f(x) = 2x2 − 30, find f(4).

Answer:

D. (0,5)

Step-by-step explanation:

Any points on the dashed line is not a solution. In this case, any points in the shade or above the dashed line is a solution.

For this case we must locate each of the points in the graph and see if they are in the region.

The border of the region is dotted, therefore equality is not included. That is, the points (-3,1) and (3,3) do not belong to the region.

On the other hand, we observe that the point (0,0) does not enter the region either.

Finally, it is observed that the point (0,5) if it is located within the region.

Answer:

(0,5)

Answer:

22.9m

Step-by-step explanation:

Using Pythagorean theorem, we can get two equations using the angles.

From Point A:

∠A = 20°

AB = 20m

From Point B:

∠B = 29°

BD = x

What we are looking for is the opposite side of each right triangle, each person makes because we have one adjacent side. We also know that both opposite sides will be equal.

So we use this formula for both point of views:

[tex]Tan\theta=\dfrac{Opposite}{adjacent}[/tex]

Where:

Opposite = height of the building

Adjacent = distance from the building

We are looking for the opposite side so we can tweak our formula to get an equation for the height

[tex]height=(Tan\theta)(distance)[/tex]

Using our given, we can solve for the distance of point B to D:

[tex](Tan20)(20+x) = (Tan29)(x)\\\\(0.3640)(20+x) = (0.5543)(x)\\\\\dfrac{(7.28+0.3640x)}{0.5543}=x\\\\13.1337 + 0.6567x = x\\\\13.1337 = x - 0.6567x\\\\13.1337 = 0.3433x\\\\\dfrac{13.1337}{0.3433}=x\\\\38.2572 = x[/tex]

The distance of point B to D is 38.2572 m.

Now that we know the distance of BD we can solve for the height of the building using only the given from point B.

[tex]height=(Tan\theta)(distance)[/tex]

[tex]height=(Tan29)(38.2572m)[/tex]

[tex]height=(0.5543)(38.2572m)[/tex]

[tex]height=21.21m[/tex]

But this is only the height from the line of sight. To get the height of the building from the ground, we just add the height of the viewer, which is 1.7m.

21.21m + 1.7m = 22.91m

The closest answer is: 22.91 m

Answer:

The sum of the first twenty-seven terms is 1,188

Step-by-step explanation:

we know that

The formula of the sum in arithmetic sequence is equal to

[tex]S=\frac{n}{2}[2a1+(n-1)d][/tex]

where

n is the number of terms

a1 is the first term

d is the common difference (constant)

step 1

Find the common difference d

we have

n=7

a1=-8

S=28

substitute and solve for d

[tex]28=\frac{7}{2}[2(-8)+(7-1)d][/tex]

[tex]28=\frac{7}{2}[-16+(6)d][/tex]

[tex]8=[-16+(6)d][/tex]

[tex]8+16=(6)d[/tex]

[tex]d=24/(6)=4[/tex]

step 2

Find the sum of the first twenty-seven terms

we have

n=27

a1=-8

d=4

substitute

[tex]S=\frac{27}{2}[2(-8)+(27-1)(4)][/tex]

[tex]S=\frac{27}{2}[(-16)+(104)][/tex]

[tex]S=\frac{27}{2}88][/tex]

[tex]S=1,188[/tex]

Answer:

A)

62/3 = 20.67 hours

B)

60 hours

C)

2074.29 miles

Step-by-step explanation:

If we assume the earth is a perfect circle, then in a complete rotation the earth covers 360 degrees or 2π radians.

A)

In 24 hours the earth rotates through an angle of 360 degrees. We are required to determine the duration it takes to rotate through 310 degrees. Let x be the duration it takes the earth to rotate through 310 degrees, then the following proportions hold;

(24/360) = (x/310)

solving for x;

x = (24/360) * 310 = 62/3 = 20.67 hours

B)

In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it takes to rotate through 5π radians. Let x be the duration it takes the earth to rotate through 5π radians, then the following proportions hold;

(24/2π radians) = (x/5π radians)

Solving for x;

x = (24/2π radians)*5π radians = 60 hours

C)

If the diameter of the earth is 7920 miles, then in 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle we have;

circumference = 2*π*R = π*D

                         = 7920π miles

Therefore, the speed of the earth is approximately;

(7920π miles)/(24 hours) = 330π miles/hr

The distance covered by a point in 2 hours will thus be;

330π * 2 = 660π miles = 2074.29 miles

Answer:

Part A). In 20 hr 24 minutes earth rotate 310°.

Part B). In 19 hr 6 minutes earth rotate 5 radians

Part C). 2072.4 miles point on equator rotates in 2 hours.

Step-by-step explanation:

Degree that earth rotate in 24 hour = 360°

Number of radian that earth rotate in 24 hour = 2π radian

Part A).

Time taken to rotate 360° = 24 hours

Time taken to rotate 1° = [tex]\frac{24}{360}=\frac{1}{15}\,hours[/tex]

Time taken to rotate 310° = [tex]310\times\frac{1}{15}=20\frac{2}{5}=20\,hr\:24\,minutes[/tex]

Part B).

Time taken to rotate 2π radian = 24 hours

Time taken to rotate 1 radian = [tex]\frac{24}{2\pi}=\frac{12}{\pi}\,hours[/tex]

Time taken to rotate 5 radian = [tex]5\times\frac{12}{\pi}=\frac{60}{\pi}=19.1\.hr=19\,hr\:6\,minutes[/tex]

Part C).

Diameter of Earth = 7920 miles

Radius of earth, r = 3960 miles

Degree of rotation in 1 hours = [tex]\frac{360}{24}=15^{\circ}[/tex]

Degree of rotation in 2 hours , [tex\theta[/tex] = 15 × 2 = 30°

Length of the arc for angle 30° of circle with radius 3960 miles = Distance covered by point in 2 hours.

Length of the arc = [tex]\frac{\theta}{360^{\circ}}\times2\pi r=\frac{30}{360}\times2\times3.14\times3960=2072.4\:miles[/tex]

Therefore, Part A). In 20 hr 24 minutes earth rotate 310°.

                  Part B). In 19 hr 6 minutes earth rotate 5 radians

                  Part C). 2072.4 miles point on equator rotates in 2 hours.

the equation of the graph should be

f(x)= 1/2x -1

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (2, 0) ← 2 points on the line

m = [tex]\frac{0+1}{2-0}[/tex] = [tex]\frac{1}{2}[/tex]

Note the line crosses the y- axis at (0, - 1) ⇒ c = - 1

y = [tex]\frac{1}{2}[/tex] x - 1 ← in slope- intercept form

f(x) = [tex]\frac{1}{2}[/tex] x - 1 ← in functional notation

Answer:

Its subtract 12.

Step-by-step explanation:

The first question mark is positive 6.

6-12= -6

The second question mark is  -22.

Negative 10 minus 12 equals negative 22

Once you understand integers, it will be really easy. I was in 6th grade last year.

Answer:

Step-by-step explanation:

[tex]\text{The sum of cubes:}\\\\a^3+b^3=(a+b)(a^2-ab+b^2)\\\\\text{Therefore}\\\\\text{for}\ a=6\ \text{and}\ b=s:\\\\6^3+s^3=(6+s)(6^2-6s+s^2)=(6+s)(36-6s+s^2)[/tex]

Answer: (6 + s)(s^2 – 6s + 36)

Step-by-step explanation:

Answer:

Is an equilateral triangle

Step-by-step explanation:

we know that

An equilateral triangle has three equal sides and three equal internal angles measures 60 degrees each

so

In this problem the triangle formed by the route has three equal sides (10 miles)

therefore

Is an equilateral triangle

Answer:

The maximum value of the equation is 1 less than the maximum value of the graph

Step-by-step explanation:

We have the equation [tex]y=-x^2+4x-8[/tex].

We can know that this graph will have a maximum value as this is a negative parabola.

In order to find the maximum value, we can use the equation [tex]x=\frac{-b}{2a}[/tex]

In our given equation:

a=-1

b=4

c=-8

Now we can plug in these values to the equation

[tex]x=\frac{-4}{-2} \\\\x=2[/tex]

Now we can plug the x value where the maximum occurs to find the max value of the equation

[tex]y=-(2)^2+4(2)-8\\\\y=-4+8-8\\\\y=-4[/tex]

This means that the maximum of this equation is -4.

The maximum of the graph is shown to be -3

This means that the maximum value of the equation is 1 less than the maximum value of the graph

Answer:

The maximum value of the equation is 1 less than the maximum value of the graph

Step-by-step explanation:

Answer:

Range :  {1, 3, 4, 7}

Step-by-step explanation:

Given function is defined as  f = {(2, 3), (5, 7), (3, 3), (5, 4), (9, 1)},

Now we need to find about  what is the range of the given function f.

we know that y-value corresponds to the range.

since each point is written in (x,y) form so we just need to collect y-values of

f = {(2, 3), (5, 7), (3, 3), (5, 4), (9, 1)},

Hence required range is {3, 7, 3, 4, 1}

But we need to remove repeated values

so correct choice is  {1, 3, 4, 7}

Answer:

26 2/3

Step-by-step explanation:

if you walked that distance 4 times last week then you walked 6 2/3 x 4

and that = 26 2/3

Answer:

T > -9/28

Step-by-step explanation:

A quadratic has two real solutions when the discriminant (b² - 4ac) is positive.

b² - 4ac > 0

3² - 4(T)(-7) > 0

9 + 28T > 0

28T > -9

T > -9/28

Answer:

x > 3

Step-by-step explanation:

Given

2(4 + 2x) < 5x + 5 ← distribute left side

8 + 4x < 5x + 5 ( subtract 5 from both sides )

3 + 4x < 5x ( subtract 4x from both sides )

3 < x ⇒ x > 3

Answer:

If x= 4 then f(x) = 4x -5 is 11.

Step-by-step explanation:

f(x) = 4x -5

We need to find the domain value that corresponds to the output f(x) = 11

In this question, we need to solve the expression for value of x such that the answer is 11.

if  x= 3

f(3) = 4(3) -5

     = 12 -5

    = 7

Since we want the answer 11 so we cannot take x= 3

if x = 4

f(4) = 4(4)-5

    = 16 - 5

    = 11

So, if x= 4 then f(x) = 4x -5 is 11.

Answer:

4

Step-by-step explanation:

The sum of the measures of all interior angles in triangle is always equal to 180°. So,

∠A+∠B+∠C=180°

∠B=180°-63°-49°=68°

Now use the sine rule:

[tex]\dfrac{c}{\sin \angle C}=\dfrac{b}{\sin \angle B}\\ \\\dfrac{3}{\sin 49^{\circ}}=\dfrac{b}{\sin 68^{\circ}}\\ \\b=\dfrac{3\sin 68^{\circ}}{\sin 49^{\circ}}\approx 3.685\approx 4[/tex]

Answer:

3

Step-by-step explanation:

The leading coefficient is the number in front of the highest power term.

We only have one term, so the leading coefficient is 3

Answer:

can you make it more specific please?

Step-by-step explanation:

I honestly don't get what you're saying in what subject this is?

Answer:

B

Step-by-step explanation:

Adjusting entries for prepaid expenses are classified as a (D) deferral. They gradually recognize the cost as expense over the period of benefit. This involves decreasing the prepaid asset account and increasing the corresponding expense account.

Prepaid expenses are costs that have been paid in advance for services or goods that will be received in the future. In accounting, prepaid expenses are considered assets because they provide future economic benefits to the company. When adjusting entries for prepaid expenses, the necessary adjusting entry is a ( D) deferral.

This means that the initial payment is recorded in a prepaid asset account, and then as the expense is incurred over time, it is gradually recognized as an expense on the income statement. For example, if a company pays a year's worth of rent in advance, each month, a portion of that prepaid rent would be moved from the prepaid asset account to the rent expense account, reflecting the usage of the space.

An adjusting entry for a deferral decreases the prepaid asset account and increases the expense account. The goal of this type of entry is to apportion the expense to the periods in which the benefits from the prepaid cost are actually realized.

Answer:

See graph below for answer

Step-by-step explanation:

Step 1) Change to y-intercept form

6y = 2x - 12

y = 1/3x - 2

Step 2) Graph.

See graph below for answer

Answer:

The radius of the silo should be [tex]16\ ft[/tex]

Step-by-step explanation:

we know that

The volume of the grain silo is equal to the volume of the cylinder plus the volume of a hemisphere

[tex]V=\pi r^{2} h+\frac{4}{6}\pi r^{3}[/tex]

we have

[tex]V=35,500\pi\ ft^{3}[/tex]

[tex]h=4D=8r[/tex]

substitute the values and solve for r

[tex]35,500\pi=\pi r^{2} (8r)+\frac{4}{6}\pi r^{3}[/tex]

Simplify

[tex]35,500=r^{2} (8r)+\frac{4}{6}r^{3}[/tex]

[tex]35,500=8r^{3}+\frac{2}{3}r^{3}[/tex]

[tex]35,500=\frac{26}{3}r^{3}[/tex]

[tex]r^{3}=35,500*(3)/26[/tex]

[tex]r=16\ ft[/tex]

To find the radius of the silo, we need to calculate the volume of the cylinder and hemisphere components of the silo, and then set their sum equal to the desired volume of grain. By substituting the given relationship between the height and radius, we can express the volumes in terms of the radius, and solve for the value of r that satisfies the equation.

To find the radius of the silo, we can start by calculating the volume of the cylinder. The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height. In this case, we are given that the height of the cylinder is 4 times the diameter of the base, so we can write h = 4r. The volume of the cylinder portion would then be V_cylinder = πr²(4r) = 4πr³.

The volume of the hemisphere on top can be calculated using the formula for the volume of a sphere, which is V = (4/3)πr³. Since the radius of the hemisphere is the same as the radius of the base of the cylinder, this volume would be V_hemisphere = (4/3)πr³.

The total volume of the silo is the sum of the cylinder volume and the hemisphere volume. So we have the equation V_total = V_cylinder + V_hemisphere = 4πr³ + (4/3)πr³ = (16/3)πr³. We know that the silo is to hold 35,500π cubic feet of grain, so we can set up the equation (16/3)πr³ = 35,500π and solve for r. Dividing both sides by (16/3)π, we get r³ = 35,500/((16/3)π), and taking the cube root of both sides, we find r = ∛(35,500/((16/3)π)). Evaluating this expression, we find that r ≈ 5.02 feet.

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Answer:

y = 90°

Step-by-step explanation:

The left side base angle of the triangle and the angle of 110° form a straight angle and are supplementary, thus

base angle = 180° - 110° = 70°

The right base angle is also 70° , thus the triangle is isosceles

The line segment from the vertex is a perpendicular bisector, hence

y = 90°

Let's pretend the base price is $100

If the shopper brings enough money to cover 25% of the base price then they are bringing $25

The bargain promises 25% off of the base price of $100, meaning that the bargain price will be $75

The shopper cannot purchase the item because they only brought $25 when they should have brought $75

The shopper went home disappointed because combining a 25% off coupon and paying 25% of the base price results in a net discount of 0%, not the expected 50%.

The shopper went home disappointed because they assumed that by combining a 25% off coupon with paying 25% of the base price, they would get a 50% discount on the item. However, these discounts are applied sequentially, so the actual discount is less than 50%. In this case, the final discount would be 25% off the base price minus 25% of the base price, resulting in a net discount of 0%. The shopper didn't get the expected bargain they were hoping for because the discounts do not add up linearly but are applied to the remaining amount after the previous discount.

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Answer:

[tex]\frac{35}{2}[/tex]

Step-by-step explanation:

To solve this problem we need to write the mixed fraction as a fractional number, as follows:

[tex]3 1/3 = 3 + \frac{1}{3} = \frac{9+1}{3} = \frac{10}{3}[/tex]

[tex]5 1/4 = 5 + \frac{1}{4} = \frac{20+1}{4} = \frac{21}{4}[/tex]

Then, evaluating the expression:

[tex]\frac{10}{3}[/tex]×[tex]\frac{21}{4}[/tex] = [tex]\frac{210}{12}[/tex]

→ [tex]\frac{35}{2}[/tex]

Answer:

35 over 2

Step-by-step explanation:

ANSWER

[tex]p + q= 7[/tex]

EXPLANATION

We determine the slope of each line using the slope formula;

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

The slope of BC is

[tex] = \frac{ q - 1}{9 - 6} [/tex]

[tex] \frac{ q - 1}{3} [/tex]

The slope of AB is

[tex] = \frac{1 - 4}{6 - p} [/tex]

[tex] = - \frac{3}{6 - p} [/tex]

The two lines are perpendicular so the product of their slopes is -1.

[tex] - \frac{3}{6 - p} \times \frac{ q - 1}{3} = - 1[/tex]

This implies that,

[tex]\frac{q - 1}{6 - p} = 1[/tex]

[tex]q - 1=6 - p[/tex]

[tex]q + p = 6 + 1[/tex]

[tex]p + q= 7[/tex]

.

Answer:

Option C. 1,493

Step-by-step explanation:

If the deer population in a region is expected to decline 1.1% from 2010 to 2020. Assuming this continued, we can say that the deer population decreases 1.1% each ten years.

From 2010 to 2060 there are 50 years. If the deer population decreases 1.1% each ten years, then it will decrease 5.5% in 50 years.

If the population in 2010 was 1,578. Then, the population in 2060 is going to be:

Using the rule of three:

If 1578 ----------------> Represents 100%

    X       <-----------------       5.5%

X = (5.5%x1578)/100% = 86.79 ≈ 87

Then the total population in 2060 is: 1578 - 87 = 1491

None of the answers equal to 1491. That's why I assume the correct answer must be Option C. 1,493. Given that it's the closest answer!

Answer:

The population would be 1,493.

Step-by-step explanation:

Given,

The initial population, P = 1,578, (  In 2010 )

Also, the decline rate per 10 years, r = 1.1 %,

And, the number of the periods of 10 years since, 2010 to 2060, n = 5,

Hence, the population in 2060 would be,

[tex]A=P(1-\frac{r}{100})^n[/tex]

[tex]=1578(1-\frac{1.1}{100})^5[/tex]

[tex]=1493.09849208\approx 1493[/tex]

Option third is correct.

Answer: [tex]x=\frac{23}{22}[/tex]≈[tex]1.04[/tex]

Step-by-step explanation:

You need to solve for the variable "x" to find its value.

To solve for "x" you need to apply the Division property of equality. This  states that:

[tex]If\ a=b\ then\ \frac{a}{c}=\frac{b}{c}[/tex]

Then, knowing this, you can divide both sides of the equation by 22. Therefore, you get that the value of "x" is the following:

[tex]\frac{22x}{22}=\frac{23}{22}[/tex]

[tex]x=\frac{23}{22}[/tex]

[tex]x[/tex]≈[tex]1.04[/tex]

Answer:

C) none

Step-by-step explanation:

The two lines are parallel (have the same slope (x-coefficient), but different y-intercepts). They have no point in common, hence there is no solution to the system of equations.

___

Another way to think about this: subtract the first equation from the second. You get ...

0 = 1

There are no values of the variables that will make this be true, hence no solutions.

Answer:

A number line with an open circle on −2, a closed circle on 5, and shading in between

Step-by-step explanation:

solve it you get x>-2

and 3x <=15

x<=5

so its close on 5 and open on -2

Answer:   173.20 ft

Step-by-step explanation:

Observe the attached image. To know how long the shadow is, we must find the length of the adjacent side in the triangle shown. Where the opposite side represents the height of the building

By definition, the function [tex]tan (x)[/tex] is defined as

[tex]tan(x) = \frac{opposite}{adjacent}[/tex]

So

[tex]opposite = 100\ feet\\x=30\°[/tex]

[tex]adjacent = l[/tex]

Then

[tex]tan(30\°) = \frac{100}{l}[/tex]

[tex]l = \frac{100}{tan(30\°)}[/tex]

[tex]l = 173.20\ ft[/tex]

The answer is:

The shadow is 173.20 feet

To solve the problem, we need to calculate the projection of the building's shadow over the ground.

We already know the height of the building (100 feet), also, we know the angle of elevation (30°), so, we can use the following formula to calculate it:

[tex]Tan(\alpha)=\frac{y}{x}=\frac{height}{x}\\\\x=\frac{height}{Tan(\alpha) }[/tex]

Now, substituting the given information and calculating, we have:

[tex]x=\frac{height}{Tan(\alpha) }[/tex]

[tex]x=\frac{100feet}{Tan(30\°) }=173.20feet[/tex]

Have a nice day!

Step-by-step explanation:

The area is

[tex] {x}^{2} - 110x + 2800 \\ = {x}^{2} - 40x - 70x + 2800 \\ = x(x - 40) - 70(x - 40) \\ = (x - 40)(x - 70)[/tex]

Since the width is

[tex]x - 40 \: (feet)[/tex]

Then, the length will be

[tex]x - 70 \: (feet)[/tex]