Persevere with Problems The table shows the highway fuel economy of various popular vehicles.

We calculate the module:

[tex]|z|\: = \: \sqrt{( - 3) ^{2} \: + \: {4}^{2} } [/tex]

[tex]|z| \: = \: \sqrt{9 \: + \: 16} [/tex]

[tex]|z| \: = \: \sqrt{25} [/tex]

[tex] \boxed{|z| \: = \: 5}[/tex]

We calculate the angle formed by "z":

[tex] \arctan( \frac{4}{ - 3} ) \: = \: \underline{0.92729521 \: \text{rad}}[/tex]

We pass it to degrees:

[tex]0.92729521 \: \times \: \frac{180}{\pi} [/tex]

[tex] \frac{166.91313924}{\pi} [/tex]

[tex] \frac{166.91313924}{3.14159265}[/tex]

[tex] \boxed{ 53.13°}[/tex]

Now we use this formula to transform it into a trigonometric form:

[tex] \boxed{z \: = \: |z| \times \: ( \cos( \alpha) \: + \: i \: \times \: \sin( \alpha))}[/tex]

[tex] \boxed{ \bold{z \: = \: 5 \times \: ( \cos( 53.13°) \: + \: i \: \times \: \sin( 53.13°))}}[/tex]

[tex] \boxed{ \bold{z \: = \: 5 \times \: ( \cos( 53.13°) \: + \: i \: \times \: \sin( 53.13°))}}[/tex]

Answer: 19.7

Step-by-step explanation:

By the Pythagorean theorem,

[tex](BD)^{2}=8^{2}+18^{2}\\\\(BD)^{2}=388\\\\BD=\sqrt{388} \approx \boxed{19.7}[/tex]

Answer:

Step-by-step explanation:

The total number of counters in the bag is 5 + 3 = 8.

and only 5 are red.

Then

the probability of obtaining a red counter is :

[tex]= \frac{5}{8} = 0.625[/tex]

The asked sum of multiples of five from 10 to 75, inclusive, is 595.

To find the sum of multiples of five from 10 to 75, inclusive, we can use the formula for the sum of an arithmetic series:

Sum = (n/2) * ([first term] + [last term])

Following the given case, the first term (a) is 10, the last term (l) is 75, and the common difference (d) between consecutive terms is 5 (since we are considering multiples of five).

The number of terms (n) can be calculated as:

n = (last term - first term) / common difference + 1

Let's calculate the number of terms first:

n = (75 - 10) / 5 + 1

n = 65 / 5 + 1

n = 13 + 1

n = 14

Now, we can determine the sum of the multiples of five:

Sum = (14/2) * (first term + last term)

Sum = 7 * (10 + 75)

Sum = 7 * 85

Sum = 595

Therefore, the asked sum of multiples of five from 10 to 75, inclusive, is 595.

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Any time we have a single positive tile pair up with a single negative tile, those two tiles cancel out.

Three positive tiles and three negative tiles will pair up and cancel out. We're left with two positive tiles only. This represents the number 2.

In other words, 5 + (-3) = 5 - 3 = 2

Answer: 1/16

Step-by-step explanation:

Given that there are 4 green marbles, when Dan takes a marble the first time, the probability is 1/4 as there are 4 green marbles. When he puts it back and draws another one, the probability is still 1/4 because Dan didn't take the marble out of the bag(this is known as with replacement)

∴ the total probability of drawing 2 green marbles with replacement is 1/4 × 1/4= 1/16

Hope this helps

Answer:

[tex]h(x) = \frac{1}{4} x[/tex]

Step-by-step explanation:

To find the inverse of a function, the steps are:

In this case, since h(x) is the inverse function of f(x), we can replace x with h(x) in step 3.

_____

f(x)= 4x

Let y= f(x) [tex]\textcolor{steelblue}{\text{ - step 1}}[/tex]

y= 4x

Divide both sides by 4:

[tex] \frac{1}{4} y = x[/tex]

[tex]x = \frac{1}{4} y \: \: \: \textcolor{steelblue}{\: \text{ - step 2}}[/tex]

Replace x with h(x) and y with x:

[tex]\bf{h(x) = \frac{1}{4} x} \: \: \: \textcolor{steelblue}{\: \text{ - step 3}}[/tex]

Additional:

For a similar question on inverse functions, do check out the following!

Answer:

a) k = 10              b) k = 7.5

Step-by-step explanation:

( 5k+ 20 ) + ( 7k + 40 ) = 180

12k + 60 = 180

12k = 120

k = 10

40 + ( 12k + 10) + 180 - ( 8k + 80 ) = 180

50 + 12k + 180 - 8k - 80 = 180

50 + 12k -8k - 80 = 0

50 + 4k - 80 = 0

30 = 4k

k = 7.5

Answer:

b =22

Step-by-step explanation:

The formula to calculate the area of a trapezoid:

1/2*(a+b)*h : (a: base, b: base, h: height)

The formula to calculate the area of a triangle:

1/2*a*h (a: base, h: height)

All inputs are given for trapezoid so let's first find the area of trapezoid then we can find the value of b:

1/2*(10+12)*7 = 77 cm^2 is the area of trapezoid

now for the area of triangle:

1/2*b*7 = 77 (it was given that the areas are equal)

first we multiply both sides by 2

7*b = 154 now divide both sides by 7

b = 22

Answer:

slope = 1

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 9 ) and (x₂, y₂ ) = (- 4, 2 )

m = [tex]\frac{2-9}{-4-3}[/tex] = [tex]\frac{-7}{-7}[/tex] = 1

Answer:

=> Expand by applying the FOIL method

[tex]2x\cdot \:3x+2x\left(-8\right)-7\cdot \:3x-7\left(-8\right)[/tex]

=> combine like terms

[tex]6x^2-37x+56[/tex]

Answer:

The value of x in the figure is 3.5

Step-by-step explanation:

When we look at the figure, we see that AB and BC, are connected, to make a longer side of a triangle. We can also see that BC is dilated from AB. When dilating, we multiply or divide by a number, to get the extended or shortened length. (Just keep multiplication and division in mind)                    To get x, we can do the same that we did to get 2, from 4. From AB to BC it goes from 4 to 2.

To get 2 from 4, you must divide 4 by 2. So when we do the same thing to 7, we should get x.

7 / 2 = 3.5

The value of x in the figure is 3.5

[tex]\\ \rm\dashrightarrow \dfrac{4}{2}=\dfrac{7}{x}[/tex]

[tex]\\ \rm\dashrightarrow 2=\dfrac{7}{x}[/tex]

[tex]\\ \rm\dashrightarrow x=\dfrac{7}{2}[/tex]

[tex]\\ \rm\dashrightarrow x=3.5[/tex]

Step-by-step explanation:

5 - 3x = -6 ( x + 2 )

5 - 3x = -6x - 12

-3x + 6x = - 12 - 5

3x = - 17

[tex]x = - \frac{17}{3} .. \\ [/tex]

Answer:

Exact Form:

x = −17/3

Decimal Form:

x = − 5.6

Mixed Number Form:

x = − 5  2/3

Answer:

2

Step-by-step explanation:

2 can go into 12,2, and 84

To obtain the greatest common divisor of (g.c.d) we must do it in simultaneous decomposition.

This method consists of extracting the common and uncommon prime factors, then

  [tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{12 \ \ \ 2 \ \ \ 84}\\ \ 6 \ \ \ 1 \ \ \ 42 \end{matrix}\right|\begin{matrix} 2\\ \: \end{matrix} \end{gathered}$}[/tex]

As we can see the number 2, is the only common prime number.

The greatest common factor of 12, 2, and 84 is 2.

Both lines are parallel because: A. both lines have a slope of 4/3.

The slope of a line = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

The slope of parallel lines are the same, while the slope of perpendicular lines are negative reciprocals.

Slope of AB = 4 units/3 units = 4/3

Slope of CD = 4 units/3 units = 4/3

Both lines have the same slope, therefore, they are parallel to each other.

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Answer:

The ans of first one is 0/8 = 0

and 6÷0 = undefined....hope this helps:)

5(3x+2)-2(4x-1)

= 15x+10-8x+2

= 7x+12

Translation: please help it's due today

Would love to help but there is no question to answer

A random sample  is a sample in which the chosen elements are removed from the population once they are chosen.

A sample is a smaller group of the population that has the desired elements of the population. A sample is sometimes necessary because it might not be feasible or cost effective to access the whole population.

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Answer:

22 plants

Step-by-step explanation:

Because 6/3 is 2/1 so 11 seed packets will grow 22 plants.

Answer:

15, 21, 27, 33, 39, 45, 51 67, 59, 51, 43, 35, 27, 19

20, 27, 34, 41, 48, 55, 62 64, 58, 52, 46, 40, 34, 28

66, 60, 54, 48, 42, 36, 30 6, 12, 18, 24, 30, 36, 42

72, 68, 64, 60, 56, 52, 48 5, 13, 21, 29, 37, 45, 53

50, 47, 44, 41, 38, 35, 32 12, 15, 18, 21, 24, 27, 30

60, 55, 50, 45, 40, 35, 30 19, 22, 25, 28, 31, 34, 37

54, 52, 50, 48, 46, 44, 42 8, 9, 10, 11, 12, 13, 14

69, 62, 55, 48, 41, 34, 27 2, 9, 16, 23, 30, 37, 44

24, 26, 28, 30, 32, 34, 36 3, 7, 11, 15, 19, 23, 27

52, 50, 48, 46, 44, 42, 40 16, 19, 22, 25, 28, 31, 34

70, 65, 60, 55, 50, 45, 40 55, 54, 53, 52, 51, 50, 49

4, 12, 20, 28, 36, 44, 52 11, 15, 19, 23, 27, 31, 35

21, 28, 35, 42, 49, 56, 63 61, 60, 59, 58, 57, 56, 55

10, 15, 20, 25, 30, 35, 40 18, 19, 20, 21, 22, 23, 24

25, 33, 41, 49, 57, 65, 73 58, 56, 54, 52, 50, 48, 46

yan yung bilang TXS me later ;-)

The height of the kite will be 53.32 feet above the ground.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

Given that:-

The height of the kite above the ground will be calculated as:-

[tex]Sin\theta = \dfrac{perpendicular}{Hypotenuse}[/tex]

[tex]Sin(29)=\dfrac{H}{110}[/tex]

H = Sin(29)  x  110

H  = 53.32 feet

The hand of the boy is 3.5 above the ground so the total height H(t) of the kite above the ground will be:-

H(t)  = 53.232  +  3.5

H(t)  = 56.28 feet.

Therefore the height of the kite will be 53.32 feet above the ground.

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Answer:

Step-by-step explanation:

\text{What function uses the \color{green}{\textbf{O}PPOSITE} and the \color{#EB0000}{HYPOTENUSE}?}

What function uses the OPPOSITE and the HYPOTENUSE?

\text{\Large \underline{S}\color{green}{O}\color{#EB0000}{H}-CAH-TOA}

S

​

OH-CAH-TOA

\text{sin }\color{purple}{29}=\frac{\color{green}{\text{opposite}}}{\color{#EB0000}{\text{hypotenuse}}}=\frac{\color{green}{x}}{\color{#EB0000}{110}}

sin 29=

hypotenuse

opposite

​

=

110

x

​

\text{sin }29=

sin 29=

\,\,\frac{x}{110}

110

x

​

\frac{\text{sin }29}{1}=

1

sin 29

​

=

\,\,\frac{x}{110}

110

x

​

110\text{ sin }29=

110 sin 29=

\,\,x

x

Cross multiply.

x=53.329058...

x=53.329058...

Type into calculator.

\text{Add 3.5, the distance from the ground to his hand:}

Add 3.5, the distance from the ground to his hand:

53.329058...+3.5=

53.329058...+3.5=

\,\,56.829058...

56.829058...

\approx

≈

\,\,56.8

56.8

Round to the nearest tenth.

\text{The kite is 56.8 feet above the ground.}

The kite is 56.8 feet above the ground.

Answer:

t=0

Step-by-step explanation:

First, we expand everything. The left-hand side is -3(2t) - 1(-3), and we expand it to be -6t+3. The right-hand side is t+t+t+3, and we can reduce it to 3t+3. Now that we have both sides of the equation, we set them to each other.

-6t+3=3t+3 (subtract 3 on both sides)
-6t=3t (add 6t to both sides)
9t =0 (divide by 9)
t=0

Using it's concept, it is found that the probability that a person chosen at random from this group has brown or green eyes is of [tex]\frac{13}{25}[/tex].

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching the problem on the internet, it is found that the group has 20 + 6 + 17 + 7 = 50 people, of which 20 + 6 = 26 have brown or green eyes, hence the probability is given by:

p = 26/50 = 13/25.

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Answer:

b=17.75 ft

Step-by-step explanation:

We will answer this using Pythagorean Theorem.
Since the bottom of a ladder is 3 feet from the wall, and the ladder is 18 ft long, the ladder is the hypotenuse. Knowing pythagorean theorem (a^2+b^2=c^2), we can plug it in.
3^2 + b^2 = 18^2

9+b^2=324

b^2=315

b=17.75 ft

The equivalent expression of [tex]-\dfrac65-\dfrac23v+\dfrac{4}{15}+\dfrac13v[/tex] is [tex]-\dfrac{15}{15}-\dfrac{v}3[/tex]

The expression is given as:

[tex]-\dfrac65-\dfrac23v+\dfrac{4}{15}+\dfrac13v[/tex]

Collect like terms

[tex]-\dfrac65+\dfrac{4}{15}+\dfrac13v-\dfrac23v[/tex]

Evaluate the like terms (take LCM)

[tex]\dfrac{-6 * 3 + 4}{15}+\dfrac{v - 2v}3[/tex]

Evaluate the like expressions

[tex]-\dfrac{15}{15}-\dfrac{v}3[/tex]

Hence, the equivalent expression of [tex]-\dfrac65-\dfrac23v+\dfrac{4}{15}+\dfrac13v[/tex] is [tex]-\dfrac{15}{15}-\dfrac{v}3[/tex]

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