Solve the following subtraction problems.
a. 8 mi 133 yd 2 ft – 5 mi 107 yd 2 ft

Answer:

5 a.m.

Step-by-step explanation:

From 11 p.m. to midnight is 1 hour.  Adding 5 hours to this result is equivalent to "eleven p.m plus six hours" and is 5 a.m.

For this case we have the following expression:

[tex]ax ^ 4[/tex]

We must find the value of the expression when:

[tex]a = 2\\x = 1[/tex]

Substituting the values in the expression we have:

[tex]2 (1) ^ 4 = 2 * 1 = 2[/tex]

Thus, the value of the expression is 2.

Answer:

The value of the expression is 2

Option A

Answer:

The correct answer is A

Step-by-step explanation:

The given expression is [tex]ax^4[/tex].

We want to evaluate this expression for: [tex]a=2,x=1[/tex].

We just have to substitute a=2 wherever we see 'a' in the expression [tex]ax^4[/tex] and x=1 wherever see x in the same expression.

We perform the substitution to get:

[tex]2(1)^4[/tex]

We evaluate the exponent to get:

 [tex]2(1)[/tex]

We now multiply to get:

 [tex]2[/tex]

Answer:

[tex]\large\boxed{_4P_3>_4C_3}[/tex]

Step-by-step explanation:

[tex]\left\begin{array}{ccc}_nP_r=\dfrac{n!}{(n-r)!}\\\\_nC_r=\dfrac{n!}{r!(n-r)!}\end{array}\right\}\Rightarrow\dfrac{n!}{(n-r)!}>\dfrac{n^!}{r!(n-r)!}\Rightarrow_nP_r>_nC_r\\\\\text{because}\\-\text{the nominators are the same}\\-\text{the denominator}\ (n-r)!\ \text{is graeter than the denominator}\ r!(n-r)![/tex]

[tex]\text{Let's check our example:}\\\\n!=1\cdot2\cdot3\cdot4\cdot...\cdot n\\\\_4P_3=\dfrac{4!}{(4-3)!}=\dfrac{1\cdot2\cdot3\cdot4}{1!}=\dfrac{24}{1}=24\\\\_4C_3=\dfrac{4!}{3!(4-3)!}=\dfrac{1\cdot2\cdot3\cdot4}{1\cdot2\cdot3\cdot1!}=\dfrac{24}{6}=4\\\\24>4\Rightarrow_4P_3>_4C_3[/tex]

[tex]nPr = \dfrac{n!}{(n-r)!} \\ \\ nCr = \dfrac{n!}{r!(n-r)!}\\ \\ \Rightarrow nPr > nCr\\ \\ \Rightarrow \boxed{4P3 > 4C3}[/tex]

[tex]4x^2+28x + 48=\\4(x^2+7x+12)=\\4(x^2+3x+4x+12)=\\4(x(x+3)+4(x+3))=\\4(x+3)(x+4)[/tex]

Answer:

A

Step-by-step explanation:

Given

4x² + 28x + 48 ← factor out 4 from each term

= 4(x² + 7x + 12)

To factor the quadratic

Consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term

The factors are + 4 and + 3, since

4 × 3 = 12 and 4 + 3 = 7, thus

x² + 7x + 12 = (x + 3)(x + 4) and

4x² + 28x + 48 = 4(x + 3)(x + 4) → A

Answer:

b and f

c and e

Step-by-step explanation:

Basically, this question is testing your knowledge on supplementary angles (angles that add up to 180) and corresponding angles (angles that are across from each other that have the same value).

Using the information the diagram has given you, you just need to plug in the correct values for each angle. Once you've completed that, you just match them up. If two of the top right corners are 90.5, then they match! I made a little diagram, though it might be a little confusing :/// I hope I helped a little :)

since 5 is the y coordinate, subtract 8. 5-8=-3!

Answer:-3

Step-by-step explanation:

Answer:

[tex]x_1=-2.9\\x_2=0.2[/tex]

Step-by-step explanation:

The first step is to move the [tex]5x[/tex] to the left side of the equation and then add the like terms:

[tex]4x^2+16x-2=5x\\\\4x^2+16x-2-5x=0\\\\4x^2+11x-2=0[/tex]

Now we can apply the Quadratic formula. This is:

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

In this case we can identify that:

[tex]a=4\\b=11\\c=-2[/tex]

Finally, we must substitute these values into the Quadratic formula. Then we get:

[tex]x=\frac{-11\±\sqrt{(11)^2-4(4)(-2)}}{2(4)}[/tex]

[tex]x_1=-2.9\\x_2=0.2[/tex]

For this case we have that by definition, an equation of the second degree is given by:

[tex]ax ^ 2 + bx + c = 0[/tex]

We have the following equation:

[tex]0.3x ^ 2 + 5x-7 = 0[/tex]

Then, according to the definition above, we have to:

[tex]a = 0.3\\b = 5\\c = -7[/tex]

Thus, b equals 5.

Answer:

[tex]b = 5[/tex]

Option C

Answer:

50

Step-by-step explanation:

You can use that sum of the opposite interior angles is equal to that exterior one.

So (30)+(4x+2)=8+6x

Combine like terms on left

32+4x=8+6x

Subtract 4x on both sides

32=8+2x

Subtract 8 on both sides

24=2x

So x=12

To find Q replace x in 4x+2 with 12 giving you 4(12)+2=48+2=50

just to add to the great reply above

Check the picture below.

Q = 4(12) + 2 = 50.

Answer:

Option B.  [tex]y-45=5(x-9)[/tex]

Step-by-step explanation:

Let

x -----> the number of hours

y ----> the number of goods

we know that

The equation of a line in point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=5\ \frac{goods}{h}[/tex] ----> the rate is the same that the slope of the linear equation

[tex]point\ (9,45)[/tex] --->(At hour 9, the company had produced 45 goods)

substitute

[tex]y-45=5(x-9)[/tex]

Answer:

The answer in the procedure

Step-by-step explanation:

we have

[tex]f(x)=a(b)^{x}[/tex]

This is a exponential function

where

a is the initial value

b is the base

we know that

The initial value of the function is the value of f(x) when the value of x is equal to zero

substitute x=0 in the function

[tex]f(0)=a(b)^{0}[/tex]

Remember that any number to the zero power is one

so

[tex](b)^{0}=1[/tex]

substitute

[tex]f(0)=a*1=a[/tex]

ANSWER

[tex]B(2,-3)[/tex]

[tex]C(-2,3)[/tex]

EXPLANATION

The given point has coordinates A(-2,-3).

The rule for the reflection across the y-axis is

[tex](x,y)\to(-x,y)[/tex]

We apply this rule to obtain the coordinates of B.

[tex]A(-2,-3)\to B(--2,-3)[/tex]

Simplify the coordinates of B to get:

[tex]A(-2,-3)\to B(2,-3)[/tex]

The rule for reflection across the x-axis is

[tex](x,y)\to (x,-y)[/tex]

When the point A(-2,-3) is reflected across the x-axis to obtain C, then the coordinates of C are:

[tex]A(-2,-3)\to C(-2,--3)[/tex]

[tex]A(-2,-3)\to C(-2,3)[/tex]

Answer:

B(2 ,-3) and C( -2, 3)

Step-by-step explanation:

i did the test lol :)

Answer:

4

Step-by-step explanation:

12 can be multipled by 4 and 4 and 8 can be multipled by 4 and 2 so 4 is the greatest common factor

Answer:

4

Step-by-step explanation:

Answer:

Yes.

Step-by-step explanation:

The longest diagonal in the box is the line between one of the top corners to the opposite bottom corner.

Calculate the length of the longest diagonal in the box:

The diagonal of the base =  √(6^2 + 8^2)

= √100 = 10 inches.

The longest diagonal = √( 24^2 + 10^2)

= √676

=  26 inches

=  26 * 2.54

=  66.04 cms.

Therefore the cylinder (length 63.5 cms) rod can fit in the box.

Answer:

Look to the bold answer down

Step-by-step explanation:

* Lets explain how to restrict the domain of the quadratic function

- The quadratic function is two-to-one function

- The inverse of it is one-to-two which is not a function

- So we can not find the inverse of the quadratic function until restrict its

 domain

- We restrict the domain at the x-coordinate of the vertex of the function

∵ f(x) = (x - h)² + k is the standard form of the quadratic function, where

  (h , k) are the coordinates of its vertex

- To restrict the domain we put x > h for the right part of the parabola

  or x < h for the left part of the parabola

* Lets solve the problem

∵ f(x) = (x - 2)²

∵ f(x) = (x - h)² + k is the standard form of the quadratic function

∴ h = 2 and k = 0

∴ The vertex of the parabola is (2 , 0)

- We will restrict the domain at x = 2

∴ The domain of the function f(x) to have inverse is x > 2 or x < 2

* The restriction domain is x > 2 or x < 2

- To find the inverse of the function switch x and y and solve for the

  new y

∵ f(x) = (x - 2)²

∵ f(x) = y

∴ y = (x - 2)²

- Switch x and y

∴ x = (y - 2)²

- take square root for both sides

∴ ± √x = y - 2

- Add 2 for both sides

∴ ± √x + 2 = y

∴ [tex]f^{-1}=\sqrt{x}+2=====OR=====f^{-1}=-\sqrt{x}+2[/tex]

* For the domain x > 2 of f(x) the inverse is [tex]f^{-1}(x) = \sqrt{x}+2[/tex]

 For the domain x < 2 of f(x) the inverse is [tex]f^{-1}(x)=-\sqrt{x}+2[/tex]

Answer:

4

Step-by-step explanation:

Recall that the equation for a straight line is y = mx + b, where m is the slope and b is the y-intercept.

we can see that the slope is negative (i.e graph goes from top left to bottom right).  hence the value for m must be negative.

By looking at the answer choices, only 2 and 4 have negative x-terms, hence we can ignore 1 and 3.

Also we notice that the graph intersects the y-axis at y = 2, hence the y-intercept must be 2.

Only Answer 4 satisfies both requirements and is the correct answer.

Answer:

587.18 in^2

Step-by-step explanation:

Given:

Diameter = d = 11 inches

Slant height = l =28.5 inches

Radius will be half of diameter

r = d/2 = 11/2 = 5.5 in

We know that the formula for surface area of cone is:

[tex]SA = \pi rl+\pi r^2\\Putting\ the\ values\\SA = (3.14*5.5*28.5)+(3.14 * 5.5 * 5.5 )\\= 492.195+94.985\\=587.18\ in^2[/tex]

Hence, second option is correct ..

Answer: second option.

Step-by-step explanation:

We know that we can calculate the surface area of a cone with this formula:

[tex]SA=\pi rl + \pi r^2[/tex]

Where "r" is the radius and "l" is the slant heigth.

We know that the radius is half the diameter, then the radius of this cone is:

[tex]r=\frac{11in}{2}\\\\r=5.5in[/tex]

Since we know tha radius and the slant height, we can substitute values into the formula, using 3.14 for π.

Therefore, we get:

 [tex]SA=(3.14)(5.5in)(28.5in) + (3.14)(5.5in)^2=587.18in^2[/tex]  

Answer:

Step-by-step explanation:

The perimeter of the circular part of the sports exhibition can be found with the formula [tex]\pi[/tex]r.The equation is halved from the 2[tex]\pi[/tex]r as it is half a circle.

perimeter of circular part=17[tex]\pi[/tex]

Perimeter of the sports exhibition:

(4000/100)+10+10+68+33+17[tex]\pi[/tex]+34+(700/100)

=202+17[tex]\pi[/tex]

=255m(nearest whole number)

For the area, find the total area of the representive shapes

The two rectangles:10*40+68*33

=2644

The area of the semi circle (:[tex]\pi[/tex]r^2)/2

=17*17*[tex]\pi[/tex]/2

=144.5 [tex]\pi[/tex]

Total area:

2644+144.5 [tex]\pi[/tex]

=3098m^2(nearest whole number)

Answer:

Step-by-step explanation:

Well, there is no given equation, but I can tell you that perpendicular lines have OPPOSITE MULTIPLICATIVE INVERSE [RECIPROCAL] rate of changes [slopes].

Ex: 2 --> -½; -2 --> ½

Answer:

Step-by-step explanation:

Well, there is no given equation, but I can tell you that perpendicular lines have OPPOSITE MULTIPLICATIVE INVERSE [RECIPROCAL] rate of changes [slopes].

Ex: 2 --> -½; -2 --> ½

From the Circle Graph, We can notice that :

★  32% of 125 teenagers chose watching Television

[tex]:\implies \mathsf{\left(\dfrac{32}{100} \times 125\right)}\;\textsf{teenagers chose watching television}[/tex]

[tex]:\implies \mathsf{\left(\dfrac{32}{20} \times 25\right)}\;\textsf{teenagers chose watching television}[/tex]

[tex]:\implies \mathsf{\left(\dfrac{8}{5} \times 25\right)}\;\textsf{teenagers chose watching television}[/tex]

[tex]:\implies \mathsf{\left(8 \times 5\right)}\;\textsf{teenagers chose watching television}[/tex]

[tex]:\implies \large\boxed{\mathsf{40}}\;\textsf{teenagers chose watching television}[/tex]

Answer:

$1326

Step-by-step explanation:

Follow the format of the reconciliation statement

The adjusted cash balances should match

Cash balance as per the bank statement, January 31        1421.95

Add: Deposit in transit                                                           100.05

Deduct: Outstanding checks                                                  (196)

Adjusted cash balance                                                            1326

Balance as per depositor's record, January 31                    1202.5

Subtract: NSF check                                                                  (18)

Subtract: Service charges                                                         (8.5)

Add: receivable collected                                                          150

Adjusted cash balance                                                              1326

The reconciled amount is $1326.

!!

Replace t with 2.3 and solve:

8(2.3)^2 +4(2.3) + 125

Simplify:

8(5.29) + 9.2 + 125

42.32 + 9.2 + 125

51.52 + 125

176.52 meters

Answer:

176.52m

Step-by-step explanation:

Given is the height of a ball as

[tex]h(t) = 8t^2+ 4t +125[/tex]

where t is time, in seconds, after the ball was thrown and h(t) is the corresponding height, in meters

When t=2.3, substitute this for t

h(2.3) = [tex]8(2.3)^2 +4(2.3)+ 125 \\=176.52m[/tex]

Answer:

36

Step-by-step explanation:

You take 1/2 the linear term's coefficient and square it.

The linear term is the term that contains just an x and a number -- in this case 12x

Take 1/2 12 = 6

and square it

6^2 = 36

So when you've done that you should get

x^2 + 12x + 36 = 11 + 36

x^2 + 12x + 36 = 47

For this case we have the following inequality:

[tex]y-x <-3[/tex]

We must evaluate each of the points and verify if the inequality is met:

[tex](6,2)\\2-6 <-3\\-4 <-3[/tex]

The inequality is met!

[tex](2,6)\\6-2 <-3\\4 <-3[/tex]

It is not fulfilled!

[tex](2, -1)\\-1-2 <-3\\-3 <-3[/tex]

It is not fulfilled!

Thus, the point that meets the inequality is (6,2)

Answer:

Option A

He is 50 years old

200-(3*50)=age

200-150= 50

Answer:

50

Step-by-step explanation:

200-(3x)=50

3x=200-50 (Collect like terms)

3x=150

3x/3=150/3 (Divide through by 3)

x=50

Answer:

Step-by-step explanation:

Error is the difference from the nominal value, hence the nominal value is what is subtracted from x. We want the magnitude of that difference, | x-11.93 |, to be less than the maximum error value, 0.02, so the inequality is ...

  |x -11.93| ≤ 0.02

__

We can solve this by "unfolding" it, then adding 11.93:

  -0.02 ≤ x -11.93 ≤ 0.02

  11.91 ≤ x ≤ 11.95

[tex]6 \frac{3}{4}[/tex] hours

First, find the time it takes to paint each section with this formula: [tex]\frac{\frac{1}{2}}{\frac{2}{3}}[/tex]

You can use keep, change, flip, to make this multiplication. [tex]\frac{1}{2} * \frac{3}{2}[/tex]

Multiply the numerators. [tex]1 * 3 = 3[/tex]

Multiply the denominators. [tex]2 * 2 = 4[/tex]

So, it takes [tex]\frac{3}{4}[/tex] hour to paint one section of fence.

Now, we just need to find how long it takes to paint 9 sections. [tex]9 * \frac{3}{4}[/tex]

Multiply. [tex]\frac{27}{4}[/tex]

Finally, simplify. [tex]6 \frac{3}{4}[/tex]