A 35-foot wire is secured from the top of a flagpole to a stake in the ground. If the stake is 1 feet from the base of the flagpole, how tall is the flagpole?

Arc XY = 2π • (PX)/ 4

. = 2π • 5/4

. = 6.28 • 5/4= 31.40/4 = 7.85

Then answer is

Option G) 7.854

Answer:

11.2 Slices / Week

Step-by-step explanation:

We know that Jake has eaten 5 slices of cake in 3 days. You can divide 5 / 3 to get an average of 1.6 slices of cake being eaten per day. The question asks what the weekly rate or eating the cake will be, do you need to multiple 1.6 x 7 for the total amount of cake eaten per week, which is 11.2 slices!

Answer:

11.6

explanation

we have 7 days.

7days-3days =4

in 3 days he has eaten 5 slices

again 4-3 days=1

so in 6 days he has eaten 10 slices

we have 1 day left.so if he eats 5 slices in 3 day,how many he eat slices in 1 day?5/3=1.6

10+1.6=11.6

ANSWER

There are 37 tens in the cash register

EXPLANATION

Given that;

The total amount in the cash register is $740

The cash register contain five dollar and ten dollar

Follow the steps below to find the number of ten dollar in the cash register.

Let x represents the number of $5 and $10 in the cash register.

Recall, that the register contain twice as many $5 as ten dollars and this can be expressed mathematically as

Evaluate x in the above expression

Therefore, we have 37 tens in the cash register

The answer is option C.

thats where there are intergers greater than 5.

First, we graph the trapezoid and the line

If we reflect the figure across the line y = 1, then we get the following figure

As you can observe in the graph, the vertices would be J'(-4,-1), K'(-2,-5), L'(2,-5), and M'(3,-1).

Explanation

The area of a portion of a circle with radius 'r' and central angle 'a' in radians is:

In this problem, the radius is r = 4cm, and the angle a = 30º.

First we have to express the angle in radians:

And now we can find the area of the shaded region:

Answer

The area of the shaded region is:

Answer:

The distance from the edge of the fountain to the centre is approximately 23.87 inches.

The water fountain forms a circle. The distance around the water fountain is the circumference of the circle formed.

Therefore,

circumference = 2πr

150 = 2πr

The distance from the edge of the fountain to the centre is the radius of the circle formed. Therefore,

75 = πr

r = 75 / 3.14159

r = 23.8732616287

r = 23.87 inches

The distance from the edge of the fountain to the centre is approximately 23.87 inches.

To answer this question, we need to use the next formula for compound interest:

From the formula, we have:

• A is the accrued amount. In this case, A = $7900.

• P is the principal amount. In this case, $4500.

• r is the interest rate. In this case, we have 4.7%. We know that this is equivalent to 4.7/100.

• n is the number of times per year compounded. In this case, we have that n = 365, since the amount is compounded daily.

Now, we can substitute each of the corresponding values into the formula as follows:

And we need to solve for t to find the number of years, as follows:

1. Divide both sides by 4500:

2. Applying natural logarithms to both sides (we can also apply common logarithms):

3. Then, we have:

4. And now, we have to divide both sides by 365:

If we round the answer to two decimals, we have that t is equal to 11.97 years.

64 ounces of cherries are displayed in all in the farm stand.

According to the question,

We have the following information:

Farm stand has cherries on 2 shelves.

Number of boxes in each shelf = 4 boxes

So, the number of boxes in 2 shelves will be (2*4) or 8.

Ounces of cherries in each box = 8 ounces

Now, the ounces of cherries in 8 boxes can be easily found by multiplying the ounces of cherries in 1 box by the number of total boxes.

Ounces of cherries in 8 boxes = (8*8) ounces

Ounces of cherries in 8 boxes = 64 ounces

Now, the expression that represents the amount is (number of shelves*number of boxes*ounces of cherries in each box).

Hence, the ounces of cherries displayed in all is 64 ounces.

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The equation of the line follows the following general structure:

Where m is the slope of the line and b is the y intercept.

Find the corresponding values in the given formula, this way:

In the given equation, m has a value of -1/2, it means the slope is -1/2.

The 30-60-90 triangle is given by

AS we can note , the hypotenuse is twice as long as the shorter leg. Additionally, the longer leg is square root of 3 tines as long as the shorter leg. Therefore, the answer is option C and F

Solution

We are given the following

Using the Area of a Rectangle we have

Therefore, the answer is

The lines are not intersecting. The system of linear equations has a solution only if the lines corresponding to the equations intersect.

The general linear equation is,

y=mx+c, where m is the slope.

The slopes of lines m=2.

Since the graphs are parallel or have the same slope and will never intersect, the system of linear equations have no solution.

we know that

the geometric mean is the product of all the numbers in a set, with the root of how many numbers there are

so

In this problem we have two numbers

so

the geometric mean is equal to

Answer:

The interval at which the function is increasing is from x = -2 to x = 0. In interval notation, it is (-2, 0).

Explanation:

See the graph below for the pattern of the function.

As you can see above, from x = -∞ until x = -2, the value of the function decreases from y = +∞ to y = -7.

Then, starting at x = -2 to x = 0, the value of the function increases from y = -7 to y = -3.

Lastly, starting at x = 0 to +∞, the value of the function decreases again from y = -3 to -∞.

Hence, the interval at which the function is increasing is at (-2, 0).

Answer: y = (-2/3)x + (4/9)

Step-by-step explanation:

y = mx + b is the form expected

-18y + 8 = 12x

subtract 8 from both sides

-18y = 12x - 8

divide both sides by -18

y = (12x/-18) - (8/-18)

Simplify the negatives and pull x out of the parenthesis (this only works if x is in the numerator).

y = (-12/18)x + 8/18

Simplify the fractions

y = (-2/3)x + 4/9

Answer:

The required value of y is,

Step-by-step explanation:

Given equation,

→ -18y + 8 = 12x

The slope-intercept form is,

→ y = mx + b

Let's rewrite the equation,

→ y = mx + b

→ -18y + 8 = 12x

→ -18y = 12x - 8

→ -y = (12x - 8)/18

→ -y = (2/3)x - (4/9)

→ y = -(2/3)x + (4/9)

Hence, this is the answer.

Simple interest is represented by the following expression:

We need to create a system of equations:

Let x be the money invested in the account that paid 6%

Let y be the money invested in the account that paid 10%

So, he received a total of $920 in interest, then:

And we know that money invested must add together $10,000:

Then, we can isolate y in equation (2):

Now, let's substitute y=10,000-x in the equation (1):

That means, he invested $2,000 in the account that paid 6% simple interest. Now, having x, we are going to substitute x in the second equation (2):

He invested $8,000 in the account that paid 10% simple interest per year.

Since the triangles are similar, we have that

then

A system of equations is consistent if the system has a solution and it is inconsistent if it has no solution.

Since the lines intersect at a point, the system has a solution and the solution is unique.

If a system has a unique solution, then the system is independent.

Therefore, the given system of equations is consistent and independent. It has a unique solution.

Solution

- Linear:

The general form of a linear function is

- Quadratic:

The general form of a quadratic function is:

- Exponential:

The general form of an exponential function is:

- Now that we know the general forms of these functions, we can proceed to solve the question.

- The amount a person is paid per hour in wages is the amount that the person collects for every hour that he works

- Let us imagine that a person receives $a for every hour worked.

- This means that:

After 1 hour, the person makes $a

After 2 hours, the person makes $a + $a = $2a

After 3 hours, the person makes $a + $a +$a = $3a

- We can therefore generalize as follows:

Thus, after x hours, the person makes:

- Thus, the function representing the amount a person makes per hour of work is given by:

- Comparing this result with the 3 function definitions above, we can see that this corresponds to a Linear function

Final Answer

The answer is Linear

The single trig function that simplifies the function is sec(t)

Trigonometry deals with the functions of angles and how they're applied.

Given cot(t)/csc(t)-sin(t)

since csc(t) =  1/sin(t) , we have:

[tex]\frac{ cot(t)}{csc(t)-sin(t)} = \frac{cot(t)}{\frac{1}{sin(t)} - sin(t) }[/tex]

[tex]\frac{ cot(t)}{csc(t)-sin(t)} = \frac{cot(t)}{\frac{1-sin^{2}(t) }{sin(t)} }[/tex]

since:

cos²(t) = 1 - sin²(t)

Therefore we have:

cot(t) / csc(t)-sin(t) = cot(t)/ cos²(t)/sin(t)

cot(t) / csc(t)-sin(t) = cot(t) / cos(t).cos(t)/sin(t)

Since  cos(t) / sin(t) = 1/tan(t) = cot(t)

Therefore:

cot(t) / csc(t)-sin(t) = cot(t)/ cot(t)×cos(t)

cot(t) / csc(t)-sin(t) = 1/cos(t)

Since   1/cost = sec(t)

Finally, cot(t) / csc(t)-sin(t) is sec(t).

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The limit of a function is the value that a function approaches as that function's inputs get closer and closer to some number.

The question asks us to estimate from the table:

To find the limit of g(x) as x tends to -2, we need to check the trend of the function as we head towards -2 from both negative and positive infinity.

From negative infinity, the closest value we can get to before -2 is -2.001 according to the values given in the table. The value of g(x) from the table is:

From positive infinity, the closest value we can get to before -2 is -1.999 according to the values given in the table. The value of g(x) from the table is:

From the options, the closest estimate for the limit is 8.03.

The correct option is the SECOND OPTION.

Step-by-step explanation:

we have a right-angled triangle.

so, we can use Pythagoras

c² = a² + b²

c is the Hypotenuse, a and b are the legs.

in our case

c² = 6² + 6² = 36 + 36 = 72

c = Hypotenuse = sqrt(72) = 8.485281374... cm

Answer:

Step-by-step explanation:

An isosceles right triangle has 6 cm legs . Find the length of the hypotenuse

hypotenuse² = 6² + 6²

hypotenuse² = 36 + 36

hypotenuse² = 72

hypotenuse = √72 (or 8.49)

1) In this problem, we can see that this is an isosceles right triangle.

2) So, one way of solving it is to make use of the Pythagorean theorem. Note that an isosceles triangle has two congruent sides, so we can write out:

Usually, we rationalize it. But since the question requests the denominator to be a rational one, so this is the answer.

Solution

- The solution is given below:

- Thus, we have:

- Thus, the plot is:

Answer:

1/4

Step-by-step explanation:

it can be simplified by dividing both the numerator and denominator with 9.

[tex] \displaystyle \large{ \sf{ \frac{9}{36}}} [/tex]

[tex]\displaystyle \large{ \sf{ \frac{9}{36} = \frac{ \cancel9}{ \cancel3 \cancel6} }}[/tex]

[tex]\displaystyle \large{ \bf{ = \frac{1}{4} }}[/tex]

simplest form is 1/4

LA rectangle has two pairs of sides of the same length. If we call W to the width of the rectangle, we know that the length is 6cm more. If we call L the length of the rectangle:

The perimeter of a rectangle is twice the length plus twice the width:

Since we know that the perimeter is 52 cm, we can write the system of equations:

We can substitute the first equation into the second one:

And solve:

We know that W = 10cm, we can now find L:

Thus, the dimensions of the rectangle are:

Length: 16 cm

Width: 10 cm

The velocity is v= 30.6 ft/ sec.

Velocity defines the direction of the movement of the body or the object. Speed is primarily a scalar quantity. Velocity is essentially a vector quantity. It is the rate of change of distance. It is the rate of change of displacement.

Given that,

We have given the height

s(t) = 0.2[tex]t^{3}[/tex] + 21t, where 0 ≤ [tex]x[/tex] ≤ 17.

To find the velocity we have to differentiate s(t) wrt to t.

s(t) = 0.2[tex]t^{3}[/tex] + 21t

    = 0.6[tex]t^{2}[/tex]+21

velocity of the particle at t = 4

s(4) = 0.6*[tex]4^{2}[/tex]+21

     = 9.6+21

     = 30.6

v= 30.6 ft/ sec

Hence, The velocity is v= 30.6 ft/ sec.

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