Let f(x)=3x-4 and g(x)=x^2-5. Find f(g(3))

Answer:

  x = -3/2

Step-by-step explanation:

To find the unknown value, substitute all known values and solve for the one remaining. After substitution, this becomes a 2-step linear equation, so is solved by the procedure for such equations.

  y = -6x +5 . . . . . given

  14 = -6x +5 . . . . substitute known value

  9 = -6x . . . . . . . subtract 5 (step 1)

  9/-6 = x = -3/2 . . . . divide by the coefficient of x (step 2);

Hello!

In order to find the value of x, we should take the value of y and plug it in and then simplify.

[tex]\bold{y=-6x+5}[/tex]

Plug in:

[tex]\bold{14=-6x+5}[/tex]

Switch places:

[tex]\bold{-6x+5=14}[/tex]

Now, subtract 5 from both sides:

[tex]\bold{-6x=14-5}[/tex]

[tex]\bold{-6x=9}[/tex]

Divide both sides by -6 in order to isolate x:

[tex]\bold{x=-\displaystyle\frac{9}{6}}[/tex]

Can this fraction be reduced? Sure, we can divide the numerator (9) and the denominator (6) by 3:

[tex]\bold{-\displaystyle\frac{3}{2}}[/tex]

As a Mixed Fraction:

[tex]\bold{1\displaystyle\frac{1}{2}}[/tex]

Hence, the value of x is:

[tex]\huge\boxed{\boxed{\mathfrak{\star{Answer:{\boxed{-\frac{3}{2} }}}}}}[/tex]

Hope everything is clear.

Let me know if you have any questions!

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[tex]\rm{A~teen~who~never~gives~up}[/tex]

Answer:

I think it's a hope this helps

Answer:

36 ,36 30,2

Step-by-step explanation:

hope it's okay to you

Answer: x<-1

Step-by-step explanation:

The answer is A!

Answer:

See below.

Step-by-step explanation:

Solving the inequality :-

Graph A shows the solution to the inequality correctly

The polynomial 400x⁶ + 600x⁶ has a degree of 6 and is a binomial.

Polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.

Polynomials are classified based on degree as linear, cubic, quadratic, etc.

A polynomial with two terms is known as a binomial. Hence:

The polynomial 400x⁶ + 600x⁶ has a degree of 6 and is a binomial.

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Answer:

0/5 = 0

0/200 = 0

0/ (-25) = 0

Step-by-step explanation: I am sure this is it because these are rational numbers

Question 1

Focus on the triangle on the left.

sine is the ratio of opposite over hypotenuse

sin(angle) = opposite/hypotenuse

sin(44) = w/30

w = 30*sin(44)

w = 20.839751 approximately

Now move onto the triangle on the right. We'll use cosine this time.

cos(angle) = adjacent/hypotenuse

cos(x) = w/45

cos(x) = 20.839751/45

cos(x) = 0.463106

x = arccos(0.463106) ... arccosine is the same as [tex]\cos^{-1}[/tex]

x = 62.412286

==========================================================

Question 2

Focus on the triangle on the left.

sin(angle) = opposite/hypotenuse

sin(32) = w/5

w = 5*sin(32)

w = 2.649596

Now move to the triangle on the right.

sin(angle) = opposite/hypotenuse

sin(x) = w/5

sin(x) = 2.649596/5

sin(x) = 0.5299192

x = arcsin(0.5299192) .... arcsine is the same as [tex]\sin^{-1}[/tex]

x = 31.999996

==========================================================

Question 3

This time we use the tangent ratio.

Focus on the triangle that has legs of w and 16.

tan(angle) = opposite/adjacent

tan(70) = 16/w

w*tan(70) = 16

w = 16/tan(70)

w = 5.823524

Now let y = x+w and focus on the largest triangle this time.

tan(angle) = opposite/adjacent

tan(41) = 16/y

y = 16/tan(41)

y = 18.405895

This leads to:

y = x+w

x = y-w

x = 18.405895 - 5.823524

x = 12.582371

Given the box-and-whisker plot, the number of employees that took a break that lasted between 37 - 41 minutes is: 180.

A box-and-whisker plot is a graphical representation of a data set showing how the data set is distributed into percentiles such as 25%, 50%, and 75%.

The range of the rectangular box covers 50% of the data set.

Thus, 37 - 41 minutes lies between 50% on the box-and-whisker plot, therefore:

50/100 × 360 = 180 employees.

In summary, given the box-and-whisker plot, the number of employees that took a break that lasted between 37 - 41 minutes is: 180.

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Answer:

The answer is 90

Step-by-step explanation:

Its not 180 I take k12 also.

Answer:

[tex]A.\,\orange{ \bold{ \frac{x - 3}{3x + 1} }}[/tex]

Step-by-step explanation:

[tex] \frac{x + 2}{ {x}^{2} + 5x + 6 } \div \frac{3x + 1}{ {x}^{2} - 9} \\ \\ = \frac{x + 2}{ {x}^{2} + 3x + 2x+ 6 } \div \frac{3x + 1}{ {x}^{2} - {(3)}^{2} } \\ \\ = \frac{\cancel{x + 2}}{ \cancel{{({x}+ 3)}} \cancel{(x+ 2) }} \times \frac{\cancel{( {x} + 3)}( {x} - {3)}}{3x + 1} \\ \\ = \purple{ \bold{ \frac{x - 3}{3x + 1} }}[/tex]

All three are similar

In ∆SUT and ∆VWX

So by SSA they are similar

In ∆PRQ and rest two

All angles are.

So

They are similar by AAA congruence

Answer:

Kai suggested the best way to produce a random sample that is not biased

Step-by-step explanation:

Answer:

The answer is Kai suggested the best way to produce a random sample that is not biased

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

If we divide the shape we can get 3 x 10 with equals 30. Then take the remaining which is 2 x 10 and we get 20. Add the two to get 50. The area is 50sq miles.

Hope this helps. pls mark brainliest

Answer:

7 1/3 inches

Step-by-step explanation:

2 (1 3/4 + 1 11/12)

9+11

3/4+11/12= -------------

12

20/12

=1 2/3+ 2

2(3 2/3)

= 7 1/3

Answer:

$750

Step-by-step explanation:

2500 divided by 100 = 25 and 25 x 30 = 750

Sorry if im wrong

The price for 2500 pencils is $750.

The unitary technique involves first determining the value of a single unit,  followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

We have,

A box of 100 personalized pencils costs $30.

So, cost of 1 pencil = $30 / 100 = 3/10

Now, the price to buy the 2500 pencils

= 2500 x 3/10

= 250 x 3

= $750

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Answer:

money left= -50•games played + 47.50

Answer:

10 feet

Step-by-step explanation:

Drawing obviously not to scale but... Red segment is the ruler, at least the part between 5 and 6 inches, 1 inch long. Brown segment is the pole, ground to the top. Leftmost point is the eye, green line is the horizontal. The triangles are similar (AAA, the vertical lines are parallel), the ratio of the side is the same as the ratio of the heights. The height of the larger triangle (measured across the green line is

[tex]40 yd \times 3\frac{ft}{yd} \times 12\frac{in}{ft}= 1440''[/tex].

Ratio of the height is then [tex]1440\div24 = 60[/tex].

At this point the height of the pole is 60 times the length of the measure on the ruler, or 60 inches, that is 5 feet. Add the 5 feet the pole was starting from, it's 10 feet.

Step-by-step explanation:

the volume of a cone is

ground area × height / 3

and the ground area is a circle.

so,

pi×r²×h/3

with r being the radius (half the diameter) and h being the height.

therefore, we get

pi×(12/2)²×11/3 = pi×6²×11/3 = pi×12×11 = 132pi =

= 414.6902303... m³

Answer:

Given equation:

[tex]\left(\dfrac{1}{27}\right)^x=3^{(-4x+6)}[/tex]

27 can be written as [tex]3^3[/tex]

Also [tex]\dfrac{1}{a^b}[/tex] can be written as [tex]a^{-b}[/tex]

[tex]\implies \dfrac{1}{27}=\dfrac{1}{3^3}=3^{-3}[/tex]

Therefore, we can rewrite the given equation with base 3:

[tex]\implies (3^{-3})^x=3^{(-4x+6)}[/tex]

To solve, apply the exponent rule [tex](a^b)^c=a^{bc}[/tex]

[tex]\implies 3^{-3 \cdot x}=3^{(-4x+6)}[/tex]

[tex]\implies 3^{(-3x)}=3^{(-4x+6)}[/tex]

[tex]\textsf{If }a^{f(x)}=a^{g(x)}, \textsf{ then } f(x)=g(x)[/tex]

[tex]\implies -3x=-4x+6[/tex]

Add [tex]4x[/tex] to both sides:

[tex]\implies x=6[/tex]

Answer:

2159.6 i think

Step-by-step explanation:

i used a rectangle calculator

[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\qquad \impliedby \textit{let's now find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{5^2-3^2}=b\implies \sqrt{25-9}=b\implies \sqrt{16}=b\implies 4=b \\\\[-0.35em] ~\dotfill[/tex]

[tex]sin(\theta )=\cfrac{\stackrel{opposite}{4}}{\underset{hypotenuse}{5}}\qquad \qquad tan(\theta )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{3}}\qquad \qquad cot=\cfrac{\stackrel{adjacent}{3}}{\underset{opposite}{4}} \\\\\\ sec(\theta )=\cfrac{\stackrel{hypotenuse}{5}}{\underset{adjacent}{3}}\qquad \qquad csc(\theta )=\cfrac{\stackrel{hypotenuse}{5}}{\underset{opposite}{4}}[/tex]

The values of the five other trigonometric functions value for the same input θ for which cos(θ) = 3/5 are:

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

We're given that:

cosθ = 3/5 for some angle θ

Since we've got:

[tex]\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}[/tex]

Therefore, we have:

[tex]\dfrac{3}{5} = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}[/tex]

Let we consider a right angled triangle in which there is hypotenuse of length 5 units and base (from the perspective of one of its non-right angle) of 3 units (as shown in the image attached below).

(we couldve taken 3x and 5x instead of 3 and 5, for any positive real number value of 'x' as when we would take their ratio, that common factor 'x' would get cancelled out. We can think of 3 and 5 as the special case of 3x and 5x when x = 1)

Then, from that perspective, let the perpendicular be of the length 'p' units, then as per the pythagoras theorem, we get:

[tex]p^2 + 3^2 = 5^2\\p = \sqrt{25 - 9} = \sqrt{16} = 4 \: \rm units[/tex]

(took only the positive root to remove the square term because the value of p denotes length, which is a non-negative quantity).

Thus, we have:

From the perspective of the angle θ:

Thus, using these values, and the definition of the trigonometric ratios, we get:

Thus, the values of the five other trigonometric functions value for the same input θ for which cos(θ) = 3/5 are:

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Answer: 33 plus 3x

Step-by-step explanation:  simplified it

Answer:

The answer is 5x3+8x2+5x

Step-by-step explanation:

Answer:

its c i just got done doing the same one

Step-by-step explanation:

got it right on my real numbers test and got 100% if you need more help comment under my answer

Answer:

sixt

Step-by-step explanation:

thats easy the sin should be six

Answer:

38.5 in²

Step-by-step explanation:

Area of circle= πr², where r is the radius

Substitute the value of the radius into the formula above:

Area of circle

= π(3.5)²

= 12.25π

= 38.5 in² (3 s.f.)

The amount of money that Han saves by using a coupon is $1.5%

The percentage off Clare's purchase with the coupon is 25%

A coupon reduces the price at which an item is sold

Amount saved = coupon discouunt x normal price

10% x $15

0.1 x $15 = $1.5

Percent off = (6/24 x 100  = 25%

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Answer:

Slope of the line is undefined

Step-by-step explanation:

(x₁, y₁) = (-1 , 3)  and (x₂, y₂) = (-1 , 8)

The line is parallel to y-axis. The slope of the line parallel to y-axis is undefined.

The standerd form 4m – 2m^4 – 6m^2 +9.

We have given that the polynomial given below we have to find the standerd form  of the polynomial.

[tex]P(x)=a_nx^n+a_{n-1}x^{n-1}+......+a_1x+a_0[/tex]

n=4

Standard form of the polynomial

[tex]4m - 2m^4 - 6m^2 + 9[/tex]

Rearranginge term we get

[tex]=-2m^4 - 6m^2 + 4m + 9[/tex]

The third term of the given polynomial is 0.

Therefore,the standard form is,

[tex]-2m^4 - 6m^2 + 4m + 9[/tex]

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Answer:

The area is about 96.06 or 96.1

Step-by-step explanation:

I tried my best to solve it, I'm sorry if it's wrong.