the angles are the same, meaning they have the same shape but are of different sizes.

Given that a 15-foot lamp casts a 9-ft shadow, we can set up the following proportion:
Lamp Height / Lamp Shadow = Building Height / Building Shadow, which simplifies to 15/9 = 70/x, where x is the length of the building's shadow we are trying to find.

By cross-multiplying, we get 15x = 9 * 70, which simplifies to 15x = 630. Dividing both sides by 15 gives us x = 42, so the shadow cast by the building is 42 feet long.

Answer:

-12

Step-by-step explanation:

think of it like this

Do -48/2 which equals -24 then cut that in half which equals -12 and thats your answer

Answer:

B

Step-by-step explanation:

Picture shows the formula to find the circumference of a circle

The circumference of a circle is calculated by multiplying the diameter by the mathematical constant π, typically approximated as 3.14159. This relationship is captured by the formula C = πd, which is fundamental in the study of geometry.

The relationship between the circumference and the diameter of a circle is described by the mathematical constant π (pi). The circumference (C) of a circle can be calculated by multiplying the diameter (d) of the circle by π. Therefore, the correct equation is b. Pi times the diameter equals the circumference, which can be expressed as C = πd.

This relationship is a fundamental aspect of Euclidean geometry. It is interesting to note that the diameter of the circle is twice the radius (d = 2r), so the circumference can also be calculated by the formula C = 2πr, where r is the radius. This equation highlights that the circumference is proportional to the diameter, with π serving as the constant of proportionality.

Answer:

Y=3

Step-by-step explanation:

The Answer is y=3-2x

The answer is 11 and 6.

Hope this helps!

The two numbers which sum up to 17 and have a product of 66 are 6 and 11. This was found by using algebra to set up and solve two simultaneous equations.

The question can be resolved using a little bit of algebra. Let's assign the values x and y to these two numbers. We know two things: x + y = 17 (because their sum is 17) and xy = 66 (because their product is 66).

First, you will make y the subject of the first equation making it y = 17 - x. Replace y in the second equation with 17 - x so we will now have x(17 - x) = 66 or 17x - x^2 = 66. Rearranging the equation gives x^2 - 17x + 66 = 0. This equation can be factored to solve for x giving (x - 11)(x - 6) = 0. Therefore, x could be base on the equation 11 or 6.

If x is 11, y will be 6 (because 17 - 11 = 6) and if x is 6, y is 11 (17 - 6 = 11). Therefore, the two numbers are 6 and 11.

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ANSWER

The correct answer is B

EXPLANATION

The given expression is:

[tex] \sqrt[3]{ {x}^{5}y } [/tex]

We split the radical sign to obtain;

[tex] \sqrt[3]{ {x}^{5} } \times \sqrt[3]{ y } [/tex]

Recall that:

[tex] {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } [/tex]

We rewrite each radical expression in exponential form to obtain:

[tex] {x}^{ \frac{5}{3} } {y}^{ \frac{1}{3} } [/tex]

The correct answer is B.

ANSWER

6

EXPLANATION

The given equation is:

[tex] \frac{1}{3} (12x - 24) = 16[/tex]

Multiply through by 3.

12x-24=16×3

12x-24=48

Group similar terms:

12x=48+24

12x=72

Divide both sides by 12

x=6

The answer is 6.hope this helps. please add brainlist

ANSWER

16

EXPLANATION

The given expression is;

[tex]3 {x}^{2} + 4 {y}^{2} [/tex]

If x=2, y=1 and z=-3, we substitute the values into the expression and solve.

We substitute to obtain;

[tex]3 {(2)}^{2} + 4 {(1)}^{2} [/tex]

We evaluate to get;

[tex]3 {(4)} + 4 {(1)}[/tex]

We multiply out to get:

[tex]12+ 4 = 16[/tex]

Therefore the value of the given expression is with the given values is 16

Answer:

y = (x+ 3)^2 - 10.

Step-by-step explanation:

Vertex form is

y =  a(x - b)^2 + c

Here b = -3 and c = -10 so we have

y = a(x + 3)^2 - 10   where a is some constant.

The y intercept is (0, -1)  so substituting:

-1 = a * 3^2 - 10

-1 + 10 = 9a

9a = 9

a = 1

So the required parabola is (x+ 3)^2 - 10.

Answer:

113.1

Step-by-step explanation:

Volume of sphere = [tex]\frac{4}{3}[/tex] × π × r²

Volume of sphere =  [tex]\frac{4}{3}[/tex] × π × 3²

Volume of sphere =  [tex]\frac{4}{3}[/tex] × π × 9

Volume of sphere =  [tex]\frac{4}{3}[/tex] × 9 π

Volume of sphere = 113.1

Answer:

[tex]V=113.1cm^3[/tex]

Step-by-step explanation:

The formula to calculate the volume of a sphere is:

[tex]V=\frac{4}{3}\pi r^3[/tex]

Where r is the radius of the sphere.

In this case we do not know the radius of the sphere, but we know the diameter.

By definition the diameter of a sphere is equal to twice the radius. This is:

[tex]d = 2r[/tex]

[tex]r = \frac{d}{2}[/tex]

In this case d=6 cm

So

[tex]r = \frac{6}{2}[/tex]

[tex]r = 3\ cm[/tex]

Finally

[tex]V=\frac{4}{3}\pi 3^3[/tex]

[tex]V=36\pi\ cm^3[/tex]

[tex]V=113.1cm^3[/tex]

let's notice something, angles α and β are both in the I Quadrant, and on the first quadrant the x-coordinate/cosine and y-coordinate/sine are both positive.

[tex]\bf \textit{Sum and Difference Identities} \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(\alpha)=\cfrac{\stackrel{opposite}{15}}{\stackrel{hypotenuse}{17}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]\bf \pm\sqrt{17^2-15^2}=a\implies \pm\sqrt{64}=a\implies \pm 8 = a\implies \stackrel{I~Quadrant}{\boxed{+8=a}} \\\\[-0.35em] ~\dotfill\\\\ cos(\beta)=\cfrac{\stackrel{adjacent}{3}}{\stackrel{hypotenuse}{5}}\impliedby \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]\bf \pm\sqrt{5^2-3^2}=b\implies \pm\sqrt{16}=b\implies \pm 4=b\implies \stackrel{\textit{I~Quadrant}}{\boxed{+4=b}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf cos(\alpha - \beta)=\stackrel{cos(\alpha)}{\left( \cfrac{8}{17} \right)}\stackrel{cos(\beta)}{\left( \cfrac{3}{5} \right)}+\stackrel{sin(\alpha)}{\left( \cfrac{15}{17} \right)}\stackrel{sin(\beta)}{\left( \cfrac{4}{5} \right)}\implies cos(\alpha - \beta)=\cfrac{24}{85}+\cfrac{60}{85} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill cos(\alpha - \beta)=\cfrac{84}{85}~\hfill[/tex]

Answer:

138 cm.

Step-by-step explanation:

So first, we find the S.A. of the front and back.

The diagram says the side length of the front is 3 cm. and 3 cm.

3x3=9. So then, the back is also 9 cm, 9+9=18.

Now to find the S.A.'s of the four sides, you have to see the side lengths of each of them. The side lengths are 3 and 10.

3x10=30. This means each of them is 30 cm.

30x4=120. 120 is the total surface area of the four sides.

To find the total surface area of the whole rectangle, you add all the surface areas.

120+18=138 cm. (Not squared, since it's surface area and not area.)

100.014. I think this is it

Answer:

He bought 3 steaks and 4 watermelons

Step-by-step explanation:

Let

x -----> the number of steaks bought

y ----> the number of watermelons bought

we know that

[tex]x+y=7[/tex]

[tex]x=7-y[/tex] ----> equation A

[tex]3x+2.50y=19[/tex] ----> equation B

Solve the system of equations by substitution

Substitute equation A in equation B and solve for y

[tex]3(7-y)+2.50y=19[/tex]

[tex]21-3y+2.50y=19[/tex]

[tex]3y-2.50y=21-19[/tex]

[tex]0.50y=2[/tex]

[tex]y=4\ watermelons[/tex]

Find the value of x

[tex]x=7-4=3\ steaks[/tex]

therefore

He bought 3 steaks and 4 watermelons

ANSWER

Option D

EXPLANATION

The given function is

[tex]f(x) = (x - 1)(x + 4)[/tex]

The graph of this function, will touch the x-axis at x=1 and x=-4.

This graph is a minimum graph.

This parabola will open up.

The correct choice is D.

Answer:

4th Graph is correct option.

Step-by-step explanation:

Given Function is ,

f(x) = ( x - 1 )( x + 4 )

f(x) = x² + 3x - 4

Since, we are given a quadratic function.

So, Graph is a parabola.

Now we find the vertex of the parabola by expressing given function in standard form of parabola.

Consider,

y = x² + 3x - 4

x² + 3x = y + 4

[tex]x^2+3x+(\frac{3}{2})^2=y+4+(\frac{3}{2})^2[/tex]

[tex](x+\frac{3}{2})^2=y+4+\frac{9}{4}[/tex]

[tex](x+\frac{3}{2})^2=y+\frac{25}{4}[/tex]

By comparing this equation with ( x - h )² = 4a( y - k )

where, ( h , k ) is vertex of the parabola.

⇒ Vertex of the given function = [tex](\frac{-3}{2},\frac{-25}{4})[/tex]

These coordinates of the vertex lie in 3rd Quadrant.

Now looking at all given graphs. Only 4th Graph has vertex in 3rd quadrant.

Therefore, 4th Graph is correct option.

Answer:

c.) 18cm²

d.) 609m²

Step-by-step explanation:

I assumed that the question is the area of the grey fields.

c.) The white triangle is proportional to the big triangle whose side are known, (6,8). Thus the white trianlge's sides are (3,4). The area of a triangle is base*height / 2. Calculating the big triangle area subtracting the white triangle area gives the area of the grey. (6*8)/2-(3*4)/2 = 24 - 6 = 18.

d.) Area of a square is multiply the two sides. Adding together the greys, subtracting the whites will give the area of the grey. Small grey (11*14) Big grey (36*17) Big white (6*18) small white (7*7) -> 154+612-108-49=609.

The missing sides of the squares can be calculated by the given sides. Small grey 36-22=14. Big grey 28-11=17. Small white 13-6=7.

170 is the answer to this

Answer:

17,000.

Step-by-step explanation:

These are all of the steps to completely and correctly solve this question.

Hope this helps!!!

Kyle.

Let's translate the sentences into equations:

One number is 20 more than another: [tex]x=20+y[/tex]

If the greater number is increased by 4: [tex]x+4\ldots[/tex]

The result is five times the smaller [/tex]\ldots=5y[/tex]

So, we have the following system:

[tex]\begin{cases}x=20y\\x+4=5y\end{cases}[/tex]

Use the expression for x given by the first equation to solve the second:

[tex]x+4=5y \iff 20+y+4 = 5y \iff 24= 4y \iff y = 6[/tex]

which easily implies

[tex]x=y+20 = 26[/tex]

Answer:

Step-by-step explanation:

R means Rosa

given:

R+b+c=36

R R c-2=b, (R+2)+2=c

b-2=R, R+2=b

.

R+b+c=36 substitute for b and c

R+(R+2)+((R+2)+2)=36 add like terms

3R+6=36 subtract 6

3R=30 divide by 3

R=10

.

check

R=10

b=12

c=14

10+12+14=36

36=36

Answer: 10

Step-by-step explanation:

The children are 10, 12, and 14. (:

Answer:

E, F and G have determinants.

Step-by-step explanation:

Only square matrices have determinants so D which is not square does not have a determinant.

Determinant of F (2*3) - (1 * -1)

= 6 +1

= 7.

The determinant of G is obtained in the same way.,

THe determinant of E is worked out as follows

I 0  -1   1 |        0 *  | -1  -3 | - ( -1) *  | 3 -3| + 1 * | 3 -1|

I 3  -1  -3 |  =           |  0  5 !            |2  5|         |2 0|

I 2   0 5  |

= 0 *  -5 + 1 * 21 + 1 * 2

= 23.

Answer:

f(x) = x² - 2x - 15 passes through (-3 , 0) , (0 , -15) , (5 , 0)

f(x) = -x² - 2x + 15 passes through (-2 , 15) , (-1 , 16) , (0 , 15)

f(x) = -x² + 2x - 15 passes through (0 , -15) , (1 , -14) , (2 , -15)

Step-by-step explanation:

* Lets explain how to solve this question

- To find the points whose graph passes through them substitute the

  x-coordinate in the function if the answer is the same with the

  y-coordinate of the point then the graph passes through this point

  lets do that

- Check the first set of points with the first function

# Pint (0 , -15)

∵ f(x) = x² - 2x - 15

∴ f(0) = (0)² - 2(0) - 15 = -15 ⇒ same value of y-coordinate

∴ The graph of the function passes through point (0 , -15)

# Pint (1 , -14)

∵ f(x) = x² - 2x - 15

∴ f(0) = (1)² - 2(1) - 15 = -16 ⇒ not same value of y-coordinate

∴ The graph of the function does not pass through point (1 , -14)

∴ The graph does not pass through this set of points

- Check the second set of points with the first function

# Pint (-2 , 15)

∵ f(x) = x² - 2x - 15

∴ f(0) = (-2)² - 2(-2) - 15 = 4 + 4 - 15 -7 ⇒ not same value of y-coordinate

∴ The graph of the function does not pass through point (-2 , 15)

∴ The graph does not pass through this set of points

- Check the third set of points with the first function

# Pint (-3 , 0)

∵ f(x) = x² + 2x - 15

∴ f(0) = (-3)² - 2(-3) - 15 = 9 + 6  -15 = 0 ⇒ same value of y-coordinate

∴ The graph of the function passes through point (-3 , 0)

# Pint (0 , -15)

∵ f(x) = x² - 2x - 15

∴ f(0) = (0)² - 2(0) - 15 = -15 ⇒ same value of y-coordinate

∴ The graph of the function passes through point (0 , -15)

# Pint (5 , 0)

∵ f(x) = x² + 2x - 15

∴ f(0) = (5)² - 2(5) - 15 = 25 - 10  -15 = 0 ⇒ same value of y-coordinate

∴ The graph of the function passes through point (5 , 0)

∴ The graph passes through this set of points

* f(x) = x² - 2x - 15 passes through (-3 , 0) , (0 , -15) , (5 , 0)

- Check the first set of points with the second function

# Pint (0 , -15)

∵ f(x) = -x² - 2x + 15

∴ f(0) = -(0)² - 2(0) + 15 = 15 ⇒ not same value of y-coordinate

∴ The graph of the function does not passes through point (0 , -15)

∴ The graph does not pass through this set of points

- Check the second set of points with the second function

# Pint (-2 , 15)

∵ f(x) = -x² - 2x + 15

∴ f(0) = -(-2)² - 2(-2) + 15 = -4 + 4 + 15 = 15 ⇒ same value of y-coordinate

∴ The graph of the function passes through point (-2 , 15)

# Pint (-1 , 16)

∵ f(x) = -x² - 2x + 15

∴ f(0) = -(-1)² - 2(-1) + 15 = -1 + 2 + 15 = 16 ⇒ same value of y-coordinate

∴ The graph of the function passes through point (-1 , 16)

# Pint (0 , 15)

∵ f(x) = -x² - 2x + 15

∴ f(0) = -(0)² - 2(0) + 15 = 15 ⇒ same value of y-coordinate

∴ The graph of the function passes through point (0 , 15)

∴ The graph passes through this set of points

* f(x) = -x² - 2x + 15 passes through (-2 , 15) , (-1 , 16) , (0 , 15)

- Now we have the first set of points and the third function

∴ The graph passes through this set of points

∴ f(x) = -x² + 2x - 15 passes through (0 , -15) , (1 , -14) , (2 , -15)

Answer:

= -3x2 - 11x + 13

Step-by-step explanation:

=( +9) + (-3x2 - 11x + 4)

= -3x2 - 11x + 4 + 9

= -3x2 - 11x + 13

Answer:

B) As x → ∞, f(x) → ∞, and as x → –∞, f(x) → –∞.

Step-by-step explanation:

Answer:  -5/21

Step-by-step explanation:

-3/7 & -4/6

common detonator is 42

-3/7 = -18/42 reduced to -9/21

-4/6 = -28/42 reduced to -14/21

difference between -9/21 and -14/21 = -5/21

y- -8=(5/2)(x-4)

so is y+8=(5/2)(x-4)

Answer:

(x - 6)(x+4)

Step-by-step explanation:

Final answer:

The quadratic expression x^2 - 2x - 24 can be factored into two binomials as (x - 6)(x + 4).

Explanation:

To factor the quadratic expression x^2 - 2x - 24 completely, we start by looking for two numbers that multiply to give -24 (the constant term) and add to give -2 (the coefficient of x). These two numbers are -6 and +4 because (-6) * (+4) = -24 and (-6) + (+4) = -2.

We can now rewrite the quadratic expression as:

(x - 6)(x + 4) = 0

Therefore, the factored form of the expression x^2 - 2x - 24 is (x - 6)(x + 4).

Any number (except zero) raised to the power of zero is one:

[tex]11^0=1[/tex]

On the other hand, by definition, the square of a number is that number multiplied by itself:

[tex]11^2=11\cdot 11 = 121[/tex]

So, the two answer are not the same:

[tex]11^0\neq 11^2[/tex]

After all, the exponential function

[tex]y=11^x[/tex]

is injective, which means that, given [tex]x_1\neq x_2[/tex], we have

[tex]11^{x_1}\neq 11^{x_2}[/tex]

Answer:

what ratio man??

Step-by-step explanation:

Answer: A

Step-by-step explanation:

'A' can't be reduced anymore because 17 is a prime number.

Prime number: a number with only two factors- 1 & itself

ANSWER

[tex] {f}^{ - 1} =\pm \sqrt{x + 1} [/tex]

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} - 1[/tex]

Let

[tex]y = {x}^{2} - 1[/tex]

Interchange x and y to get:

[tex]x= {y}^{2} - 1[/tex]

Solve for y,

[tex]x + 1 = {y}^{2} [/tex]

Take square root of both sides to get,

[tex] \pm \sqrt{x + 1} = y[/tex]

This is the same as:

[tex]y = \pm \sqrt{x + 1} [/tex]

Therefore the inverse is

[tex] {f}^{ - 1} =\pm \sqrt{x + 1} [/tex]

Answer:

y=72

x=0

Step-by-step explanation:

In the given question, Stuart is not correct.

The sum of all internal angles of a triangle is always equal to 180°.

Value of ∠1 = 65°(given)

Value of ∠7 = 55°(given)

Now let's look into Stuart's reasoning:

Step 1 : It is correct because according to angle sum property of triangle, ∠1 + ∠7 + ∠8 = 180°.

Step 2 : This step is wrong, because ∠4 and ∠8 are corresponding angles and not ∠12 and ∠8, so ∠4 = 60°.

Step 3 : This step is also wrong , ∠4 + ∠12 = 180°

             So ∠12 = 180 - 60 = 120°

Hence, Stuart's value of ∠12 is not correct.

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