If f(x) = −3x 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true. x =

The value of the car is January 2003 is  $199,148.54.

Depreciation is the rate of decline in the value of an asset with the passage of time.

The exponential equation that can be used to determine the value of the car is:

Value of the car = purchase value(1 - rate of decline)^time

400,000 x (1 - 0.16)^(2003 - 1999)

400,000 x (0.84^4) = $199,148.54

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[tex]\bullet\:{\boxed{\tt{\red{{Given :}}}}}[/tex]

• Length of the wooden box [tex](l)[/tex] = 80cm.

• Breadth of the wooden box [tex](b)[/tex] = 40cm.

• Height of the wooden box [tex](h)[/tex] = 20cm.

• Side of the square sheet paper = 40cm.

[tex]\bullet\:{\boxed{\tt{\red{{To : Find :}}}}}[/tex]

The number of sheets required.

[tex] \bullet\:{\boxed{\tt{\red{{Formula \: \: used :}}}}}[/tex]

[tex] \star{\underline{\boxed{{\sf{{{TSA}} = \underline{\underline{{\purple\sf 2(lb+bh+hl)}}}}}}}} \star[/tex]

[tex]\star{\underline{\boxed{{\sf{{{Area \: of \: square}} = \underline{\underline{{\purple{\sf side \times side }}}}}}}}}\star[/tex]

[tex]\star{\underline{\boxed{{\sf{{{Number \: of \: sheets \: required} = {{{\purple{\sf \dfrac{TSA}{area \: of \: one \: sheet}}}}}}}}}}} \star[/tex]

[tex] \bullet\:{\boxed{\tt{\red{{Concept :}}}}}[/tex]

As Quayleen wants to place the tree on a wooden block covered with coloured paper with picture of Santa Claus on it. So for knowing the number of sheets required, we need two things one the TSA and Area of one sheet. Once, we will get the values we will divide them to get the answer. Let's Start !!

[tex] \bullet\:{\boxed{\tt{\red{{Solution :}}}}}[/tex]

As we know that ::

Total surface area of cuboid [tex]\large[ \sf 2(lb+bh + hl)][/tex]

Here,

✧ Length [tex](l)[/tex] = 80cm

✧ Breadth [tex](b)[/tex] = 40cm

✧ Height [tex](h)[/tex] = 20cm

Now, by putting the values we get :

[tex] \longrightarrow 2 \bigg[ (80 \times 40) + (40 \times 20) + (20 \times 80) \bigg]\sf {cm}^{2}[/tex]

[tex]\longrightarrow 2 \bigg[ (3200) + (800) + (1600) \bigg] \sf {cm}^{2} [/tex]

[tex] \longrightarrow 2 \bigg[ 5600 \bigg] \sf {cm}^{2} [/tex]

[tex] \longrightarrow 11200 \: \sf {cm}^{2}[/tex]

Hence, the total surface area of the wooden box is 11200 cm²

Now,

The area of each sheet of paper will be :

[tex] \sf \longrightarrow side \times side[/tex]

[tex]\sf \longrightarrow (40 \times 40) \: {cm}^{2} [/tex]

[tex]\longrightarrow \sf (1600) \: {cm}^{2} [/tex]

Hence, the area of each sheet of paper is 1600 cm²

Now,

For finding the number of sheets required

[tex] \longrightarrow \tt \dfrac{total \: surface \: area \: of \: box}{ area \: of \: one \: sheet} [/tex]

[tex]\longrightarrow \sf\dfrac{ \cancel{11200}_{7}}{\cancel{1600}_{1}}[/tex]

[tex] \longrightarrow \purple{ \sf 7}[/tex]

Therefore, Quayleen requires 7 sheets.

[tex]\rule{280pt}{2pt}[/tex]

Answer:

side QR = 12.6 cm, side RS = 7 cm, side QS = 10 cm

Step-by-step explanation:

The side opposite to biggest angle is the longest side

         In ΔQRS,

∠S > ∠R > ∠Q

∠S is the biggest and ∠ Q is the smallest angle.

So, the side opposite to ∠S, QR is the longest side and the side opposite o ∠Q , RS is the smallest side.

QR > QS > RS

QR = 12.6 cm  ; QS = 10 cm and  RS = 7 cm

Answer:

Largest total : [tex]\mathsf {\frac{69}{20}}[/tex]

Smallest total : [tex]\mathsf {\frac{121}{40} }[/tex]

Step-by-step explanation:

Finding the largest total :

Finding the smallest total :

Answer:

Largest Totals : 69/20

Smallest Totals : 121/40

Step-by-step explanation:

Given:

Charlie adds together two of his four number cards. Find the largest and smallest totals that Charlie can make. Give your answers as improper fractions in their simplest form.  

Solve:

First let change all to improper fractions:
7/4      {already a improper fractions}

1 3/8  = 11/8

1 7/10 = 17/10

33/20       {already a improper fractions}

Thus we have:

7/4

11/8

17/10

33/20

According to the solving above ,

⇒ 70/40 , 55/40, 68/40, 66/40

⇒ 70/40 > 68/40 > 66/40 > 55/40

⇒ 7/4 > 1 7/10 > 33/20 > 1 3/8

⇒ Largest Totals : 7/4 + 1 7/10 = 69/20 = 3 9/20

⇒ Smallest Totals : 33/20 + 1 3/8 = 121/40 = 3 1/40

Since, it says given your answers as improper fractions in their simplest form:

Thus,

Largest Totals : 69/20

Smallest Totals : 121/40

RevyBreeze

Answer:

in a rectangle, opposite sides are equal in length

Step-by-step explanation:

now in this question, Pythagoras theorem is being used to find the length

we know both sides by using Pythagoras theorem find third side and get the sum to find ac+bd

Step-by-step explanation:

So it tells you that AB = 21 and AD = 28
and you to find what BD + AC is and since BD is the same length as AC
you only need to find one of them, then double it
There is a formula you use called the Pythagorean theorem
The Pythagorean theorem is A²+B²=C²  
In this problem A = 21    B = 28  and C = the length of BD
so it'll look like  21²+28²=Length of BD²  or BD²=21²+28²  now you find BD
first do 21²+28² --> 441+784 --> 1225   Now you know that 21²+28²=1225
so BD²=1225  Then to find BD, you find √1225(square root of 1225)
Which is 35     So BD=35 and you want to know what BD+AC is
so 35+35=70        

Answer:

x = 70 and the labeled angles are 110 and 70

Step-by-step explanation:

This is a trapezoid, the bases are parallel.

Since the bases are parallel, given two angles are supplementary and their sum is equal to 180:

x + 40 + x = 180 add like terms

2x + 40 = 180 subtract 40 from both sides

2x = 140 divide both sides by 2

x = 70 and the labeled angles are 110 and 70

Answer:

x = 4

Step-by-step explanation:

The figure in the picture is a parallelogram. In parallelograms diagonals bisect each other. That means that they divide each other in half. That means that 6x + 1 is the same as 4x + 9.

6x + 1 = 4x + 9

2x + 1 = 9

2x = 8

x = 4

Triangle ABC was rotated 90° around the point, then translated using the rule (x, y) → ( x + 5, y + 3) to form triangle A'B'C'.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and translation.

Triangle ABC was rotated 90° around the point B, then translated using the rule (x, y) → ( x + 5, y + 3) to form triangle A'B'C'.

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The inverse function of the function f(x) will be f⁻¹(x) = 4x + 48. Then the correct option is D.

The complete question is attached below.

Suppose that the given function is

f: X → Y

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

 f⁻¹: Y → X

It simply means, inverse of 'f' is an undo operator, that takes back the effect of 'f'

The function is given below.

f(x) = (1/4)x – 12

Then the inverse function of the function f(x) will be

(1/4)f⁻¹(x) - 12 = x

            f⁻¹(x) = 4x + 48

Then the correct option is D.

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Answer:

  (c)  (-30, 10)

Step-by-step explanation:

Two points will be on the same graph of a proportional relationship if the ratio of values y/x is the same.

__

The given point (x, y) = (60, -20) has a ratio k = y/x = -20/60 = -1/3.

The offered points have y/x ratios ...

(a) 30/-10 = -3

(b) -15/30 = -1/2

(c) 10/-30 = -1/3 . . . . . . the point you are looking for is (-30, 10)

(d) -30/80 = -3/8

The best conclusion for her to come to: D. this could easily happen with a fair coin after only 3 flips.

A fair coin can be defined as an idealized type of coin that has an equal probability of revealing both heads and tails when randomly tossed.

This ultimately implies that, the best conclusion for her to come to is that this could easily happen with a fair coin after only 3 flips considering 2 of the three coins come up tails.

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Answer:

That is the answer for you step 2

Answer: Choice C  [tex]f(x) = 5(x+4)^2 - 80[/tex]

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

Reason:

The expression [tex]x^2+8x+16[/tex] factors to [tex](x+4)^2[/tex] using the perfect square trinomial formula [tex](a+b)^2 = a^2 + 2ab + b^2[/tex]. In this case, a = x and b = 4.

The -5(16) simplifies to -80

Therefore, [tex]5(x^2+8x+16) - 5(16)[/tex] turns into [tex]5(x+4)^2 - 80[/tex]

Compare this to [tex]a(x-h)^2 + k[/tex] to see that h = -4 and k = -80. The vertex is located at (h,k) = (-4, -80)

Answer:

c) 5(x+4)² - 80

Step-by-step explanation:

You have already gotten the third (second-last) step for finding the vertex as follows:

f(x) = 5(x² + 8x + 16) -5(16)

= 5(x+4)² - 80

Additional remarks: to find the vertex, you can just use find the value of x when x+4 = 0, meaning x = -4 and y = -80. Hence, the vertex is (-4, -80).

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Answer:

27

depth ×breadth×width=3×3×3

= 27

The "middle" of a sorted list of numbers. To find the Median, place the numbers in value order and find the middle number.

When there are two middle numbers we average them.

We have:

3.9, 7, 3.3, 1, 1.4, 1.7, 2.1, 3.3, 5.2

Let's sort the numbers from the smallest to the largest

1, 1.4, 1.7, 2.1, 3.3, 3.3, 3.9, 5.2, 7

Answer:

3.3

Step-by-step explanation:

The first thing you have to do is put them in order from least to greatest.

1, 1.4, 1.7, 2.1, 3.3, 3.3, 3.9, 5.2, 7

Check off one from the left side and one from the right side until you are left with the one in the middle.

When you do that, you are left with 3.3

Answer: Yes

Step-by-step explanation:

[tex]\frac{123}{2}=\frac{246}{4}=\frac{369}{6}=\frac{492}{8}=61.5[/tex].

Since the ratio of distance in miles and the time in hours is constant, the relationship is proportional.

Answer:

A) 48

B) -30

Step-by-step explanation:

Hello!

To compute f(-1) and f(5), we simply replace x with -1 and -5.

The answer to A is 48

We have the values for f(-1) and f(5), so we just switch the operation

The answer to B is -30

Step-by-step explanation:

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Answer:

Step-by-step explanation:

Givens

x + y = 2

x - y = 6

Solution

Just add the two equations together. The y's will drop out.

x + y = 2

x - y = 6             Add

2x = 8                 Divide by 2

2x/2 = 8/2          Combine

x = 4                   Substitute x = 4 into the top equation

x + y = 2

4 + y = 2             Subtract 4 from both sides

4-4+y=2-4          Combine

y = - 2    

Answer

x = 4

y = -2

The values of the trigonometry ratios are:

1: sin α = -12/13 and tan α > 0, find cos α and cot α

Because tan α > 0, then it means that cos α and sin α are negative

So, we have:

sin²α + cos²α = 1

Substitute sin α = -12/13

(-12/13)² + cos²α = 1

This gives

cos²α = 1 - (-12/13)²

Evaluate the squares

cos²α = 1 - 144/169

Evaluate the difference

cos²α = 25/169

Take the square root of both sides

cos α = - 5/13

The cotangent ratio is represented as:

cot α = cos α/sin α

This gives

cot α = (-5/13)/(-12/13)

Evaluate

cot α = 5/12

Hence, cos α = - 5/13 and cot α = 5/12

2: tan α = -12/5 for α in quadrant IV, find sec α and cot α

Because α is in quadrant IV, then it means that sec α is positive

cot α = 1/tan α

This gives

cot α = 1/(-12/5)

Evaluate

cot α = -5/12

Also, we have:

sec²α = 1 + tan²α

Substitute tan α = -12/5

sec²α = 1 + (-12/5)²

Evaluate the squares

sec²α = 1 + 144/25

Evaluate the sum

sec²α = 169/25

Take the square root of both sides

sec α = 13/5

Hence, cot α = -5/12 and sec α = 13/5

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Answer:

y=-4 is a function

Step-by-step explanation:

It passes the vertical line test, and each x has only one y, so it is a function.

x = -4 is NOT a function because one x has multiple y values. It does not pass the vertical line test.

Answer:

[tex]\boxed {cot T = -\frac{5}{12}}[/tex]

Step-by-step explanation:

Finding the missing side :

Taking the cot value :

Answer:

csc T =13/12

(cot T)^2=csc^2T -1

Cot T)^2=(13/12)^2-1

(cot. T )^2=169/144-1

(cot T)^2=169-144/144

(cot T)^2=25/144

cot T =√ 25/144

cot T=5/12

where cot is negative in WE

so Cot T=-5/12

Step-by-step explanation:

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Answer:

a₃ = 1.25

Step-by-step explanation:

the sum to infinity is calculated as

S ∞ = [tex]\frac{a_{1} }{1-r}[/tex]

a₁ is the first term and r the common ratio

given a₁ = 5 and S∞ = 10 , then

10 = [tex]\frac{5}{1-r}[/tex] ( multiply both sides by (1 - r)

10(1 - r) = 5

10 - 10r = 5 ( subtract 10 from both sides )

- 10r = - 5 ( divide both sides by - 10 )

r = 0.5

then

a₂ = a₁ × r = 5 × 0.5 = 2.5

a₃ = a₂ × r = 2.5 × 0.5 = 1.25

The velocity of the wind will be 50 km per hour.

The quantity which has magnitude, direction and follows the law of vector addition is called a vector.

A motorcyclist riding North along a straight road at 50 km per hour observes that the wind appeared to have a velocity of 50 km per hour from the direction North 60 degrees West.

Then the velocity of the wind will be

Let x be the speed of the wind. Then we have

x² = 50² + 50² - 2 x 50 x 50 x cos 60°

x² = 2500 + 2500 - 2500

x² = 2500

x = 50 km per hour

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The solution to the inequality, -2(8x – 4) < 2x + 5, is: B. x > 1/6.

To find the solution to an inequality, solve the inequality to isolate the variable.

Given the inequality, -2(8x – 4) < 2x + 5, open the bracket:

-16x + 8 < 2x + 5

Combine like terms

-16x - 2x < -8 + 5

-18x < -3

Divide both sides by -18 then reverse < to >

-18x/-18 > -3/-18

x > 1/6

The solution is: B. x > 1/6

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