Question 3
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Question 3
Without finding the unlabeled side of the triangle, a group of students were in a disagreement about how to solve for x in the figure. Which method(s) are correc
30°
A
B
C
D
F
x
Q Zoom
Use 45-45-90 triangles.
Use the Pythagorean theorem.
Use sin 30°.
Use cos 30º.
Use 30-60-90 triangles.
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Answer:

the probability is 1.01

A la sala de cine ingresaron 180 niños y 165 adultos.

De acuerdo con el enunciado, la sala de cine tiene capacidad para 345 espectadores y cobra 3 dólares por cada niño y 5 dólares por cada adulto. Asimismo, esta sala tiene un recaudo diario de 1365 dólares. La situación puede ser sintetizada en la siguiente ecuación algebraica:

3 · x + 5 · (345 - x) = 1365

Donde x es el número de niños que asistieron a la sala de cine.

Ahora despejamos la variable correspondiente mediante propiedades algebraicas:

3 · x + 1725 - 5 · x = 1365

1725 - 2 · x = 1365

2 · x = 1725 - 1365

2 · x = 360

x = 180

Ahora, el número de adultos es:

y = 345 - 180

y = 165

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The integer number that represents the situation running up 24 steps is given as follows:

+24.

Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.

For altitudes, the signs are given as follows:

In this problem, we have an increase of altitude of 24 steps, hence the integer number is given as follows:

+24.

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Answer:

s = 2 1/3 + 1/2

t = 2/3 + 3/2

We have to find the sum of both s and t.

2 1/3 + 1/2 = 2 2/6 + 3/6 = 2 5/6

2/3 + 3/2 = 4/6 +  9/6 = 13/6 = 2 1/6

If we look at the number lines, we can see that c matches with both points.

Answer:

Step-by-step explanation:

The equation of line H in fully simplified slope-intercept form is y = 15x + 10.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would find the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (40 - 10)/(2 - 0)

Slope (m) = 30/2

Slope (m) = 15.

At data point (0, 10) and a slope of 15, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 10 = 15(x - 0)

y = 15x + 10

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

$12

Step-by-step explanation:

5 + 7 = 12

The equivalent exponential equations are given as follows:

\(2^{4x} = 2^{3(x - 3)}\)

The exponential expression for this problem is defined as follows:

\(2^{4x} = 8^{x - 3}\)

The number eight is the third power of 3, that is:

8 = 2³.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:

\(8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}\)

Meaning that the correct option is given by the fourth option.

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For the population to double, it takes around 7.07 hours.

The continuous exponential growth model is given by:

\(N(t) = N0 * e^{rt}\)

Where:

N(t) is the population size at time t

N is the initial population size (at t = 0)

r is the growth rate parameter

t is the time elapsed

We want to find the time t it takes for the population size to double, which means N(t) = 2N. Substituting into the growth model, we get:

\(2N = N * e^{rt}\)

Dividing both sides by N, we get:

\(2 = e^{rt}\)

Taking the natural logarithm of both sides, we get:

ln(2) = rt

Solving for t, we get:

t = ln(2)/r

Substituting r = 0.098 (9.8% as a decimal), we get:

t = ln(2)/0.098

t ≈ 7.07 hours

Therefore, it takes approximately 7.07 hours for the population size to double.

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Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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Answer:

$4.50

Step-by-step explanation:

Cuz 30-12 is $18 and 18÷4=4.50

Based on the distance that Jill is above sea level, and the distance of the whale, the difference in elevation is 1.35 km.

Jill's elevation relative to sea level is:

= +5/4 km

The whale's elevation relative to sea level is:

= - 0.1 km

The difference is therefore:

= 5/4 - (-0.1)

= 1.25 + 0.1

= 1.35 km

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The measure of the angle B of the triangle is 78.15 degrees

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

A = 25 degrees

a = 9.5 units

b = 22 units

Using the law of sines, the angle B is calculated as

sin(A)/a = sin(B)/b

So, we have

sin(25)/9.5= sin(b)/22

This gives

sin(b) = 22 * sin(25)/9.5

Evaluate

sin(b) = 0.9787

Take the arc sin of both sides

b = 78.15

Hence, the measure of the angle is 78.15 degrees

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Answer:

Step-by-step explanation:

9 tins of cat food feed her 2 cats for 18 days

Step-by-step explanation:

Sally has 2 cats

food eaten by 1 cat each day =

food eaten by 2 cat each day=  tins

sally buys 9 tins of cat food

then

tins  required in = 1 day

1 tin required in

i.e  1 tin required in  2 days

9 tin  required  for = 9×2 = 18 days

hence ,  9 tins of cat food feed her 2 cats for 18 days

#Learn more :

Sue has 2 cats. Each cat eats 1/4 tin of food each day. Sue buys 8 tine of cat food. Has sue got enough cat food to feed her 2 cats for 14 days?

Answer:

24

Step-by-step explanation:

because three fourths = 18

there for 18÷3 =6

there for 6×4 = 24

because it's value will always be same

Answer:

This value doesn't depend on x or y

It'll be the same things always

Step-by-step explanation:

please refer to the 3 pages of sketch for details

Answer:

a) 23

b) 0.4

c) 0.7

d) 0.08

e) 3.9

f) 1.6

g) 5.5

h) 12.4

Step-by-step explanation:

We see here that new thousand is actually liken to be the result in thousand that is gotten after carrying out an operation.

A thousand is a number that denotes the sum of 1,000 units or ten hundreds.

The word "thousand" is frequently used in daily speech to denote a significant but limited amount, such as a thousand money, a thousand individuals, or a thousand pages. Alternatively, it can be used as a round number to denote an approximation, as in "a thousand times" or "a thousand and one nights."

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Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of \(f(x)=(x-1)(x+7)\) has clear zeroes at \(x=1\) and \(x=-7\), showing that \(f(x) > 0\) when \(x < -7\) and \(x > 1\). To determine where the vertex is, we can complete the square:

\(f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16\)

So, we can see the vertex is (-3,-16), meaning that where \(x > -3\), the function will be increasing on that interval

By using the formula for the distance we will see that the correct option is B:

√52

We will use the general formula to find the distance between two points (a, b) and (c, d)

it is:

distance = √( (a - c)^2 + (b - d)^2)

Here we want to find the distance between the points (-2,-3) and (4,1), if we use the above formula we will get:

distance = √( (-2 - 4)^2 + (-3 - 1)^2) = √( 36 + 16)

distance = √52

The correct option is B.

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Answer:

\(7\frac{5}{16}\) ANSWER (C.

Step-by-step explanation:

Multiply \(9\frac{3}{4}\) by \(\frac{3}{4}\) to get \(\frac{117}{16}\)

-

\(7\frac{5}{16} = \frac{117}{16}\)

because 7 multiply by 16 plus 5 = 117

So 117 over 16

is the same as  \(7\frac{5}{16}\) .

Subtract 50 from 125

75

Divide by 15 (number of dollars per day)

5

If Maisie walks her neighbors dogs for 5 days, she will save up to a total of 125

Hope this helps :)

Answer:

✔ 50 + 15d = 125

What equivalent equation can you write after combining like terms?

✔ 15d = 75

How many days will Maisie have to walk the dogs?

✔ 5 days

Step-by-step explanation:

took. test.

The round trip distance in miles from city 1 to city 3 is given as follows:

30 miles.

The matrix corresponding to the distances between each of the cities is given by the image presented at the end of the answer.

Looking at row 1, column 3, we have that the distance from city 1 to city 3 is of 15 miles.

For the round trip distance, we have to go back from city 3 to city 1, more 15 miles, hence the distance is given as follows:

2 x 15 = 30 miles.

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Answer:

arithmetic sequence

Step-by-step explanation:

Each new member of this sequence is less than the previous member by a fixed number, which means this is an arithmetic sequence.

The expression in the form of Quotient, Remainder is:

x + 1, R 4

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(x² + 3) ÷ (x - 1)

Using synthetic division.

x - 1 ) x² + 3 ( x + 1

       x² - x

    (-)     (+)

             x + 3  

             x - 1

          (-)    (+)

                 4

This means,

The remainder is 4.

The quotient is x + 1.

Now,

Quotient, Remainder = x + 1, R 4

Thus,

Quotient, Remainder = x + 1, R 4

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Answer:

27 1/2

Step-by-step explanation: