Claire is cycling at a speed of 12 miles per hour. Han is cycling at a speed of 8 miles per hour. If they start at the same position, chosen at zero, and bike in straight, opposite directions, what will the distance between them be after 45 minutes?

Answer:

x = -7 or x = 2/3

Step-by-step explanation:

I'm assuming you meant solve for x when f(x) = 0.

f(x) = 3x(x + 7) - 2(x + 7)

0 = (x + 7)(3x - 2) -- Both terms have a common factor of (x + 7) so we can group them

x + 7 = 0 or 3x - 2 = 0 -- Use ZPP

x = -7 or x = 2/3 -- Solve

Answer:

Step-by-step explanation:

If you aren't supposed to do this on your calculator, then you'd have to figure out a way to get the bases of 10 to have the same power somehow in order to use the properties of exponents. This is the problem (you multiply the 2 dimensions together to find area, remember):

[tex](5.5*10^5)(4.2*10^4)[/tex]You cannot simply add the exponents on the 10's and say your power is 9...cuz it's not. It needs to be rewritten so that there is a power of 4 on the 10 in the parenthesis on the left. Do that this way:

[tex](5.5*10^4*10^1)(4.2*10^4)[/tex] Now you've got a common power of 4 between the 2 sets of parenthesis. 10 to the first is the same as 10, so multiplying that into the 5.5 gives us

[tex](55*10^4)(4.2*10^4)[/tex]

55 * 4.2 is 231 and 10 to the 4th times 10 to the 4th is 10 to the 8th.

[tex]231*10^8[/tex] But that's not in correct scientific notation. If we move the decimal to places to the left, we have to add 2 to the exponent of 8, giving us, finally,

[tex]2.31*10^{10}m^2[/tex]

Next use the hint to convert that to kilometers:

[tex]2.31*10^{10}m^2*\frac{1km^2}{1*10^6m^2}[/tex]

Dividing like bases means we subtract the lower exponent from the upper. 10 - 6 = 4, so the equivalent number of km squared is

2.31 × 10⁴ km²

Kilometers are comparable to miles, which is how we measure large things, like pieces of land. So it would be better to measure the forest in kilometers squared instead of meters squared.

The required length of the base is 18 units for the square pyramid.

The square pyramid shown below has a slant height of 17 units and a vertical height of 15 units. What is the length of one of the bases of the pyramid to be determined?

In a right-angled triangle, its side, such as hypotenuse, perpendicular, and the base is Pythagorean triplets.

The verticle height = 15
Slant height = 17
Let the base length be a,
For the half slant profile applying the Pythagorean theorem,
slant heigth² = vertical height² +  base length ²
17² = 15² + ( a/2 )²
289 - 225  =  ( a/2 )²
( a/2 )² = 64
a/2 =8
a = 16

Thus, the required length of the base is 18 units for the square pyramid.

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Answer:

cos(30)

Step-by-step explanation:

Answer:

sin(15)

Step-by-step explanation:

Answer:

A. [tex] \frac{7x^2}{6x - 10} [/tex]

Step-by-step Explanation:

To get the quotient, which is the result of

What we get by dividing the above, we would turn the divisor upside down, while the division sign would change to multiplication. This rule applied is known as "multiplying by the reciprocal".

[tex] \frac{7x^2}{2x + 6} [/tex] ÷ [tex] \frac{3x - 5}{x + 3} [/tex]

[tex] \frac{7x^2}{2x + 6} * \frac{x + 3}{3x - 5} [/tex] => multiplying by the reciprocal.

[tex] \frac{7x^2}{2(x + 3)} * \frac{x + 3}{3x - 5} [/tex]

[tex] \frac{7x^2}{2} * \frac{1}{3x - 5} [/tex] => (x + 3) cancels (x + 3)

[tex] \frac{7x^2(1)}{2(3x - 5)} [/tex]

[tex] \frac{7x^2}{6x - 10} [/tex]

Quotient = [tex] \frac{7x^2}{6x - 10} [/tex]

Answer: A

Step-by-step explanation:

Hey there! :)

Answer:

Slope = 2/5.

Step-by-step explanation:

Use the slope formula to solve for the slope of the line:

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

Plug in the coordinates of each point into the equation:

[tex]m = \frac{8 - 6}{10 - 5}[/tex]

Simplify:

m = 2/5. This is the slope of the line.

Answer:

The answer is option 2.

Answer: Choice C. No error. Molly is correct

Note how BC is 4 units high while FG is 5 units high. We don't have a match. So there is no way the figures are the same regardless of rigid transformations.

Answer:

Its c

Step-by-step explanation:

I got it right on khan academy

Answer:

[tex]f(x) =\sqrt[3]{x}[/tex]

Step-by-step explanation:

Hello!

Considering the parent function, as the most simple function that preserves the definition. Let's take the function given:

[tex]g(x) = \sqrt[3]{x-5}+7[/tex]

To have the the parent function, we must find the parent one, let's call it by f(x).

[tex]f(x) =\sqrt[3]{x}[/tex]

This function satisfies the Domain of the given one, because the Domain is still [tex](-\infty, \infty)[/tex] and the range as well.

Check below a graphical approach of those. The upper one is g(x) and the lower f(x), its parent one.

Answer:

5 units to the right and 7 units up (B on edge)

Step-by-step explanation:

Answer:

172.83 kg

Step-by-step explanation:

A cylindrical container has a radius (r) of 0.3 meter and a height (h) of 0.75 meter and density of 815 kg/m³.

The density of a substance is the mass per unit volume, it is the ratio of the mass of a substance to the volume occupied. The density is given by the formula:

Density = Mass / volume

The volume of a cylinder is given as:

V = πr²h

V = π × (0.3)² × 0.75 = 0.212 m³

Density = Mass/ volume

Mass = Density × Volume

Mass = 815 kg/m³ × 0.212 m³

Mass = 172.83 kg

Answer:

The answer is 173

Step-by-step explanation:

The other guy's answer was correct, but he forgot to round up to the nearest whole number so just in case you didn't notice the question saying that!

Answer:

x = 74°

Step-by-step explanation:

The diagram shown in this question, is a Quadrilateral inscribed in a circle

It is important to note that

The sum of opposite angles in a Quadrilateral = 180°

93° + z = 180°

z = 180° - 93°

z = 87°

In a cyclic quadrilateral,

Intercepted angle = 1/2(Intercepted arc)

Intercepted angle = 93°

Intercepted arc = x + 112°

Hence,

93° = 1/2(x + 112)°

93° × 2 = x + 112°

186° = x + 112°

x = 186° - 112°

x = 74°

Answer:

It’s 87° for mine

Step-by-step explanation:

7x - 14 = 4x + 19

7x - 4x = 14 + 19

3x = 33

x = 11

Answer:

[tex]4\sqrt{2}\\\\7\sqrt{2} \\\\13\sqrt{2}[/tex]

Step-by-step explanation:

Well the diagonal using pythagora's theorem:

[tex]x\sqrt{2}[/tex] where x is the lenght is the side of the square

so when x=4

[tex]4\sqrt{2}[/tex]

when x=7

[tex]7\sqrt{2\\}[/tex]

when x=13

[tex]13\sqrt{2}[/tex]

The length of diagonal is for (a=4) is [tex]4\sqrt{2}[/tex], for(a=7) is [tex]7\sqrt{2}[/tex] and for (a=13) is[tex]13\sqrt{2}[/tex].

Given side of squares.

We have to calculate the length of diagonal.

We know that in square shape,

length of diagonal [tex]=\sqrt{2} a[/tex], here a is the side of square.

So when square has a side of 4 then its diagonal becomes [tex]4\sqrt{2}[/tex].

when square has a side of 7 then its diagonal becomes [tex]7\sqrt{2}[/tex].

when square has a side of 13 then its diagonal becomes [tex]13\sqrt{2}[/tex].

Hence the length of diagonal is for (a=4) is [tex]4\sqrt{2}[/tex], for(a=7) is [tex]7\sqrt{2}[/tex] and for (a=13) is[tex]13\sqrt{2}[/tex].

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Answer:

28 cm²

Step-by-step explanation:

The area of Δ BDF is the area of the rectangle subtract the area of the 3 white triangles.

Since the area of the rectangle = 80 cm² and

area = length × breadth, then

breadth = 80 ÷ 10 = 8 cm

Thus CE = EF = 8 cm and CD = DE = BC = 4 cm

Area of Δ DEF = 0.5 × 10 × 4 = 20 cm²

Area of Δ ABF = 0.5 × 8 × (10 - 4) = 0.5 × 8 × 6 = 24 cm²

Area of Δ BCD = 0.5 × 4 × 4 = 8 cm²

Thus

area of Δ BDF = 80 - (20 + 24 + 8) = 80 - 52 = 28 cm²

Answer:

Triangle in isosceles, scalene or equilateral forms and

quadrilateral in trapezoid, rectangle or square forms

Step-by-step explanation:

Refer to pictures attached

Shapes can be formed are:

when perpendicular  to base

when  angle cross section to base

when base is isosceles triangle and parallel cross section to base,

or angle cross section

when base is scalene triangle and parallel cross section to base,

or angle cross section

when base is equilateral triangle and parallel cross section to base,

or angle cross section

Answer:

We have an extrema (local minimum) at x = -0.125

An inflection point at x = 0.25

Step-by-step explanation:

The given function is given as follows;

[tex]f(x) = 3x^{1/3} + 6x^{4/3}[/tex]

At the extrema points, f'(x) = 0 which gives;

[tex]0 = \dfrac{\mathrm{d} \left (3x^{1/3} + 6x^{4/3} \right )}{\mathrm{d} x} = \dfrac{(8 \cdot x+1) \times \sqrt[0.3]{x} }{x}[/tex]

(8x + 1) =x- (0/((x)^(1/0.3)) = 0

x = -1/8 = -0.125

f''(x)  gives;

[tex]f''(x) = \dfrac{\mathrm{d} \left (\dfrac{(8 \cdot x+1) \times \sqrt[0.3]{x} }{x} \right )}{\mathrm{d} x} = \dfrac{ \left (\dfrac{8}{3}\cdot x^2 - \dfrac{2}{3} \cdot x \right ) \times \sqrt[0.3]{x} }{x^3}[/tex]

Substituting x = -0.125 gives f''(x) = 32 which is a minimum point

The inflection point is given as follows;

[tex]\dfrac{ \left (\dfrac{8}{3}\cdot x^2 - \dfrac{2}{3} \cdot x \right ) \times \sqrt[0.3]{x} }{x^3} = 0[/tex]

[tex]\dfrac{8}{3}\cdot x^2 - \dfrac{2}{3} \cdot x \right }{} = 0 \times \dfrac{x^3}{ \sqrt[0.3]{x}}[/tex]

[tex]\dfrac{8}{3}\cdot x - \dfrac{2}{3} \right }{} = 0[/tex]

x = 2/3×3/8 = 1/4 = 0.25

We check the value of f''(x) at x = 0.24 and 0.26 to determine if x = 0.25 is an inflection point as follows;

At x = 0.24,   f''(x) = -0.288

At x = 0.26,   f''(x) = 0.252

0.25 is an inflection point

Louis traveled 7,144 miles

Answer:

[tex]x=-1,5[/tex]

Step-by-step explanation:

[tex]x^2-4x-5=0[/tex]

In order to solve this quadratic, we have many methods. We can factor, complete the square, or use the quadratic formula. I'm going to factor since it's the easiest method.

To factor, find two numbers that when multiplied equal a(c) and when added equal b.

a=1, b=-4, and c=-5.

So we want two numbers that when multiplied equals 1(-5)=-5 and when added equals -4.

-5 and 1 are the possible numbers. Therefore:

[tex]x^2-4x-5=0\\x^2+x-5x-5=0\\x(x+1)-5(x+1)=0\\(x-5)(x+1)=0\\x=5, -1[/tex]

Answer:

[tex]a^2+2ab+b^2[/tex]

Step-by-step explanation:

If we have [tex](a+b)^2[/tex] we can calculate this as:

[tex](a+b)*(a+b)[/tex]

So, applying distribution property, we get:

[tex](a+b)*(a+b)=a*a+a*b+b*a+b*b[/tex]

Where:

[tex]a*a=a^{2}[/tex]

 [tex]b*b=b^2[/tex]

[tex]a*b=b*a=ab[/tex]

so:

[tex](a+b)*(a+b)=a^2-ab+ab+b^2\\(a+b)*(a+b)=a^2+2ab+b^2[/tex]

The correct answer is C. Four pies

Explanation:

Marginal cost refers to an increase in the cost of production as additional units are made. In the case of apple pies, the graph shows the cost for one is $1.00. Moreover, this decreases when two or three pies are produced because the cost is between $0.60 and $0.30. However, if the producer makes four or more units, the cost increases. For example, at four units the cost per unit is $0.60, while at six units the cost is $1.50. Thus, the marginal cost begins to increase at four pies.

Answer: four pies

Step-by-step explanation:

The graph is a marginal cost curve that compares expenses therefore it would equal four pies because the marginal cost rises on the graph starting at 4.

Answer:

Step-by-step explanation:

Area of trapezoid:

[tex] \frac{1}{2} \times \: sum \: of \: parallel \: sides \: \times height[/tex]

plugging the values:

[tex] \frac{1}{2} \times (21 + 5) \times 2[/tex]

Calculate the sum

[tex] \frac{1}{2} \times 26 \times 2[/tex]

Reduce the numbers with G.C.F 2

[tex]13 \times 2[/tex]

Calculate the product

[tex]26[/tex] feet squared.

Hope this helps...

Best regards!

Answer:

Step-by-step explanation:

Given figure : Trapezoid

Base sides,

a = 2.5

b = 7.5

Height ( h ) = 2.5

Now, finding the area:

[tex] \frac{1}{2} (a + b) \times h[/tex]

Plug the values

[tex] = \frac{1}{2 } \times (2.5 + 7.5) \times 2.5[/tex]

Calculate the sum

[tex] = \frac{1}{2} \times 10 \times 2.5[/tex]

Reduce the numbers with G.C.F 2

[tex] = 5 \times 2.5[/tex]

Calculate the product

[tex]12.5 \: \: {units}^{2} [/tex]

Hope this helps...

Best regards!

Answer:

Step-by-step explanation:

It is half of equilateral triangle where 2√3 is its hight so:

[tex]2\sqrt3=\frac{k\sqrt3}2\\\\4\sqrt3=k\sqrt3\\\\k=4[/tex]

Step-by-step explanation:

Keeping,  one angle FDE, many triangles are possible since length of no segment is fixed and only one angle is fixed.

At many instances, triangle ABC and DEF have same angle measurements. Referring to the image attached here.

As point G moved on the ray EF, many triangles with same angle measurements as of ABC can be formed.

Answer:

Since no segment length is fixed and only one angle is fixed, multiple triangles are possible while maintaining one angle FDE. Triangles ABC and DEF frequently have the same measured angles. referring to the picture that is attached. Numerous triangles with the same angle measurements as ABC can be constructed when point G moves along ray EF.

Step-by-step explanation:

Answer:

x = -7

Step-by-step explanation:

5x+8=3x-6

Subtract 3x from each side

5x-3x+8=3x-3x-6

2x+8 = -6

Subtract 8 from each side

2x+8-8 = -6-8

2x = -14

Divide by 2

2x/2 = -14/2

x = -7

Answer: x= -7

Step-by-step explanation:

[tex]5x+8=3x-6[/tex]

[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}[/tex]

[tex]5x+8-8=3x-6-8[/tex]

[tex]5x=3x-14[/tex]

[tex]\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}[/tex]

[tex]5x-3x=3x-14-3x[/tex]

[tex]2x=-14[/tex]

[tex]\mathrm{Divide\:2\:\:on\:\:both\:sides\:}[/tex]

[tex]-14/2=-7[/tex]

[tex]x=-7[/tex]

Answer:

y= 0.15x - 1, y = x, y = x + 100, y = 15x + 5.

Step-by-step explanation:

When the slope of a line is less than 1 (if the slope is a decimal), the slope will not be steep. But when the slope is more than 1, the slope will be steeper than the average.

According to that rule, the steepest will be y = 15x + 5.

The next steepest equations will be y = x and y = x + 100 (they are both at the same degree of steepness; the intercept does not impact the steepness of the line).

The least steepest will bey = 0.15x - 1.

So, the order, from least steep to most steep, will be y= 0.15x - 1, y = x, y = x + 100, y = 15x + 5.

Hope this helps!

Answer:

Step-by-step explanation:

The easiest way to think about increasing area is by taking a square, if you double the dimensions, let's say they were 1 by 1 and then was made into a 2x2 square, you can fit four of the original cube (1x1) into the 2x2. So when the dimensions are doubled the area is quadrupled.

Even easier shortcut:

Take the cube idea, when the dimensions are messed with for anything, (works for volume too) always think of the smaller piece as 1x1 or 1x1x1. Then if the dimensions are double make it 2x2 or 2x2x2. If the dimensions are tripled then do 3x3 or 3x3x3, etc... 1x1=1x1x1, they are both equal to 1. So think of that as the numerator. the 2x2 in this case is equal to 4 so the smaller piece is 1/4 of the bigger one. Shown with volume if you double the dimensions of a cube that was 1x1x1 into 2x2x2. 1x1x1 still equals 1 so that's still the numerator and 2x2x2 is equal to 8 so the 1x1x1 cube is 1/8 of the 2x2x2, in other words you can fit eight 1x1x1 cubes into the 2x2x2 cube.

Hope this helps with area and volume.

The plus 7 at the end will shift the graph 7 units up. Replace y with f(x).

Then we have g(x) = f(x) + 7. Adding 7 to y = f(x) will increase the y value by 7.

The statement correctly describes the graph of y = x + 7 as choice A.

The graph is moved 7 units up

We have given that,

The graph of y = x.

Each statement describes a transformation of the graph of y = x.

The plus 7 at the end will shift the graph 7 units up.

Replace y with f(x).

Then we have g(x) = f(x) + 7.

Adding 7 to y = f(x) will increase the y value by 7.

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Answer:

B

Step-by-step explanation:

to find the inverse of a function, repalace f(x) with x, and replace x with y, proceed to solve for y and the answer you get is B

Answer:

B

Step-by-step explanation:

f(x)=5x/3+5

y=5x/3+5

x=5y/3+5

now solve for y

3x=5y+15

5y=3x-15

y=3x/5-3 or 3(x-5)/5