.10. for each of the gcd(a, b) values in exercise 1.9, use the extended euclidean algorithm (theorem 1.11) to find integers u and v such that au bv

Answer: 72 square units

Step-by-step explanation: It is 72 square units because if you count the sides p and q you get 9 and the same with sides q and r you get 8 and if you multiply them together you get 72.

Using translation concepts, the function f(x) was evaluated by comparing to the graph of a base function g(x) = x².

A translation is signified by a change with in function graph, based on operations in its definition including such multiplication or sum/subtraction.

Thus, the resultant function is obtained as (X)=4(X+9)²

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The value of a missing number is 9.

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called proportional.

Given

The ratio is,

⇒ 3 / 8 = __ / 24

Now, Let the missing number = x

So, We get;

⇒ 3/8 = x/24

Solve for x;

⇒ 3 × 24 / 8 = x

⇒ x = 3 × 3

⇒ x = 9

Hence, the missing value is 9.

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Answer:

Take your time to complete the equation. Don't rush. This is very easy you just need to be patient..

Step-by-step explanation:

Answer:

(a) Expanded form:

\(((X_1 + X_1Y_1) - X_1Z_1) + ((X_2 + X_2Y_2) - X_2Z_2) + ((X_3 + X_3Y_3) - X_3Z_3) + ((X_4 + X_4Y_4) - X_4Z_4)\)

(b) The value of the expression: -21

Step-by-step explanation:

Given

\(\sum \limit^4_{i=1}\ ((X_i+X_iY_i) - X_iZ_i)\)

Solving (a): The expanded form:

This means that we substitute the values of i from 1 to 4 in the above expression.

So, the expression becomes:

\(((X_1 + X_1Y_1) - X_1Z_1) + ((X_2 + X_2Y_2) - X_2Z_2) + ((X_3 + X_3Y_3) - X_3Z_3) + ((X_4 + X_4Y_4) - X_4Z_4)\)

Solving (b): The value of the expression

To do this, we simply substitute the given values of X1, X2....... in the expression.

This gives:

So, the expression becomes:

\(((0 + 0*5) - 0*0) + ((1 + 1*26) - 1*-2) + ((12 + 12*-2) - 12*3) + ((-1 + -1*25) - -1*24)\)

Simplify each bracket

\(((0 + 0) - 0) + ((1 + 26) +2) + ((12 -24) - 36) + ((-1 -25) +24)\)

\(0 + 29 -48 -2\)

\(-21\)

Hence, the result of the expression is -21

Answer:

Set your calculator to Degree mode.

a² = 17² + 20² - 2(20)(17)cos(89°)

a² = 677.13236

a = 26.0 in.

sin(89°)/26.02177 = (sin B)/17

sin B = 17sin(89°)/26.02177

B = 40.8°

C = 50.2°

Complete question :

The chamber of commerce for a summer resort is trying to determine how many tourists will be visiting each season over the coming years. A marketing research firm has estimated that the number of tourists can be predicted by the linear equation: P(x)= 278000 + 7550x

where p = number of tourists per year and t = years (measures from this current season). Thus t=0 identifies the current season, t=1 is the next season, etc. If p is plotted on the vertical axis:

(a) Graph the equation.

(b) Identify the slope and y intercept (p intercept, here).

(c) Interpret the meaning of the slope and p intercept in this application.

Answer:

B.) 7550 ; 278000

C.) kindly check explanation

Step-by-step explanation:

From the equation given,

At x = 0 ; p(x) = 278000

-- x = 1 p(x) = 278000 + 7550 = 285550

B.) general form of a linear equation :

y = mx + c

Equation given :

P(x)= 278000 + 7550x

Slope (m) = 7550

Intercept ; p intercept = 278000

C.) the slope means ; the number of tourist visutun each season increases at the rate of 7550 per year

The intercept, means the initial number of tourist at the time t = 0 = 278000

Answer:

maybe it's d.

Step-by-step explanation:

because 30*6=180 and 50*3=150

so total of 330 as I observed

Answer:

931   10/54

Step-by-step explanation:

First you multiply 19 x 7 x 7 to get 931, then you multiply 1/3 x 2/3 x 5/6 to get 10/54. Finally you put them together to get 931 10/54

Answer:

Option (C)

Step-by-step explanation:

Given expression is,

\(4+4\times \text{log}_2(x)=14\)

By subtracting 4 from both the sides of the equation.

\(4\times \text{log}_2(x)=14-4\)

Now divide the equation by 4

\(\text{log}_2(x)=\frac{10}{4}\)

\(\text{log}_2(x)=2.5\)

[If \(\text{log}_ab=x\) , then \(b=a^{x}\)]

\(x=(2)^{2.5}\)

\(x = 5.657\)

x ≈ 5.66

Therefore, Option C will be the correct option.

4+4•log2 x=14

x= 5.66

Check the picture below.

\(\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+56}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)\)

\(\left(-\cfrac{ 56}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (56)^2}{4(-16)}\right) \implies \left( - \cfrac{ 56 }{ -32 }~~,~~0 - \cfrac{ 3136 }{ -64 } \right) \\\\\\ \left( \cfrac{7}{4}~~,~~49 \right)\implies \stackrel{seconds\qquad feet}{\left(1\frac{3}{4} ~~ ~~,~ ~~ ~49 \right)}\)

The total number of possible outcomes when flipping a coin three times is 8, since there are two possible outcomes for each flip (heads or tails).

Combination is a way of selecting items from a set where order does not matter. Combinations are written as a set of n distinct objects taken r at a time, where n is the total number of objects and r is the number of objects taken.

Of these 8 outcomes, 3 include exactly one head. These are the outcomes HHT, HTH, and THH.

The total number of possible outcomes is calculated using the formula 2ⁿ, where n represents the number of flips. In this case, n = 3, so the total number of outcomes is 2³ = 8.

To find the number of outcomes with exactly one head, we can use the formula nCr, which stands for n choose r.

This formula is used to calculate the number of combinations of r elements that can be chosen from a set of n elements.

In this case, n = 3 (the number of flips) and r = 1 (the number of heads).

This gives us 3C1 = 3, which is the number of outcomes with exactly one head.

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Answer:

x^2

Step-by-step explanation:

1^2=1

2^2=4

3^2=9

Oliver's number is bigger than that of Chen.

It is a number equal to 10 times 10.

Given is that Oliver and Chen both write down a number. Oliver says, my number has 8 hundreds and Chen's number only has 3 hundreds, my number must be bigger.

Oliver number can be written as follows -

8 x 10 x 10

Chens number can be written as follows -

3 x 10 x 10

It can be concluded that Oliver's number is bigger than that of Chen.

Therefore, Oliver's number is bigger than that of Chen.

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Answer:

TO MAKE A NUTTY CEREAL ........

Answer:

  2:21

Step-by-step explanation:

You want the meeting time of two bikers traveling at 12 mph and 14 mph, closing a distance of 6 miles between them, when the first starts at 2:05, and the second starts at 2:09.

The first biker starts at 2:05 and peddles for 4 minutes before the 2nd biker starts. In that time, the distance traveled is ....

  distance = speed × time

  (12 mi/h) × (4/60 h) = 48/60 mi = 0.8 mi

The gap between the bikers has been reduced from 6 miles to 6 -0.8 = 5.2 miles by the time the second biker starts at 2:05 + :04 = 2:09 on the clock.

After the second biker starts at 2:09, the 5.2 mile gap between them is being closed at their combined rate of travel: 12 mph +14 mph = 26 mph. The time required to close that 5.2 mile gap is ...

  time = distance/speed

  time = (5.2 mi) / (26 mi/h) = 0.2 h = 0.2(60 min) = 12 min

The bikers will meet 12 minutes after the second biker starts, at ...

  2:09 + :12 = 2:21

The bikers will meet at 2:21.

The attached graph shows equations for the distance from the 2nd biker's end of Main street (y1), and the distance the 2nd biker travels (y2). The value of x is the clock time in hours. It shows the two bikers meet at hour 2.35. That fraction of an hour is (0.35 h)×(60 min/h) = 21 min, so their meeting time is 2:21 on the clock. (They meet 2.8 miles from the 2nd biker's starting location.)

Answer:

1460

Step-by-step explanation:

rounding to the nearest ten, that is nearest to 1456 which would be 1460 (hope this helps! ) ♡

Answer:

1460

Step-by-step explanation:

Original number is 1 4 5 6

To round to the nearest ten, look at the digit in the 10's place and the digit immediately to the right of it

The digit in the tens place is 5

If the digit to the immediate right of this digit is 5 or greater, round the digit in the tens place up by one digit and set the immediate right digit to 0

So 5 rounds up to 6

The 6 to the immediate right(units place becomes 0)

1 4 5 6 rounded to nearest ten==> 1 4 6 0

Answer:I’m pretty sure ( not 100% thou ) the awnser would be A) 4

Answer:

t = 60

t/4+5=20

Step 1:

multiply both sides of equation by 4 to separate t from the fraction t/4.

t + 20 = 80

Step 2:

Subtract 20 from both sides of the equation ( you have to put constant values on the same side)

t= 80 - 20

Step 3:

Do the math

80-20=60 so t=60

Step-by-step explanation:

hope this helps! please give brainiest ^^^

Answer: -1/3

Step-by-step explanation:

The slope of the given line is \(\frac{7-1}{5-3}=\frac{6}{2}=3\).

Thus, since perpendicular lines have slopes that are negative reciprocals of each other, the answer is -1/3

Answer: \(x=0, -\frac{3}{2}\)

Step-by-step explanation:

\(4x^2 +6x=0\\\\2x(2x+3)=0\\\\2x=0, 2x+3=0\\\\x=0, -\frac{3}{2}\)

Answer:

C.  g(x)=3√x+4+3

Step-by-step explanation:

g(x) shift left 4, shift up 3, with no compression or stretch.

a=1

h=-4

k=3

The function f(x) after the transformation can be written as -

g(x) = \($\sqrt[3]{x-4} +3\)

A function is a relation between a dependent and independent variable. We can write the examples of function as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is that function g(x) is a transformation of the cube root parent function f(x) = \($\sqrt[3]{x}\).

The function f(x) is shifted up by three units and left by 4 units. So, we can write the rule for the function transformation as -

g(x) = \($\sqrt[3]{x-4} +3\)

Therefore, the function f(x) after the transformation can be written as -

g(x) = \($\sqrt[3]{x-4} +3\)

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Answer:

10¢

Step-by-step explanation:

First, to be able to differentiate between the B&W and Color copies, use x in place of the B&W copies and y in place of the Color copies.

Then, write a system of equations to solve (the system of equations input was not working, so there is no brace):

 8x + 2y = $1.20

 10x + 10y = $3.00

Then, solve the system of equations:

   8x +  2y = $1.20

 10x + 10y = $3.00

Isolate x to be able to substitute:

8x + 2y = $1.20

8x = -2y + 1.2

x = -2/8y + 1.2/8

x = -0.25y + 0.15

Substitute:

10x + 10y = $3.00

10 (-0.25y + 0.15) + 10y = 3

-2.5y + 1.5 + 10y = 3

7.5y + 1.5 = 3

7.5y = 1.5

y = $0.20

Now that you have the cost of the Colored copies, you can plug it in to find the B&W copies:

8x + 2y = $1.20

8x + 2(0.2) = 1.2

8x + 0.4 = 1.2

8x = 0.8

x = $0.10

Answer:

-18/x+3

Step-by-step explanation:

Answer:

$75

Step-by-step explanation:

The distance between Basti and Cian is approximately 138.2 ft. Option D

To find the distance between Basti and Cian, we can use the Law of Sines, which relates the lengths of sides to the sines of their opposite angles in a triangle.

Let's label the points: A, B, and C. Ali is at point A, Basti is at point B, and Cian is at point C.

Given:

Angle ABC = 50 degrees (angle opposite side AC)

Angle BAC = 60 degrees (angle opposite side BC)

Ali is 150 ft away from Basti (side AB)

We want to find the distance between Basti and Cian, which is side BC.

Using the Law of Sines, we have:

BC/sin(50) = AB/sin(60)

Substituting the known values:

BC/sin(50) = 150/sin(60)

To find BC, we can rearrange the equation:

BC = (150/sin(60)) * sin(50)

Using a calculator to evaluate the expression:

BC ≈ 138.2 ft

Option D is correct.

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