What is the product of -9.56 x 8.5? A. -81.26 B. -73.06 C. 81.26 D. 73.06

The length of AE¯¯¯¯¯ is 5√2 cm.

Since quadrilateral ABCD is a square, all four sides are congruent. Let's denote the length of one side as s. Therefore, the length of BD¯¯¯¯¯ is equal to s.

Given that the length of BD¯¯¯¯¯ is 10 cm, we can conclude that s = 10 cm.

Now, we need to find the length of AE¯¯¯¯¯. Looking at the square, AE¯¯¯¯¯ is the diagonal connecting opposite corners.

In a square, the diagonal divides the square into two congruent right triangles. We can use the Pythagorean theorem to find the length of the diagonal.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the diagonal (the hypotenuse) is the same as the side length, s.

Applying the Pythagorean theorem:

s^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

10^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

100 = 2 * AE¯¯¯¯¯^2

AE¯¯¯¯¯^2 = 50

Taking the square root of both sides:

AE¯¯¯¯¯ = √50

Simplifying the square root:

AE¯¯¯¯¯ = √(25 * 2) = 5√2 cm

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a) The value of x is 42.6 when k =16/3 is directly proportional to y.

b) The value of x is -56 when k is -7  is directly proportional to y.

What kind of variation is one where x and y are directly proportional?

x varies directly as y

x α y

x = ky

a) x=6 ; y = 32

x = ky

6 = k(32)

k = 16/3

if y = 8

then,

x = (16/3) * 8

= 128/3

x = 42.6

Hence, the value of x is 42.6 when k =16/3 is directly proportional to y.

b) x= 14 and y = -2

x = ky

14 = k(-2)

k = -7

if y = 8

then,

x = ky

x= (-7) 8

x = -56

Hence, the value of x is -56 when k is -7  is directly proportional to y.

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Answer:

345 miles

Step-by-step explanation:

So we know that 2 cities are 5.75 inches apart on the map and the scale reads for every 0.5 inch its 30 miles. So we can first start of by diving 5.75 by 0.5, since we need to know how many “0.5” inches are in 5.75 inches. You’d get 11.5. Now 11.5 multiply that by 30 which would get you 345 miles.

\(f^(-1)(2) = 6\), which is consistent with our earlier result.

A function that "undoes" another function is known as an inverse function. If f(x) is a function, then f(x inverse, )'s indicated by f-1(x), is a function that accepts f(x output )'s as an input and outputs f(x initial )'s input.

Given the function f(x) = √(2x - 8), if f^(-1)(x) is the inverse function of f(x), what is \(f^(-1)(2)\)?

Solution:

To find f^(-1)(2), we need to find the value of x such that  \(f(x) = 2\) . We can set up an equation:

\(f(x) = \sqrt(2x - 8) = 2\)

Squaring both sides, we get:

\(2x - 8 = 4\)

\(2x = 12\)

\(x = 6\)

Therefore, \(f^(-1)(2) = 6.\)

We can also verify this result by using the definition of an inverse function. If f^(-1)(x) is the inverse function of f(x), then by definition:

\(f(f^(-1)(x)) = x\)

We can substitute x = 2 and solve for f^(-1)(2):

\(f(f^(-1)(2)) = 2\)

\(f^(-1)(2) = (f(6))^(-1)\)

f(6) = √(2(6) - 8) = √4 = 2

Therefore,\(f^(-1)(2) = 6\), which is consistent with our earlier result.

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Answer:

The answer is y=-1 (answer is C).

According to the equation the given all necessary math work are:

\(A: (x -f)^2 +(y -g)^2 = h^2\)

B:  domain: [-5, 11]; range: [-9, 7]

C:  yes, inside

The hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides if a triangle has a straight angle (90 degrees), accοrding tο the Pythagοras theοrem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypοtenuse BC are all used in this equatiοn. The lοngest side οf a right-angled triangle is its hypοtenuse, it shοuld be emphasized.

Part A:

Use οf the Pythagοrean theοrem gets yοu tο the equatiοn fοr a circle in essentially οne step:

sum οf squares οf sides = square οf hypοtenuse

\((x -f)^2 +(y -g)^2 = h^2\) . . . . . . circle cantered οn (f, g) with radius h

Part B:

The circle will be defined fοr values οf x in the dοmain f ± h, and fοr values οf y in the range g ± h.

dοmain: 3 ± 8 = [-5, 11]

range: -1 ±8 = [-9, 7]

Part C:

The distance frοm pοint (10, -4) tο (f, g) is ...

\(h^2 = (10 -3)^2 +(-4 -(-1))^2\)

\(h^2 = 7^2 +(-3)^2 = 49 +9 = 58\)

h = √58 < 8 . . . . the distance tο the pοint is less than h=8.

The pοint is inside the circle.

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To find the y-intercept we need to remember that this happens when x=0. Then, in our case, the y-intercept is 6.

Answer:

(4,2), (1,-3), m=5/3

Step-by-step explanation:

I kinda just used trial and error I guess. Since you find the slope by doing y-y1/x-x1. I did P--3 over 4-p =5/3 and just used logic to see which numbers fit

Answer:

\( 6^7 \)

Step-by-step explanation:

\(6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6 = 6^7 \\ \)

Hey there!

6 * 6 * 6 * 6 * 6 * 6 * 6 ➡️ 6^7
= 36 * 36 * 36 * 6

= 1,296 * 36 * 6

= 46,656 * 6

= 279,936

Therefore, your answer is: 6^7

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The required maximum point of the function \($f(x)=-x^2+8x+40$\) is (4,24).

A quadratic equation is an algebraic equation with a maximum degree of two. Where a 0, the equation is provided by ax² + bx + c = 0.

To find the maximum point of the quadratic function \($f(x)=-x^2+8x+40$\), we can use the formula for the x-coordinate of the vertex, which is given by \(x=-\frac{b}{2a}$\), where a is the coefficient of the \(x^2$\) term and b is the coefficient of the x term.

In this case, a=-1 and b=8, so the x-coordinate of the vertex is:

\($x=-\frac{b}{2a}=-\frac{8}{2(-1)}=4$$\)

To find the y-coordinate of the vertex, we can plug this value of x into the original function:

\($$f(4)=-4^2+8(4)+40=24$$\)

Therefore, the maximum point of the function \($f(x)=-x^2+8x+40$\) is (4,24).

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Note that the angles are found using the principle of the circle theorems.

The angle of the circumference is half of the angle at the center of the circle by an arc.

AB = 78°

∠5 = 39°

Angles intercepted by the same arc are equal.

∠4 = 39°

FE= 105°

∠16 =105°

ED = 27°

∠17 =27°

CD = 42°

∠10 =21°

∠3 =21°

The angle of the semi-circle is 90°.

∠2 =90°

∠8=∠9 = (180-48)/2

∠8= 66°

∠9= 66°

∠7=90°-∠8 = 90°-66°

∠7=24°

∠17 = 180°-∠15-∠16

∠17 = 180°-48°-105°

∠17 =27°

∠6=∠15/2 = 48/2

∠6=24°

∠21 = 180°-∠7-∠16

∠21 = 180°-24°-105°

∠21 =51°

∠19 =51°

∠18 = 180°-∠17-∠6

∠18 = 180°-27°-24°

∠18 = 129°

∠20 = 129°

BC = 60°

∠1 = 60/2

∠1 =30°

∠11=180°-∠1-∠2

∠11=180°-30°-90°

∠11=60°

∠13=60°

∠12=180-∠11

∠12=180°-60°

∠12=120°

∠14=120°

∠15=48°

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Answer:

3n = 9n - 110

Step-by-step explanation:

Let's suppose that Patrick and Hall play n number of songs to earn the same amount of money.

For Patrick, the amount of money he earns is given by:

Money earned by Patrick = 3n

For Hall, the amount of money he earns after paying the $110 fee is given by:

Money earned by Hall = 9n - 110

To find the number of songs they will have to play in order to earn the same amount of money, we need to set these two expressions equal to each other and solve for n:

3n = 9n - 110

Simplifying this equation, we get:

6n = 110

Dividing both sides by 6, we get:

n = 110/6

n = 18.33 (rounded to two decimal places)

Since n represents the number of songs, it cannot be a fractional value. Therefore, we can conclude that they will have to play 18 songs to earn the same amount of money.

Therefore, the equation that could be used to find n, the number of songs they will have to play in order to earn the same amount of money, is:

3n = 9n - 110

Hope this helps!

Answer:

43.96 or C

Step-by-step explanation:

c=(pi)(d)

pi --> 3.14

d --> diameter (in your case 14.)

c=3.14*14

c= 43.96

Both formulas work, 2(pi)r and (pi)(d)

But, if they give you the diameter then use (pi)(d).

If they give you the radius then use 2(pi)r

Answer:

Step-by-step explanation:

Ronald's walking speed is 3 miles per hour, and he walks for 2 hours, so he covers 3 * 2 = 6 miles. In the next hour, he runs at a speed of 6 miles per hour, covering an additional 6 miles. Therefore, Ronald traveled a total of 6 + 6 = 12 miles.

Answer:

Diameter is 11.5 inches

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The slope is: (y2 - y1) ÷ (x2-x1)

In this question y2 is 5, y1 is 8, x2 is 0, and x1 is -3.

5-8=-3

0-(-3)=3

-3 ÷ 3 = -1

the slope is negative 1

Answer:

114 cents

Step-by-step explanation:

1. 66÷22=3 cents per inch

2. 3×38=114

3. 114 cents ($1.14) for 38 inches

From the graph attached below, the solution to the system of linear inequalities are (1, 4)

A system of linear inequalities is a collection of linear inequalities in the same variables. The solution is any ordered pair that satisfies each of the inequalities.

In the problem given;

y < - x + 5 ...eq(i)

y ≥ 3x + 1 ...eq(ii)

To determine the solution to the system of linear inequalities, it is easier for us to use graphical method. This is simply done by plotting the points and determine the coordinate at which both inequalities intersect.

From the graph of the system of linear inequalities, the solution to this is (1, 4) which is option E

Kindly find attached graph below

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Archimedes went to sleep about 9.24 meters away from the rock where its shadow should end when it was 7 AM.

Trigonometric ratios are ratios of the sides of a right triangle to its angles. The three primary trigonometric ratios are

Sine = opposite/hypotenuse.

Cosine = adjacent/hypotenuse.

Tangent = opposite/adjacent.  

Here we have

Archimedes wanted to get up at 7. AM, but the alarm clock was yet to be invented. Archimedes knew that at 7.AM, the sunlight reaches the ground at an angle of 31°.

The rock beside which he slept was 5.55 meters tall.

Let's assume that the distance from the rock where Archimedes went to sleep is "x".  

Form a right triangle where the height of the triangle is the height of the rock (5.55 meters) and the angle between the ground and the sunlight at 7 AM is 31° and the opposite side to that angle is x.

Using trigonometry, we can solve for x as follows

tan(31°) = 5.55 / x

x = 5.55 / tan(31°)

x = 5.55/0.60086

x = 9.24 meters    

Therefore,

Archimedes went to sleep about 9.24 meters away from the rock where its shadow should end when it was 7 AM.

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Answer:

x = 11

Step-by-step explanation:

using the rule of logarithms

\(log_{b}\) x = n ⇒ x = \(b^{n}\)

given

\(log_{3}\) (2x + 5) = 3 , then

2x + 5 = 3³ = 27 ( subtract 5 from both sides )

2x = 22 ( divide both sides by 2 )

x = 11

Answer:

Hi

Please mark brainliest ❣️

Answer:

C. x + y = 743        

    x – y = 75

Step-by-step explanation:

Got it right.

Answer:

C. x + y = 743        

     x – y = 75

Step-by-step explanation:

I did the test so trust me :)

The length of the adjacent side is approximately 69.94 cm.

To find the length of the adjacent side, we can use the trigonometric function called tangent.

The tangent of an acute angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

Given that one acute angle has a measure of 31° and the length of the opposite side is 42 cm, we need to find the length of the adjacent side.

Let's denote the length of the adjacent side as 'x'.

Using the tangent function, we have:

tan(31°) = opposite side / adjacent side

tan(31°) = 42 cm / x

To solve for 'x', we can rearrange the equation:  

x = 42 cm / tan(31°)

Now, let's calculate the value of 'x' using a calculator:  

x ≈ 42 cm / 0.6009

x ≈ 69.94 cm (rounded to two decimal places).  

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The solution of the inequality 15n>8n-21 is given by, n<-3.

Inequality is a relation between two or more mathematical expression or quantities via unequal signs i.e. greater, less, greater or equal, less or equal, not equal.

Given that the inequality is 15n<8n-21

Solving the inequality we have,

15n<8n-21

15n-8n<8n-21-8n, subtracting from both sides

7n<-21

n<-3, dividing 7 from both sides

So the solution of the given inequality is, n<-3.

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Answer:

Isosceles

Obtuse

Step-by-step explanation:

1) When two sides of a triangle are the same length, the triangle is an isosceles triangle.

2) When one angle of the triangle is greater than 90 degrees, the triangle is an obtuse triangle.

I hope this helps! Have a great day!

Answer:

Isosceles, obtuse

Step-by-step explanation:

There are three types of triangles based on their sides:

This triangle here as sides of 28 cm, 16 cm, and 16 cm

There are three types of triangles based on their angles:

This triangle has angles of 26°, 26°, and 128°

Answer:

To determine the amount of the investment after 7 years, we can use the formula:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment (the amount after 7 years)

P = the initial principal or investment amount ($2750)

r = the annual interest rate (3.5%)

n = the number of times the interest is compounded per year (quarterly)

t = the number of years the investment is held (7)

First, we convert the annual interest rate to a decimal: 3.5% = 0.035

Then we convert the interest rate to a quarterly rate by dividing by the number of times it is compounded per year: 0.035 / 4 = 0.00875

We can now substitute these values into the formula:

A = $2750(1 + 0.00875)^(4*7)

A = $2750(1.00875)^28

A = $2750(1.3471)

A = $3710.82

So, the amount of the investment after 7 years is $3710.82, rounded to the nearest hundredth.

The function f ( x ) = 2 x² + 5 will have the value 23 for f (- 3).

We are given the function:

f ( x ) = 2 x² + 5

We need to find the value of f ( -3 ).

We will do this by substituting the value of x = - 3 in the function and then evaluating the expression.

Putting x = -3 in the function, we get that:

f ( x = - 3 ) = 2 (- 3)² + 5

Solving the square, we get that:

f (- 3) = 2 ( 9 ) + 5

Simplifying the expression, we get that:

f (- 3) = 18 + 5

f (- 3) = 23

Therefore, we get that, the function f ( x ) = 2 x² + 5 will have the value 23 for f (- 3).

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Answer:

2

Step-by-step explanation:

x^2 = 16

x = + √16

x = + 4

therefore

x= -4 or 4

there are 2 solutions in the equation