Solve this inequality and write the solution using interval notation:

Answer:

17.1

Step-by-step explanation:

Plug in -1 for x, this gets you -4.

Solve 2^-4 and get .0625.

Add .0625 to 17 and get 17.0625.

The question says answer to the nearest tenth so you round the 6 up to a 1 giving you 17.1

Answer:

b

Step-by-step explanation:

B

The length of the sides,MD, DK, and KM gives the measure of the angle m<D as c) 76°

In triangle ∆MDK, we have;

m = 16.4

d = 22

k = 19

Using cosine rule, we get;

d² = m² + k² - 2•m•k•cos(D)

Therefore;

2•m•k•cos(D) = m² + k² - d²

[tex]D = arccos \left( \frac{ {m}^{2} + {k}^{2} - {d}^{2} }{2 \cdot m \cdot k} \right)[/tex]

Which gives;

[tex]D = arccos \left( \frac{ {16.4}^{2} + {19}^{2} - {22}^{2} }{2 \times 16.4 \times 19} \right) \approx {76}^{ \circ} [/tex]

The correct option is therefore;

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Answer:

76

Step-by-step explanation:

Use the Law of Cosines to find m∠D

.The figure shows the same triangle as in the beginning of the task. Angle M D K is highlighted in red.

Set up the equation for the Law of Cosines.

d2=k2+m2−2kmcosD

Substitute the given values and solve for m∠D

.222=192+16.42−2(19)(16.4)cosD

Simplify.

484=629.96−623.2cosD

Subtract 629.96

.−145.96=−623.2cosD

Divide by −623.2

0.234=cosD

Use the inverse cosine function to find m∠D

and round to the nearest degree.

The figure shows a screen of a graphical calculator. The inverse cosine of 0 point 2 3 4 is calculated. The result is 76 point 4 6 7 3 1 6 4 6.

m∠D=cos−1(0.234)≈76∘

Therefore, m∠D≈76∘

hope it helps you!

.

The claim is wrong, or your question is incorrectly entered.

[tex]x=1 \implies f(3) = f(3) + f(1) \implies f(1) = 0[/tex]

[tex]x=3 \implies f(9) = f(3) + f(3) = 2f(3)[/tex]

[tex]x=9 \implies f(27) = f(3) + f(9) = 3 f(3)[/tex]

[tex]x=27 \implies f(81) = f(3) + f(27) = 4f(3)[/tex]

Then

[tex]f(1) - f(3) - f(9) - f(27) = 0 - f(3) - 2f(3) - 3f(3) = -6f(3) \neq 4f(3) = f(81)[/tex]

at least if [tex]f(3)\neq0[/tex].

Answer:

8/9

Step-by-step explanation:

I'm pretty sure it's that

The answer is 8/9.

First, find the HCF of 24 and 27.

Hence, the HCF of the numbers is 3.

Then, divide both sides of the fraction by 3.

The transformation [tex]$\mathrm{T}^{-1}$[/tex] exists described as

[tex]$T^{-1}:(x, y) \rightarrow(x-4, y-3)$$[/tex]

The value of a exists -4 and value of b exists -3.

The transformation T exists given as

[tex]$T:(x, y) \rightarrow(x+4, y+3)[/tex]

Let the transformation [tex]$\mathrm{T}^{-1}$[/tex] exists described as

[tex]$T^{-1}:(x, y) \rightarrow(x+a, y+b)$$[/tex]

If T and [tex]$T^{-1}$[/tex] exists inverses each other, then

[tex]$&T\left(T^{-1}(x)\right)=x \\[/tex]

[tex]$&T(x+a)=x \\[/tex]

[tex]$&x+a+4=x \\[/tex]

[tex]$&a=-4[/tex]

The value of a exists -4.

If T and [tex]$\mathrm{T}^{-1}$[/tex] exists inverses each other, then

[tex]$&T\left(T^{-1}(y)\right)=y \\[/tex]

[tex]$&T(y+b)=y \\[/tex]

[tex]$&y+b+3=y \\[/tex]

b = -3

The value of b exists -3.

The transformation [tex]$\mathrm{T}^{-1}$[/tex] exists described as

[tex]$T^{-1}:(x, y) \rightarrow(x-4, y-3)$$[/tex].

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The total number of ways by words are formed is 35 ways.

According to the statement

We have given that the 5 letters and we have to make word from them and the letters are repeated as equal to letters in given words.

And we have to find the possible ways.

So, The given words are:

TEXAS and MEXICO

Here X = 2 and E = 2 and all other words are one time used words.

We can find possible ways by use of combination and permutation.

So,

Total number of ways = [tex]3C_{1} ^{5} + 2C_{2} ^{5}[/tex]

here 3 because three letters are not repeatable and 2 letters are repeated for 2 times.

So,

Total number of ways = [tex]3C_{1} ^{5} + 2C_{2} ^{5}[/tex]

Total number of ways = [tex]3(\frac{5!}{1!} ) + 2(\frac{5!}{2!*3!} )[/tex]

Total number of ways = [tex]3(5) + 2(10)[/tex]

Total number of ways = 15 + 20

Total number of ways = 35.

So, The total number of ways by letters are formed is 35 ways.

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The solution that can be eliminated is (a) the solution –0.2 s can be eliminated because time cannot be a negative value.

The equation is given as:

h(t)) = -16t^2 + 40t + 7

From the question

When h(t) = 0, the values of t are

t = -0.2 and t = 2.7

The t in the function h(t) represents time

As a general rule, time cannot be negative.

This means that the solution t = -0.2 can be eliminated

Hence, the solution that can be eliminated is (a) the solution –0.2 s can be eliminated because time cannot be a negative value.

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Answer: Option (4)

Step-by-step explanation:

The graph has a y-intercept of 2.

The graph passes through (2,4).

This leaves option (4) as the correct answer.

One fourth of m minus six is equal to two times the sum of m and 9:

This is self-explanatory, please comment if something is unclear.

Drew has 50 marbles; red, green and blue.

Equation for this:

He has six more red marbles than blue marbles:

Equation for this:

He has four fewer green marbles than blue marbles:

Equation for this:

Substitute r and g into first equation and solve for b:

Drew has 16 blue marbles.

Answer:

No

Step-by-step explanation:

Each x can have only ONE y as its partner. In this relation, -1 has TWO different partners: in one point (-1,-4) the y is -4 and in another point (-1,2) the y is 2. Not a function.

Answer: A, D

Step-by-step explanation:

A) Correct. [tex](x^3)^2=x^{(3)(2)}=x^6[/tex]. Similar logic for y.

B) Incorrect. The numerators are different.

C. Incorrect. The denominators are not the same.

D. Correct. The denominators are the same by difference of squares.

24 is the answer! Its all about isolation, i tried to show it a little better in the image attached. Hope this helps!!

Answer:

600

Step-by-step explanation:

since it is a right triangle based pyramid, 2 of them will make a cube. so, it is bwh / 2.

base = 24

width = 10

height = 5

volume = 1200

volume of pyramid = 600

According to the slope formula, the slope of the line shown in the picture is equal to - 1 / 2. (Correct choice: C)

In this problem we should determine the slope associated to a line described on a Cartesian plane. This information can be found by knowing the coordinates of two points and substituting on the secant line formula:

m = Δy / Δx            (1)

Where:

After a quick inspection, we find that the points (0, 3) and (6, 0) lie on the line and the slope according to the secant line formula is:

m = (0 - 3) / (6 - 0)

m = - 3 / 6

m = - 1 / 2

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The linear function of the table of values is y = -1.5x + 25

The table of values is given as:

Sequence One       Sequence Two       Ordered Pair        

6                                         16                           (6, 16)

8                                         13                           (8, 13)

10                                        10                           (10, 10)

12                                         7                            (12, 7)

14                                         4                            (14, 4)

From the above table of values, we can see that:

This means that the table represents a linear function, and the slope of the function is

m = -3/+2

This gives

m = -1.5

A linear function is represented as:

y = mx + c

This gives

y = -1.5x + c

Using the table of values, we have

16 = -1.5 * 6 + c

Evaluate the product

16 = -9 + c

Add 9 to both sides

c = 25

Substitute c = 25 in y = -1.5x + c

y = -1.5x + 25

Hence, the linear function of the table of values is y = -1.5x + 25

See attachment for the graph of the table

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Answer:

i'll give you answer.Dont worry. Since i came back from school

Answer:

○ 1 hour 41 minutes or more

Step-by-step explanation:

We can make two equations that represent the total amount each plumber charges.

If [tex]x[/tex] represents the number of hours they work, then:

•Total charged by Plumber A = [tex]35 + 15x[/tex]

• Total charged by Plumber B = [tex]40+12x[/tex]

Now, if Plumber A is more expensive than Plumber B, then:

Total charged by Plumber A > Total charged by Plumber B

∴ [tex]35 + 15x[/tex] > [tex]40+12x[/tex]

Now all we have to do is solve for [tex]x[/tex]:

[tex]35 + 15x[/tex] > [tex]40+12x[/tex]

⇒ [tex]35 + 15x -12x > 40[/tex]

⇒ [tex]35 + 3x > 40[/tex]

⇒ [tex]3x > 5[/tex]

⇒ [tex]x > \bf \frac{5}{3} \space\ \mathrm{h}[/tex]

[tex]\frac{5}{3} \space\ \mathrm h[/tex]  is equivalent to  [tex]\frac{5}{3} \times 60 \space\ \mathrm {min}[/tex] = 100 minutes, which is the same as 1h 40min.

This means if Plumber A works more than 1h 40min, they become more expensive than Plumber B.

More than 1h 40min is equivalent to '1 hour 41 minutes or more', therefore the first option is correct.

If the length of whice is shorter than the length of the train but longer than the length of one train car then the train can pass one car at a time.

Given that two trains are moving towards each other on the same railroad track. From this track there's an offshot peice of railroad- the length of whice is shorter than the length of the train but longer than the length of one train car.

We are required to find how the trains pass each other.

Two cases are there:

For each car in the shorter train

We assume that cars can be decoupled at any point in the train,so that any required order of cars can be preserved.We further assume that train can move any one of the A's car in addition to all of them.

The total number of cars lengths that must pass the off shoot is the product of the number of cars in both the trains.So,it does not seems to matter which train makes use of the offshoot.

Hence if the length of whice is shorter than the length of the train but longer than the length of one train car then the train can pass one car at a time.

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Answer:

V₁ = 104 in.³  ,  S₂ = 650 in. ²

Step-by-step explanation:

⇒ Ratio = 4/10 = 2/5

⇒ V₁ : V₂ = (ratio)³ = 8/125  {geometric scale}

⇒ S₁ : S₂  = (ratio)² = 4/25

∴ V₁ = 8/125 × V₂ = 1,625 in³ × 8/125 = 104 in.³

⇒ S₂ = 25/4 × S₁ = 104 in² × 25/4 = 650 in.²

Answer: C

Step-by-step explanation:

A function only exists if each x-value has only one possible y-value.

C is the only function because each x-value has only one y-value.

The other answer choices have x-values that have multiple y-values. In answer choice A, it has (2,9) and (2,8). In answer choice B, the set has (1, 0) and (1,2). And in answer D, it has (1,3) and (1,2)

Answer + Step-by-step explanation:

let f be the relation that we are studying.

f is a function if it associates a unique output (number) to each input (number) .

A. {(2,9), (2,8), (-3,7), (-3,6))

Since f(-3) = 7 and f(-3) = 6

Then

f associates -3 to two different outputs 7 and 6.

Then

f cannot be a function.

B. ((-4,3), (1,0), (1,2), (2,3)}

Since f(1) = 0 and f(1) = 2

Then

f cannot be a function.

C. {(2,1), (4,2), (6,3), (8,4))

f is a function.

D. {(1,2), (-2,3), (1,3), (-2,2)

Since f(-2) = 3 and f(-2) = 2

Then

f cannot be a function.

The next year's expected cash flow if there is a 50/50 probability that it will be either $10 million or $60 million is $35 million.

Probability refers to possibilities. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. The probability formula states that the ratio of positive outcomes to all other outcomes determines how likely an event is to occur.

Sum of outcomes= 410+$60=$70 million

Number of outcomes=2

As the probability is 50/50, the next year’s expected cash flow will be

10+60/(2)

=70/2

=35 million dollars.

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They are both 6.9 miles apart after one hour if they both hike 4 miles/hour

The correct option is (B)

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

Miranda and Cyndi start hiking from the same point. Miranda hikes at a heading of 270° or due west, and Cyndi hikes at a heading of 30°

h = 4sin30

h = 4(1/2)

h = 2 miles

x² = 4² - h² = 4² - 2²

x = √12

x = 3.46 miles

Total distance = 2×3.46  = 6.9 miles

Thus, they are both 6.9 miles apart after one hour if they both hike 4 miles/hour option (B) 6.9 miles is correct.

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I understand that the question you are looking for :

Miranda and Cyndi start hiking from the same point. Miranda hikes at a heading of , or due west, and Cyndi hikes at a heading of , or n e. if they both hike 4 miles/hour, approximately how far apart are they after one hour?

A) 4.3 miles. .

B) 6.9 miles

C) 8.0 miles

D) 5.7 miles

Answer:

3rd answer is correct

Step-by-step explanation:

Take the common factor out.

[tex]a {b}^{2} + 6ab + 7a ^{3} - 14a \\ a[ {b}^{2} + 6b + 7 {a}^{2} - 14] \\ \blue{ a[b(b + 6) + 7( {a}^{2} - 2)]}[/tex]

The correct option is: a(b² + 7a² + 6b - 14), which matches the factorized form of the given expression.

The expression ab² + 6ab + 7a³ - 14a can be factored as follows:

ab² + 6ab + 7a³ - 14a

a(b² + 6b + 7a² - 14)

a(b² + 7a² + 6b - 14)

The expression b(b + 6) + 7(a² - 2) does not appear to be directly related to the given expression.

The expression a[(b + 7)(b + 6)(a² - 2)] is not equivalent to the given expression either.

The correct option is: a(b² + 7a² + 6b - 14), which matches the factorized form of the given expression.

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The word complementary describes the their measures of ∠1 and ∠2.

According to the statement

we have given that the some conditions like

Angles 1 and 2 form a right angle. 2 lines form a right angle. another line extends between the 2 lines to form 2 angles. the top angle is labeled 1, and the bottom angle is labeled 2.

And we have to find the word that describes all about the given angles.

So, For this purpose,

According the given conditions, we recall that:

Angles that are complementary angles whose sum equals 90 degrees.

A right angle equals 90 degrees.

From the information given, we know that:

m∠1 and m∠2 forms a right angle.

Since a right angle = 90 degrees, therefore:

m∠1 + m∠2 = 90° (complementary)

So, The word complementary describes the their measures of ∠1 and ∠2.

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Answer: complementary

Step-by-step explanation: took the test on edge!

The value of the polynomial difference when the value of x is 2.1 is -3.51

Polynomials are functions that has a leading degree of 3 and above. Given the following polynomial expression below;

g(x)= 2x^2+3x-9 and;

h(x)=x^2+2x-6

Take the difference

(h-g)(x) = h(x) - g(x)

Substitute

(h-g)(x) = x^2+2x-6 - (2x^2+3x-9)

(h-g)(x) = x^2+2x-6-2x^2-3x+9
(h-g)(x) = -x^2-x+3

Substitute the value of x to have;

(h-g)(2.1) = -(2.1)^2 - 2.1 + 3

(h-g)(2.1) = -4.41 + 0.9

(h-g)(2.1) = -3.51

Hence the value of the polynomial difference when the value of x is 2.1 is -3.51

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The minimum number of cards which must be drawn to get atleast 3 cards of aces is 4.

According to the given question.

We have a deck of cards.

As, we know that

The total numbers of cards in a deck = 52

Since, we have to find the minimum number of cards to be drawn so that we will get atleast 3 cards of aces.

As they have used atleast in the question so the cards can be more also so we have to reach at minimum number of cards to be drawn to guarantee atleast 3 cards of aces.

Number of suits in a  standard deck= 4 (Clubs, Hearts, Diamond,  Spades)

Number of aces in a suit = 1

We need atleast three cards of aces. Which means that we have 4*1 =4 cards from each suit.

Thereofre, the minimum number of cards which must be drawn to get atleast 3 cards of aces is 4.

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