Need help with this I’d really appreciate it

Answer:

[tex]\displaystyle \large{f^{-1}(7)=5}[/tex]

Step-by-step explanation:

Given:

[tex]\displaystyle \large{f(x)=2x-3}[/tex]

To find:

[tex]\displaystyle \large{f^{-1}(7)}[/tex]

Inverse Function Definition:

Notation Definition (Example - Exponential Function and Logarithm are Inverse to each other.)

[tex]\displaystyle \large{f(x) = \{(x,y) \in \mathbb{R} \times \mathbb{R^{+}} \ | \ y=a^x, a\neq 1, a > 0 \}}\\\displaystyle \large{f^{-1}(x) = \{(x,y) \in \mathbb{R^{+}} \times \mathbb{R} \ | \ y=\log_a x, a\neq 1, a > 0 \}}[/tex]

Notice that both functions have swapped domain and range. Domain is set of all x-values while range is set of all y-values.

Inverse Property:

Back to the question, first, we have to find an inverse of linear function. We can do by swapping x and y [f(x)] variables.

[tex]\displaystyle \large{f(x)=2x-3 \to x=2f(x)-3}[/tex]

Solve for f(x):

[tex]\displaystyle \large{x=2f(x)-3}\\\displaystyle \large{x+3=2f(x)}\\\displaystyle \large{f(x)=\dfrac{x+3}{2}}\\\therefore \displaystyle \large{f^{-1}(x)=\dfrac{x+3}{2}}[/tex]

Therefore, the inverse is (x+3)/2. Next, we find [tex]\displaystyle \large{f^{-1}(7)}[/tex] which we can do by simply substituting x = 7 in the inverse.

[tex]\displaystyle \large{f^{-1}(7)=\dfrac{7+3}{2}}\\\displaystyle \large{f^{-1}(7)=\dfrac{10}{2}}\\\displaystyle \large{f^{-1}(7)=5}[/tex]

Therefore, the answer is 5.

Answer:

C number of binders because the teacher would have to order binders depending on how many students there are.

Step-by-step explanation:

Answer:

first choice

Step-by-step explanation:

First, observe the axis.

The graph has labeled:

vertical axe as h (hight) and

horizontal axe as t (time).

Second, observe on the graph that the object is dropped from the height 120 feet because at the point t = 0 (when the drop did not start yet) the height is h = 120.

→We can eliminate the last choice that said "object is dropped from -16 feet"

Third, the equations for the hight of the object after t seconds are when the object is dropped from 120 feet are:

h(t) = -16t² + 120

if t= 0 then hight should be 120

h(t) = -16·0² + 120 = 120 ✅

and

h(t) = -16t² - 120

if t= 0 then hight should be 120

h(t) = -16·0² - 120 = - 120 ❌

→Eliminate the second choice that said at t=0 , h(t) = -120

→The first choice is the correct one

Answer:

  D.  F(G(H(x))) depends on G(H(x))

Step-by-step explanation:

A function depends on its argument (the stuff in parentheses after the function name). The argument of function F in F(G(H(x))) is G(H(x)).

  F(G(H(x))) depends on G(H(x))

__

Answer choices A and C do not make any statement about the given composition. Answer choice B shows a composition (H(G(x))) that has no relation to the argument of function F.

Answer:  D.  F(G(H(x))) depends on G(H(x))

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

not really sure so yeah B

To convert any given angle from the measure of degrees to radians, the value has to be multiplied by π/180.

hope it helps...!!!

Answer:

there are 2pi radians in a circle

there are also 360 radians in a circle

let r = radians and d = degrees

2*pi*r=360*d

2pi/360*radians = degrees

(pi/180)*radians = degrees

Answer:

The two events are independent

Step-by-step explanation:

Since the king was placed back in the deck and the deck was re-shuffled,

the drawing of a king does not effect the probability of subsequently drawing a queen.

The probability of picking the queen is independent of the probability of picking the king.

pick a card from a shuffled pack and draw a king. You put it back in the pack, shuffle, and then pick another card. This time you draw a queen. How are the two events of picking a king and picking a queen related to be justified

Probability can be defined as the ratio of favorable outcomes to the total number of events.

There is a 52-card deck.
Pick a card from a shuffled pack and draw a king. You put it back in the pack, shuffle,
Probability can be given as for the draw of the king,
p = 1/52

Put it back in the pack, shuffle, and then pick another card. This time you draw a queen.
Probability can be given as for the draw of the queen,
p = 1/52

Since both probabilities is the same it implies the probability of one event is independent of the other.

Thus, the probability of picking the queen is independent of the probability of picking the king.

Learn more about probability here:

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Answer:

First, evaluate 3^3

3^3 means three times itself three times.

[tex]3 * 3 * 3 = 27[/tex]

[tex]\sqrt{27} = 5.19[/tex]

Next, square root eight.

[tex]\sqrt{8} = 2.82[/tex]

Now, divide the two numbers.

[tex]5.19 / 2.82 = 1.84[/tex] if needed, include full form: 1.840425531914894

(3n)³ = 27

= 27√8 = 2.82

= 27√8 = 2.82√27 = 5.19

5.19/2.82 = 1.84

Here is your answer buddy..

Leila will run less than 25 miles this week. This means the inequality symbol will be this: "<". Since she has already ran 13 miles, we need to plug-in a variable for the additional miles she must run. The inequality should be like this when plugged-in: 25 < 13 + t.

The final answer to your question is 25 < 13 + t.

Answer:

v = 15/7, or 2.14

Step-by-step explanation:

Find a common denominator, or multiply both denominators by each other, and well as the numerator.

v/5 = 3/7 can be written as 7v/35 = 15/35

multiplying both sides with 35, we are left with 7v = 15

v = 15/7, or 2.14

Answer:

a=13m

Step-by-step explanation:

that's it in the picture

Answer:

[tex]\sf a=\boxed{13}\:cm[/tex]

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

[tex]\implies \sf \sin(31^{\circ})=\dfrac{a}{25}[/tex]

[tex]\implies \sf a=25\sin(31^{\circ})[/tex]

[tex]\implies \sf a=12.87595187...\:cm[/tex]

Therefore, a = 13 cm (to the nearest whole number)

Answer: Is in the screenshot

The linear model for the daily cost is C(x) = $1378 + $1.83(x).

The cost of producing 267 widgets is $1,866.61

Fixed cost is the cost the remains constant with the number of widgets produced. Variable cost increases with  the number of widgets produced. Daily cost is the sum of fixed cost and variable cost.

Fixed cost = fixed cost + (variable cost x number of widgets)

C(x) = $1378 + $1.83(x).

C(x) = $1378 + $1.83(267) = $1,866.61

To learn more about fixed cost, please check: https://brainly.com/question/25879561

Answer:

Summary:

The solution to 2.5 - 1.2x < 6.5 - 3.2x lies in the interval (-∞, 2).

Answer:

452.16

Step-by-step explanation:

di is twice the radius and to get area you need radius so 24/2=12

now insert 12 into the formula 12^2*3.14 now use pemdas

12^2=144

144*3.14

452.16

Answer:

Area of circle = 452.16

Step-by-step explanation:

Conversion of diameter into radius,

→ r = 24/2

→ [ r = 12 ]

Formula we use,

→ Area = π × r²

Now the area of circle will be,

→ π × r²

→ 3.14 × (12)²

→ 3.14 × 144

→ 452.16

Hence, area of circle is 452.16.

Answer:

1100/7

Step-by-step explanation:

Because, this is half circle then if we need the length of it we will use the circumference (2 x pie x r) x 1/2

[tex]~~~~~\sin 30^{\circ} = \dfrac{\text{Perpendicular}}{\text{Hypotenuse} }\\\\\\\implies \dfrac 12 = \dfrac{8}x\\\\\\\implies x = 8\cdot2\\\\\\\implies x = 16 ~ \text{cm.}[/tex]

Answer:

56503

Step-by-step explanation:

this grows exponentialy so at the start it would be 50,000 growing by 5% every ten years. but since there is only 2 ten years in 25 years we must cut the percent in half making 2.5%

Step 1

(50,000×5%)+50,000= 52500

Step 2

(52500×5%)+52500= 55125

step 3

(55125×2.5%) +55125= 56503

The two equations that could be used to determine the number of pictures (x) and songs (y) is x + y = 16  and 650x + 2200y = 18150

An equation is an expression that shows the relationship  between two or more numbers and variables.

Let x represent the number of pictures and y represent the number of songs, hence:

x + y = 16    (1)

And:

650x + 2200y = 18150    (2)

The two equations that could be used to determine the number of pictures (x) and songs (y) is x + y = 16  and 650x + 2200y = 18150

Find out more on equation at: https://brainly.com/question/2972832

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Answer:

30

Step-by-step explanation:

total length = 180 = (5 + 1) sections

shorter wire = 1 section = 30

Answer:

Standard form of 400000000 (four hundred million) is 4 x [tex]10^{8}[/tex]

Step-by-step explanation:

Because there are 8 0s, and its 400 million

Hope this helps!

Answer:

1. C(d)=0.69x+25.95

2. C(d)=0.69(57)+25.95

[0.69 times 57 is 39.33]

=  65.28 dollars

3. 136.3 miles

Step-by-step explanation:

For the first question....

Since this is a function, we have to start with C(d). Even if you drive 0 miles, you still have to pay $25.95 just for renting the truck, so that is constant. For every mile you drive, you pay $0.69. Since we don't know how far anyone is going to drive, we will put 'x' as the amount of miles driven. The number of miles driven (x) multiplied by 0.69 will be the cost of that. The final function would be C(d)=0.69x+25.95.

For the second question....

We know the general function now, so driving 57 miles would mean substituting "x" for 57, and doing the multiplication (if necessary), 0.69 times 57 equals 39.33 (the dollar amount for driving 57 miles, not including the starting fee of 25.95)

Doing the math, you can get $65.28 (39.33+25.95).

For the third question...

If we have a budget, we know that C(d) is the amount of money spent, so we'll substitute the budget (120) for that. We'll solve the equation for x from there, and should get 136.3 miles (rounded to the nearest hundredth).

Hope this helps!

Answer:

π/6 , 7π/6

Step-by-step explanation:

3sinx = sinx + 1 ⇒ 2sinx = 1 ⇒ sinx = 1/2

At which value(s) of x does sinx equal 1/2?

x = arcsin(1/2) at π/6 and 5π/6

Answer:

[tex] {4x}^{2} - 20x + 25[/tex]

Step-by-step explanation:

[tex] {(2x - 5)}^{2} = {(2x)}^{2} - 2(2x)(5) + {5}^{2} = 4 {x}^{2} - 20x + 25[/tex]

Step-by-step explanation:

[tex] \longmapsto\: \purple{hello \: mate }[/tex]

i,e

60×50/100

= 60 x 1/2

=30

Answer:

50%

Step-by-step explanation:

[tex]30\div 60\times 100[/tex]

[tex]\cfrac{1}{2}\times \:100[/tex]

[tex]\cfrac{1}{2}\times \cfrac{100}{1}[/tex]

[tex]\cfrac{1\times \:100}{2\times \:1}[/tex]

[tex]\cfrac{100}{2}[/tex]

[tex]50[/tex]

Answer:

13/12 or 1  1/12

Step-by-step explanation:

First you change 2/3 to 8/12 by multiply both the numerator and denominator by 4. Then, you add the numerators but DO NOT change the denominators. Therefore, your answer is 13/12 which = 1  1/12.

[tex]6e+3(e-1)\\\\=6e+3e-3\\\\=9e-3[/tex]

Answer: B

Step-by-step explanation: