Given f(x) = x² + 8x and g(x) = x4, choose
the expression for (fºg)(x).

Answer:

Quotient =(3x²-5x-1)  and reminder = 1

Step-by-step explanation:

[tex]\frac{9x^3-18x^2+2x+2}{3x-1}[/tex]

3x-1)9x³-18x²+2x+2(3x²-5x-1

      9x³-3x²

    ------------------------

          -15x²+2x+2

          -15x²+5x

           ------------------

                  -3x+2

                   -3x+1

                    --------

                         1

Therefore 9x³-18x²+2x+2=(3x²-5x-1)(3x-1)+1

Quotient =(3x²-5x-1)  and reminder = 1

x + (-4) = 10.

We can use the positive - negative rule.

x + (-4) = 10.

x - 4 = 10.

x = 10 + 4

x = 14.

Answer: x = -6, and y = -6  (-6, -6)

Step-by-step explanation: What we have here is a pair of simultaneous equations. Since we have been instructed to solve by substitution, we shall begin with the one which has one of the variables as having a coefficient of 1. We shall start with equation 2 which is,

y = 2x + 6

Having taken note of this, we can now go on to the other equation and substitute for the value of y.

Hence, from equation 1,

4x - 4y = 0 (substitute for the value of y)

4x - 4(2x + 6) = 0

4x - 8x - 24 = 0

-4x -24 = 0

Add 24 to both sides of the equation

-4x = 24

Divide both sides of the equation by -4

x = -6

Having calculated the value of x, we can now go on to substitute for the value of x in equation 2.

Therefore,

y = 2x + 6

y = 2(-6) + 6

y = -12 + 6

y = -6.

So, x = -6 and y = -6

Answer:

x= - 3.5

y= - 6.5

Step-by-step explanation:

-3x+y = 4 equation 1

-9x + 5y = -1 equation 2

and

equation 1 can be written as

y = 4+ 3x

so put this in equation 2

-9x + 5 ( 4+ 3x) = -1

-9x +20 +15x = -1

6x = -21

X= -21 ÷ 6

X = - 3.5

so put this value of x in equation 1 to find value of y

-3 ( -3.5) + y = 4

10.5 + y = 4

y = 4 - 10.5

Y = - 6.5

Answer:

x= - 3.5

y= - 6.5-

Answer:

49.5

Step-by-step explanation: 11x9=99/2

Step-by-step explanation:

We find,

[tex](x+2y)^7[/tex]

To find, the binomial expansion of of [tex](x+2y)^7[/tex] = ?

We know that,

[tex](x+y)^{n} =^nC_0x^n+^nC_1x^{n-1}y+nC_2x^{n-2}y^2+nC_3x^{n-3}y^3+...+^nC_ny^n[/tex]

∴ [tex](x+2y)^7[/tex]

Here, n = 7, x = x and y = 2y

[tex](x+2y)^7[/tex]= [tex]^7C_0x^7+^7C_1x^{7-1}(2y)+^7C_2x^{7-2}(2y)^2+^7C_3x^{7-3}(2y)^3+^7C_4x^{7-4}(2y)^4+^7C_5x^{7-5}(2y)^5+^7C_6x(2y)^6+(2y)^7[/tex][tex]=x^7+7x^{6(2y)+21x^{5}4y^2+35x^{4}8y^3+^35x^{3}16y^4+21x^{2}32y^5+7x64y^6+128y^7[/tex]

[tex]=x^7+14x^{6}y+84x^{5}y^2+280x^{4}y^3+560x^{3}y^4+672x^{2}y^5+448xy^6+128y^7[/tex]

∴ The binomial expansion of of [tex](x+2y)^7[/tex]

[tex]=x^7+14x^{6}y+84x^{5}y^2+280x^{4}y^3+560x^{3}y^4+672x^{2}y^5+448xy^6+128y^7[/tex]

Thus, the required "option 4)"  is correct.

Answer:

D. x7 + 14x6y + 84x5y2 + 280x4y3 + 560x3y4 + 672x2y5 + 448xy6 + 128y7

Step-by-step explanation:

Answer:

18.19

Step-by-step explanation:

$20-15%=$17

$17+7%=18.19

Lin's father pays $18.19 for the meal after the 15% discount and 7% sales tax.

To find out what Lin's father pays for the meal after the discount and sales tax, we need to follow these steps:

Let's apply these steps to the given information:

Step 1: Discount amount = $20 x 15% = $3

Step 2: Discounted price = $20 - $3 = $17

Step 3: Sales tax amount = $17 x 7% = $1.19

Step 4: Total amount paid = $17 + $1.19 = $18.19

Therefore, Lin's father pays $18.19 for the meal after the discount and sales tax.

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Answer:

E

Step-by-step explanation:

Given the system of two equations:

[tex]\left\{\begin{array}{l}\dfrac{2}{3}x-\dfrac{1}{2}y=1\\ \\-\dfrac{4}{3}x+y=-3\end{array}\right.[/tex]

Multiply the first equation by 6 and the second equation by 3 to eliminate fractions:

[tex]\left\{\begin{array}{l}4}x-3y=6\\ \\-4x+3y=-9\end{array}\right.[/tex]

Add these two equations:

[tex]4x-3y-4x+3y=6-9\\ \\0=-3[/tex]

You get false equality [tex](0\neq -9)[/tex], so the system of two equations has no solution (two equations represent parallel lines)

Answer:

A, D, E

Step-by-step explanation:

180 is the speed of the motorboat. I don't know the speed of the current.

........................................

120÷4=30

30×6=180

[tex]\boxed{g(x)=2x^2+31x+130}[/tex]

Hello! Remember to write complete questions in order to get good and exact answers. Here you haven't provided any quadratic equation, so I could help you in a general way. A quadratic equation is given by the form:

[tex]f(x)=ax^2+bx+c \\ \\ a,b,c \ constant \ and \ a\neq 0[/tex]

Suppose you have the following quadratic equation:

[tex]f(x)=2x^2+3x+6[/tex]

Perform the following transformation:

Then, we get:

[tex]g(x)=2(x+\mathbf{7})^2+3(x+\mathbf{7})+6+\mathbf{5}[/tex]

[tex]\left(x+7\right)^2:\quad x^2+14x+49 \\ \\ g(x)=2\left(x^2+14x+49\right)+3\left(x+7\right)+6+5 \\ \\ \\ g(x)=\:2x^2+28x+98+3x+21+6+5 \\ \\ \boxed{g(x)=2x^2+31x+130}[/tex]

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Answer:

Jose has completed 60% of his total deliveries.

Step-by-step explanation:

Given:

Jose needs to make a total of 25 deliveries this week. So far he has completed 15 of them.

Now, to find the percentage of his total deliveries has Jose completed.

Total deliveries = 25.

Deliveries completed = 15.

Now, to get the percentage of his total deliveries has Jose completed:

[tex]\frac{Deliveries\ completed}{Total\ deliveries} \times 100[/tex]

[tex]=\frac{15}{25} \times 100[/tex]

[tex]=0.6\times 100[/tex]

[tex]=60\%.[/tex]

Therefore, Jose has completed 60% of his total deliveries.

Answer:

20

Step-by-step explanation:

-4/-0.2

When dividing numbers with the same sign, the result is always positive. In this case, -4 divided by -0.2 is equal to 20.

When dividing numbers with the same sign, the result is always positive. In this case, -4 divided by -0.2 is equal to 20.

Answer:

Step-by-step explanation:

 ∠ABC =   ∠ DEF         {GIVEN}

            =      ∠GHI      {   ∠DEF =   ∠GHI - given}

 ∠ ABC =  ∠GHI

Answer:

180km

Step-by-step explanation:

Times both values by 1.8

1.8 : 1800000

You have 1,800,000 dm

Turn to m by dividing by 10 you get 180,000 m

Turn to km by dividing by 1000 you get 180km

Answer:

180

Step-by-step explanation:

Answer:

s = 5/4

Step-by-step explanation:

Solve for s:

86 = 8 s + 76

86 = 8 s + 76 is equivalent to 8 s + 76 = 86:

8 s + 76 = 86

Subtract 76 from both sides:

8 s + (76 - 76) = 86 - 76

76 - 76 = 0:

8 s = 86 - 76

86 - 76 = 10:

8 s = 10

Divide both sides of 8 s = 10 by 8:

(8 s)/8 = 10/8

8/8 = 1:

s = 10/8

The gcd of 10 and 8 is 2, so 10/8 = (2×5)/(2×4) = 2/2×5/4 = 5/4:

Answer:  s = 5/4

Answer: s = 1.25

Step-by-step explanation:

Answer:

12.5% is the answer for this question. the other answer is not correct,

Final answer:

The number 18 expressed as a percent is 100%. This is found by using the formula (Number / Total × 100%) and considering 18 as both the part and the whole.

Explanation:

To express the number 18 as a percent, you need to understand that a percent is a way of expressing a number as a part of 100. The word percent comes from the Latin phrase 'per centum' which means 'by the hundred'. So, the task at hand is to determine what part of 100 is 18.

The formula for converting a number to a percent is:

Number / Total × 100%

Since we are converting the whole number 18 into a percent, we treat it as 18 out of 18 or the 'part' as 18 and the 'whole' as also 18:

18 / 18 × 100% = 100%

Therefore, the number 18 expressed as a percent is 100%.

Answer:

Scalene triangle

Step-by-step explanation:

It is a scalene triangle because none of the sides are equal .equilateral triangle have the three sides equal. isosceles triangle have only two equal sides

Answer:

hotdog is $7.50

Step-by-step explanation:

hotdog = d soda = s

s + 2.5 = d

2d + s = 20

3s + 5 = 20

s = 5

5 + 2.5 = d

7.5 = d

Answer:

120.6

Step-by-step explanation:

Since we know that 67 percent of coins are quarters.

Total coins = 180

67% of 180= 180 * 67/100

120.6.

So he has about 120.6 quarters.

Answer:

126 quarters

Step-by-step explanation:

67% ≈ 70%

70% = 70/100

70% = 7/10

180 * 7/10 = 126 quarters

The problems relate to airspeed and altitude in avionics and involve using mathematical concepts such as differential equations and differentials. The differential pressure when the indicated airspeed is 157 knots can be found by rearranging the given equation. Changes in airspeed can be determined based on differences in differential pressures. The equation for true airspeed in terms of altitude and differential pressure can be found by substituting the equation for indicated airspeed into the equation for true airspeed.

The subject of these problems is differential calculus, which deals with differential equations and differentials. We're using these mathematical concepts to solve problems related to airspeed and altitude in avionics.

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To find differential pressure at 157 knots, solve the equation S = 136.4√p + 4.5, yielding p ≈ 1.25. For changes in pressure from 218 to 195 knots, calculate both pressures then find the difference: Δp ≈ 0.50 in Hg. For true airspeed in terms of altitude and differential pressure, use T = (1 + A/50,000) ⋅ (136.4√p + 4.5). Estimating differential pressure for a true airspeed of 280 knots at 20,000 feet involves solving the combined equation to find p ≈ 2.05.

Let's tackle each problem step-by-step.

Problem 1

Given the indicated airspeed, S, of 157 knots, we need to find the differential pressure p.

The relationship is given by:

S = 136.4√p + 4.5

Substitute S = 157 into the equation:

157 = 136.4√p + 4.5

Subtract 4.5 from both sides:

152.5 = 136.4√p

Divide both sides by 136.4:

√p = 152.5 / 136.4 ≈ 1.118

Square both sides to solve for p:

p ≈ 1.118² ≈ 1.25 inches of mercury

Problem 2

We need to find the change in the differential pressure when the airplane slows down from 218 knots to 195 knots.

First, find the differential pressure at 218 knots:

218 = 136.4√p + 4.5

213.5 = 136.4√p

√p = 213.5 / 136.4 ≈ 1.565

p1 ≈ 1.565² ≈ 2.45 inches of mercury

Next, find the differential pressure at 195 knots:

195 = 136.4√p + 4.5

190.5 = 136.4√p

√p = 190.5 / 136.4 ≈ 1.397

p2 ≈ 1.397² ≈ 1.95 inches of mercury

Change in differential pressure:

Δp = p1 - p2 ≈ 2.45 - 1.95 ≈ 0.50 inches of mercury

Problem 3

We need to write the equation for true airspeed T in terms of altitude A and differential pressure p.

From the given formulas:

S = 136.4√p + 4.5

T = (1 + A/50,000) ⋅ S

Combining these, we get:

T = (1 + A/50,000) ⋅ (136.4√p + 4.5)

Problem 4

An airplane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet. We need to estimate the differential pressure p.

First, express the indicated airspeed S in terms of true airspeed T:

T = (1 + A/50,000) ⋅ S

280 = (1 + 20,000/50,000) ⋅ S

280 = 1.4S

S = 280 / 1.4 ≈ 200 knots

Next, solve for p using S = 136.4√p + 4.5:

200 = 136.4√p + 4.5

195.5 = 136.4√p

√p = 195.5 / 136.4 ≈ 1.433

p ≈ 1.433² ≈ 2.05 inches of mercury

This estimate is correct because it falls within the logical range for differential pressure at this indicated airspeed.

6 3/11 that well be the answer

Answer:6 3/5

Step-by-step explanation: 10 2/5 - 3 4/5 = 33

5

= 63

5

= 6.6

Answer:

4x, 2y, 3

Step-by-step explanation:

The terms are the number and variables separated by the minus sign and plus sign.

The three terms in the expression 4x - 2y + 3 are 4x, -2y and 3.

The given expression is 4x-2y+3.

A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms.

In the given expression 4x-2y+3, the three terms are 4x, -2y and 3.

Therefore, the three terms in the expression 4x - 2y + 3 are 4x, -2y and 3.

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Answer:

4

Step-by-step explanation:

Answer:

One triangle

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Verify the length sides of triangle

Applying the triangle inequality theorem

1) 3+5 > 6 ---> is true

2) 3+6 > 5 ---> is true

3) 5+6> 3----> is true

therefore

One triangle can be drawn with the given lengths

With side lengths of 3 inches, 5 inches, and 6 inches, only one triangle can be drawn as these dimensions meet the triangle inequality theorem, allowing for the creation of one unique triangle.

The question is about determining if a triangle can be constructed with given side lengths. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the third side. In this case, the side lengths are 3 inches, 5 inches, and 6 inches.

Adding the lengths of the two shorter sides, 3 inches + 5 inches = 8 inches, which is greater than the length of the longest side, 6 inches. This means a triangle with these side lengths can be drawn. However, it is important to note that the lengths provided can only create one unique triangle, since the lengths are fixed and there can't be another triangle with different angles with the same side lengths.

Therefore, with side lengths of 3 inches, 5 inches, and 6 inches, exactly one triangle can be drawn.

Answer:

Step-by-step explanation:

Since 8^2+15^2 = 289 and 17^2 = 289 then 8^2+15^2 = 17^2

8^2+15^2 = 17^2 Then according to the reciprocal of the Pythagorean theorem

it’s a right triangle

Answer:

YES

Step-by-step explanation:

Answer:

y=(x+1)(x-1)(x+8)

Step-by-step explanation:

When creating a factor with a known zero, use (x-ZERO)

For instance: a zero of -1 would be reprsented as (x+1)