A bridge AB is to be built across a river. The point C is located 62m from B, and angle A is 80 degrees, angle C is 60 degrees. How long is the bridge

Tenemos lo siguiente:

Lo primero es calcular las kilocalorías para las proteínas y para los carbohidratos y grasas, de la siguiente día:

Ahora sumamos todas las kilocalorías y nos queda lo siguiente:

Es decir que en total en los 50 gramos de pechuga hay en total de 58 kilocalorías, ahora debemos calcular el tiempo dividiendo el numero de kilocalorías por la cantidad de consumo de kilocalorías al jugar baloncesto

Es decir que debe jugar 0.138 horas o un total de:

Es decir que debe jugar 8.28 minutos

Answer:

  y = 4/9x +10/3

Step-by-step explanation:

You want the slope-intercept equation of the line through point (-3, 2) that is perpendicular to the line y = -9/4x +1.

The slope-intercept form of the equation for a line is ...

  y = mx + b . . . . . . m is the slope, b is the y-intercept

In order to write the desired equation, we need to know the desired slope and the y-intercept that makes the line go through the given point.

The slope of the perpendicular line is the opposite reciprocal of the slope of the given line. The given line equation is in slope-intercept form, so the coefficient of x is the slope of it: -9/4.

The slope of the perpendicular line is the opposite reciprocal of this:

  m = -1/(-9/4) = 4/9

Solving the slope-intercept form equation for b, we find ...

  b = y - mx

Using the values of x and y for the given point, and the slope we just found, we have ...

  b = 2 -(4/9)(-3) = 2 +4/3 = 10/3

The slope-intercept equation for a line with slope 4/9 and y-intercept 2/3 is ...

  y = 4/9x +10/3

__

Additional comment

It can also be useful to start from the point-slope equation:

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

Your line is ...

  y -2 = 4/9(x +3) . . . . . . use m=opposite reciprocal of -9/4; (h, k) = (-3, 2)

  y = 4/9x +(4/9)(3) +2 = 4/9x +10/3 . . . . . . add 2 and simplify

The doubling time for the general price levels in the eonomy given the average annual inflation rate is 18 years.

Inflation is a period where the general price levels in an economy rise persistently. When there is an inflation, the prices of goods and services increase. Inflation can either be as a result of an increase in the cost of production or an increase in the demand of a good.

The rule of 72 can be used to determine the doubling time. The rule of 72 is a rule of thumb that determines the number of years it would take an investment to double given its rate of growth.

The rule of 72 = 72 / inflation rate

72 / 4 = 18 years

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Given

initial velocity = 60 feet per second

initial height = 95 feet

Find

Maximum height attained by the ball

Explanation

we have given

put h'(t) = 0

to find the maximum height find the value of h(1.875)

Final Answer

Therefore , the maximum height attained by the ball is 151.25 feet

we have

then find c

therefore the distance is:

answer: 21.5 ft

First, lets calculate how much the expended in the perfume:

So, for 11 ounces of perfume, they need $28.55, so the minimum that the perfume need to cost per ounce is:

So, about $2.6 per ounce of perfume.

56÷1/3

We have to model a problem where the solution is 56÷1/3.

So, we take something that is 56 and we have to divide it by 1/3rd.

So, we can say:

George had 56 large cakes.

Giving 1/3rd of each cake to each person is enough.

If George used all of the cake, how many person could he feed?

The average number of persons admitted in one year is X/5.

What is average number?

Average By adding a collection of numbers, dividing by their count, and then summing the results, the arithmetic mean is determined.

If X persons are admitted in last 5 years in a hospital.

Then we get the average value of admitted persons are X/5 per year.

If Y persons are recovered in last 5 years in a hospital.

Then we get the average value of recovered persons are Y/5 per year.

Therefore, the average number of persons admitted in one year is X/5.

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Explanation:

The first thing is to state the coordinates of Quadrilateral PQRS

P (5, 5), Q (3, 5), R (3, 1), S (5, 1)

Then we find the distance between two points using the distance formula

It is a quadrilateral, meaning the two lengths are equal. Like wise the two widths are equal.

length PQ = length SR = 2

Length QR = length PS = 4

Scale factor = 3/4

Scale factor = corresponding side of new image/ corresponding side of original image

PQRS = original image, P'Q'R'S' = new image

3/4 = P'Q'/PQ

3/4 = P'Q'/2

P'Q' = 2(3/4) = 6/4 = 3/2

Since P'Q' = S'R'

S'R' = 3/2

3/4 = Q'R'/QR

3/4 = Q'R'/4

Q'R' = 3/4 (4) = 12/4 = 3

Since Q'R' = P'S

P (5, 5), Q (3, 5), R (3, 1), S (5, 1)

PQRS to P'Q'R'S' = 3/4(

P' = 3/4 (5, 5) = (15/4, 15/4)

Q' = 3/4 (3, 5) = (9/4, 15/4)

R' = 3/4 (3, 1) = (9/4, 3/4)

S' = 3/4 (5, 1)

Given -

Equilateral Triangle

To Find -

The number of rotations that will carry this equilateral triangle onto itself =?

Step-by-Step Explanation -

We know that in an equilateral triangle each question is of 60°

So,

Since it is a three-sided symmetry So, a rotation of 120° will carry this equilateral triangle onto itself.

Final Answer:

C. 120° counterclockwise rotation about its center P

The correct representations of the inequality -3(2x-5)<5(2-x) are -6x + 15 < 10 - 5x  and  "an open circle is at 5 and a bold line that starts at 5 and is pointing to the right" , the correct option is (c) and (d) .

In the question ;

it is given that

the inequality -3(2x-5)<5(2-x)

on solving this inequality further , we get

-3(2x-5)<5(2-x)

-6x+15<10-5x

which is option (c) .

Further solving

Subtracting 15 from both the sides of the inequality  , we get

-6x + 15 -15 < 10 -5x -15

-6x < -5 -5x

-6x +5x < -5

-x < -5

multiplying both sides by (-1) ,

we get

x > 5 .

x> 5 on number line means  an open circle is at 5 and a bold line starts at 5 and is pointing to the right .

Therefore , the correct representations of the inequality -3(2x-5)<5(2-x) are -6x + 15 < 10 - 5x  and  "an open circle is at 5 and a bold line that starts at 5 and is pointing to the right" , the correct option is (c) and (d) .

The given question is incomplete , the complete question is

Which are correct representations of the inequality -3(2x - 5) < 5(2 - x)? Select two options.

(a) x < 5

(b) –6x – 5 < 10 – x

(c) –6x + 15 < 10 – 5x

(d) A number line from negative 3 to 7 in increments of 1 , An open circle is at 5 and a bold line that starts at 5 and is pointing to the right.

(e) A number line from negative 7 to 3 in increments of 1,  An open circle is at negative 5 and a bold line that starts at negative 5 and is pointing to the left.

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the given expression is,

-14.4 + x = -8.2

x = 14.4 - 8.2

x = 6.2

thus, the answer is x = 6.2

We have to multiply the expression (2x + 4)(2x - 4):

The answer is:

B. 4x^2 - 16

The interval (1, 6) contains all the real numbers between 1 and 6, not including any of the endpoints.

This can be written in inequality notation as:

x >1 AND x < 6

But there is a shorter way to write the interval by combining both inequalities:

1 < x < 6

Let us write out the coordinates of the parent image given

Let us name the triangle ABC

Therefore, the rule for the rotation 90 degrees counterclockwise about the origin is,

Let us now obtain the coordinates of the transformed image

Hence, the coordinates of the transformed image are

Let us now plot the transformed image

The domain of a function is the possible values of "t" that the given function can take.

Since the variable "t" is in the denominator, the denominator cannot be equal to zero because it would make the function undefined.

Hence, t - 4 must be greater than zero. For t - 4 to be greater than zero, the value of t must be greater than 4.

In addition, since the variable is inside the radical sign, then the function itself cannot be negative.

Hence, the domain of this function must be greater than 4. In interval notation, it is (4, ∞).

Explanation:

We are to draw the angle that is equivalent to 5pi/4

First we need to convert the radian value to degree

Since pi rad = 180degrees

5pi/4 = x

Cross multiply

pi * x = 5pi/4 * 180

x = 5/4 * 180

x = 5 * 45

x = 225 degrees

This can also be written as 225 = 180 + 45

225degrees = 180 + pi/4

Note that 180degrees is an angle on a straight line. Find the digaram attached

The remaining angle which is pi/4 is the reason for the angle extensionon for the angle extension

5pi/4 = x

Cross multiply

pi * x = 5pi/4 * 180

x =

3) The given inequality is

The inequality symbol is that of less than. Since it has an equal to sign attached, then, the meaning is h is less than or equal to 9. In words, h is at most 9, no more than 9.

The line θ=π/2 is the vertical line in the polar grid, the polar axis is the horizontal line and the pole is the center of coordinates. Now let's analyze the symmetries:

If the grpah is symmetric with respect to θ=π/2 then the graph at the left of this line has to be the mirrored image of the graph at the right side. This is the case of this graph so it does have symmetry with respect to θ=π/2.

For the polar axis is the same, the graph above the axis has to be the mirrored image of that below the axis. However in this case we have two "petals" above the polar axis and one below so the upper part is not the mirrored version of the lower part so it has no symmetry with respect to this axis.

For the pole we must rotate the graph 180°. If the graph remains unchanged then it is symmetric with respect to it. In this case if we rotate the graph 180° the lower petal ends up in the opposite direction so the graph changes after a 180° rotation and it has no symmetry with respect to the pole.

Then the only type of symmetry is with respect to the line θ=π/2 and the answer is option a.

So first of all let's take:

Then we get:

The next step would be operate with the inequalities and the equation so we end up having only the term y at the left side of each:

So now we have the following inequalities and equality:

If we take the three inequalities and replace their symbols by "=' we'll have three equations of a line:

The following step is graphing these three lines and delimitating a zone in the grid that meets the inequalities:

Where the blue area is under the graph of y=150-(2/5)x which means that it meets:

And it is also above the x-axis, y=400-2x and y=300-x which means that it also meets:

All of this means that the values of x and y that give us the correct minimum of z are given by the coordinates of a point inside the blue area. The next thing to do is take the four possible values for Min(z) and use them to graph four lines using this equation:

Then we have four equations of a line:

The line that has more points inside the blue area is the one made with the closest value to Min(z). Then we have the following graph:

As you can see there are two lines that have points inside the blue area. These are:

That where made using:

Taking a closer look you can see that the part of the orange line inside the blue area is larger than that of the red line. Then the value used to make the orange line would be a better aproximation for the Min z. The orange line is -(3/4)x+450/2 which means that the answer to this problem is the first option, 450.

In one day the total number of hours is 24 hours.

So, in 5 days the number of hours is,

So, the required number of hours is 120 hours.

In this case, we can write out the parameters

Thus, substitute the coordinates in the mid-point formula and simplify

Hence, the coordinate of the mid-point is (50, 70)

Solution:

Let b represent the cost of 1 banana

Let p represent the cost of 1 pear

From the first statement, The cost of 4 bananas and 6 pears is $1.68

4b + 6p = 1.68 ----------------------------equation (1)

From the second statement, Nine bananas and 2 pears cost $1.48

9b + 2p = 1.48 -----------------------------equation (2)

Solve both equations simultaneously

4b + 6p = 1.68 ----------------------------equation (1)

9b + 2p = 1.48 -----------------------------equation (2)

Multiply equation (2) by 3 to eliminate p

27b + 6p = 4.44

4b + 6p = 1.68

Subtract both equatuions above

23b = 2.76

b = 2.76/23

b= 0.12

Substitute b = 0.12 into equation (1)

9b + 2p = 1.48

9(0.12) + 2p = 1.48

1.08 + 2p = 1.48

2p = 1.48 - 1.08

2p = 0.4

p = 0.4/2

p = 0.2

Hence, the cost of each banana is $0.12 while the cost of each pear is $0.2

Answer:

Hughes Family: 40 L/ hour
Gonzalez family: 25L/hour

Step-by-step explanation:

Let us use the following variables to denote the output rates for each sprinkler.

Let H = water output rate for the Hughes family

Let G = water output rate for the Gonzalez family

(I am using H ang G rather than the traditionally used X and Y to easily identify which rate belongs to which family)

The general equation for the volume of water outputted, V,  in time h hours at a rate of r per hour is
V = r x h

Given r

Using this fact
Water Output for Hughes family at rate H for 15 hours = 15H

Water Output for Gonzalez family at rate G for 35 hours = 35 G

The total of both outputs = 1475

That gives us one equation
15H + 35G = 1475    [1]

We are given the combined rate as 65 L per hour
Sum of the two rates = combined rate

H + G = 65   [2]

Answer:

2-×+3-×-4=0

Step-by-step explanation:

×=1\2

0.5,2`1

Let A be the event "person under 18" and B be the event "employed part-time". So, we need to find the following probability

which is given by

Since the total number od people in the table is equal to n=4089, we have that

and

and

we have that

which gives

Therefore, the answer the searched probability is: 0.296

f = 202

Step-by-step explanation:

[tex]7 \times 5f = 7070[/tex]

[tex]5f = \frac{7070}{7} [/tex]

[tex]5f = 1010[/tex]

[tex]f = \frac{1010}{5} [/tex]

[tex]f = 202[/tex]

Verification to check the given answer is correct, then put the value of f in the given question.

[tex]7 \times 5(202) = 7070[/tex]

[tex]35(202) = 7070[/tex]

[tex]7070 = 7070[/tex]

L.H.S. = R.H.S

[tex]{ \green { \boxed{ \red{ \sf{f = 202}}}}}[/tex]

Step-by-step explanation:

The given Eqⁿ is, [tex]{ \purple{ \sf{7 \times 5f = 7070}}}[/tex]

We need to find the value of f. So, let us cancel the numbers one by one.

First, let us cancel 7 by dividing both the sides by 7 in the given Eqⁿ.

[tex]{ \purple{ \sf \frac{ \cancel7 \times 5f}{ \cancel7}}} = { \purple{ \sf{ \frac{ \cancel{7070} ^{ \green{ \tt{1010}}} }{ \cancel 7_{ \green{ \tt{1}}}}}}}[/tex]

[tex]{ \purple{ \sf{5f = 1010}}}[/tex]

Now, let us cancel 5 by dividing both the sides by 5. then,

[tex]{ \purple{ \sf{ \frac{ \cancel5}{ \cancel5}f}}} = { \purple{ \sf{ \frac{ \cancel{1010^{ \red{ \tt{ \: \:202}}}}}{ \cancel 5_{ \red{ \tt{1}}}}}}}[/tex]

[tex]{ \boxed{ \blue{ \sf{f = 202}}}}[/tex]

ANSWER

$530,663

EXPLANATION

The amount the account will have in t years is given by,

Where n = 12, t = 13 years, r = 0.095 and A = 749,791. We have to find P,

Replace with the values and solve,

The interest earned is the difference between the initial deposit P and the final amount A,

Hence, the interest earned would be $530,663.

Amount deposited = $8500

Rate = 5%

time for interest = 6years

Compounded semiannually

The formula for semiannually is

From the given information

P = $8500

r = 5

t = 6

Since the investment was compounded semiannually then

n = 2

Substitute the values into the formula

This gives

Solve for A

To find the interest

Recall

Where I, is the interest

Hence

Given:

a.) Nguyen deposited $35 in a bank account.

b.) It earns 14% interest.

To be able to determine how much interest will he earn in 72 months, the following formula will be used for Compound Interest:

Where,

P = Principal amount

r = Interest rate

n = No. of times the interest is compounded = annually = 1

t = Time in years = 72 months = 72/12 = 6 Years

We get,

Therefore, the interest he will be earning is $41.82