Would an experience downhill skier want the slope of the hill to be 1/10 or 9/10?  Why?

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Final answer:

The sum 42 + 24 can be expressed as 24 + 42 using the commutative property of addition, or by decomposing into tens and units for easier mental calculation.

Explanation:

The student is asking for another way to express the sum 42 + 24. One way to approach this is by performing a common mathematical technique known as commutation (or the commutative property of addition), which states that numbers can be added in any order and the sum will remain the same.

So, another way to express 42 + 24 would be 24 + 42. You can also decompose the numbers into tens and units to simplify mental calculation: (40 + 20) + (2 + 4) = 60 + 6 = 66. This demonstrates that there are multiple ways to approach addition, making it easier to perform in my head. Thus, we affirm that mathematics indeed offers many paths to the same answer.

Answer:

x=.5x

25 miles

Step-by-step explanation:

Answer:

A = (1/2)(16 cm)(12 cm) = 96 cm^2

Step-by-step explanation:

Because this is a right triangle, we know that the leg lengths are 12 cm and 16 cm respectively, and that these legs are at right angles to one another.

We can assume that the base of this triangle is 16 cm and that the height is 12 cm.  Then, according to the area-of-a-triangle formula, A = (1/2)(base)(height), the area of this particular triangle is

A = (1/2)(16 cm)(12 cm) = 96 cm^2.

Answer:

A

Step-by-step explanation:

The hypotenuse is the longest side of a triangle, meaning the hypotenuse is 20 cm. The equation for the area of a triangle is base multiplied by height multiplied by one half. (1/2bh) 12 × 16 = 192. 192 × 1/2 = 96. The area of this triangle is 96 cm^2.

Final answer:

To find the simplified form of the quadratic equation at² + bt + c = 0 with constants a = 4.90, b = -14.3, and c = -20.0, we use the quadratic formula to calculate the discriminant and then the two possible solutions for t.

Explanation:

The original expression provided: [tex](m^3/4c^5)-4[/tex] does not match the information given about quadratic equations. Instead, here's how we would solve a quadratic equation using the provided constants:

A quadratic equation is of the form at² + bt + c = 0. Given constants a = 4.90, b = -14.3, and c = -20.0, the solutions to the quadratic equation can be found using the quadratic formula, which is t = (-b ± √(b²-4ac)) / (2a).

To find the solutions for the given quadratic equation, plug in the values for a, b, and c into the quadratic formula:

The simplified form of the quadratic equation will be two solution values of t.

Answer:

The correct answer is y = cos (x - π)

Step-by-step explanation:

2. The answer after that is y = sin x + π

3. Zero, minimum, zero, maximum, zero

4. Graph C

5. The answer is 4

Hope this saved some time for some people

The equation of the translation y = cos x, shifted π units to the right is y = cos (x − π).

A translation is a slide from one location to another, without any change in size or orientation.

The given equation is;

y = cosx

We want to translate the graph in the x-direction, so our final equation should look like:

y = cos(x-b)

Where b is the number of units translated.

We are translating the graph π units to the right, so b should be equal to π. Therefore, our final equation should look like:

[tex]\rm y = cos(x-b)\\\\y = cos(x-\pi )[/tex]

Hence, the equation of the translation y = cos x, shifted π units to the right is y = cos (x − π).

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ANSWER

c.

[tex]5{e}^{i \frac{5\pi}{3} }[/tex]

EXPLANATION

The exponential form of complex numbers is given by;

[tex]z =r {e}^{i \theta} [/tex]

The given complex number in polar form is:

[tex]5( \cos( \frac{5\pi}{3} + i \sin( \frac{5\pi}{3}) ) [/tex]

We have r=5 from the question and

[tex] \theta = \frac{5\pi}{3} [/tex]

We substitute these values to obtain the exponential form:

[tex]z =5{e}^{i \frac{5\pi}{3} }[/tex]

The correct answer is C

[tex]\bf x^2=0.0025\qquad \textit{let's convert the decimal to a fraction} \\\\[-0.35em] ~\dotfill\\\\ 0.\underline{0025}\implies \cfrac{00025}{1\underline{0000}}\implies \cfrac{25}{10000} \\\\[-0.35em] ~\dotfill\\\\ x^2=0.0025\implies x^2=\cfrac{25}{10000}\implies x=\sqrt{\cfrac{25}{10000}}\implies x=\cfrac{\sqrt{25}}{\sqrt{10000}} \\\\\\ x=\cfrac{5}{100}\implies x=\cfrac{1}{20}[/tex]

Answer:

(4, 11)

Step-by-step explanation:

Given the 2 equations

y = 5x - 9 → (1)

y = x² - 3x + 7 → (2)

Substitute y = x² - 3x + 7 = 5x - 9 ( subtract 5x - 9 from both sides )

x² - 8x + 16 = 0 ← quadratic equation in standard form

(x - 4)² = 0 ← in factored form as a perfect square, so

x - 4 = 0 ⇒ x = 4

Substitute x = 4 into (1) for corresponding value of y

y = 20 - 9 = 11

Solution (x, y) → (4, 11)

Kwan would have 6.75 crayons in each box

Answer:

the answer is 8 because...

Step-by-step explanation:

You forgot to put in that he LOST 5 crayons. He has 27 AFTER he lost the five. using inverse operations we would add 5 to 27 to get 32, and then we divide that by the number of boxes he had, we get 8.

Answer is: 213, 278 , 108, 213, 157

213 is repeated 2 times; more than any other number.

A number that appears most often is the mode.

Answer:

213, 278, 108, 213, 157

Step-by-step explanation:

The mode is the number with the highest frequency in a given list of data. Simply, it is the number with most occurrence.

Now, let us chart the frequency of each numbers in the list provided:

1........ 111, 108, 213, 198, 205

Arrange in ascending order

108, 111, 198, 205 and 213

Numbers Frequency

108 1

111 1

198 1

205 1

213 1

No modal value

2..... 212, 215, 213, 211, 220

Arranging in ascending order:

211, 212, 213, 215 and 220

Numbers Frequency

211 1

212 1

213 1

215 1

220 1

No modal value

3......213, 278, 108, 213, 157

Arranging in ascending order:

108, 157, 213 and 278

Numbers Frequency

108 1

157 1

213 2

278 1

The mode here is 213. It has a frequency of 2 compared to other numbers whose mode is 1

4........ 210, 200, 213, 221, 221

Arranging in ascending order:

200, 210, 213, 221

Numbers Frequency

200 1

210 1

213 1

221 2

The mode here is 221

answer : (A) q>p , where p= jacks pet is a pig and q= jacks pet cannot fly

The converse of an implication reverses the order of the original statement. Therefore, the converse of 'If Jack’s pet is a pig then Jack’s pet cannot fly' is 'If Jack's pet cannot fly, then Jack's pet is a pig'.

In this problem, we're dealing with a form of logical statement known as an implication, which can be symbolized as p → q. In the original statement, 'If Jack’s pet is a pig (p) then Jack’s pet cannot fly (q)', the implication is that being a pig causes or results in the inability to fly. The converse of an implication reverses the order of the original statement, so 'if q then p'. Therefore, the converse of the given statement would be 'If Jack's pet cannot fly, then Jack's pet is a pig', or symbolically represented as q → p.

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Answer: the first answer

| 2 1/5 - 4.35 |

Step-by-step explanation:

this is the integer of the answer. not a negative of it.

Answer:

(2,3)

Step-by-step explanation:

The given equations  are:

[tex]y=-4x+11[/tex]

and

[tex]y=\frac{1}{2}x+2[/tex]

Equate both equations:

[tex]\frac{1}{2}x+2=-4x+11[/tex]

Multiply through by 2:

[tex]x+4=-8x+22[/tex]

[tex]x+8x=22-4[/tex]

[tex]9x=18[/tex]

x=2

Put x=2 into the first equation:

[tex]y=-4(2)+11[/tex]

[tex]y=-8+11[/tex]

y=3

The solution is (2,3)

Answer:

C. (2, 3)

Step-by-step explanation:

A system of linear equations is a set of (linear) equations that have more than one unknown. The unknowns appear in several of the equations, but not necessarily in all of them. What these equations do is relate the unknowns to each other.

Solve a system of equations is to find the value of each unknown so that all the equations of the system are met.

Ordering both equations

First equation

[tex]y=-4y+11[/tex]

[tex]4x+y=11[/tex]

Second equation

[tex]y=\frac{1}{2} x+2[/tex]

[tex]-\frac{1}{2}x+y=2[/tex]

Ordering in a system of equations

[tex]\left \{ {{4x+y=11} \atop {-\frac{1}{2}x+y=2}} \right.[/tex]

Using the reduction method which consists of operating between the equations, such as adding or subtracting both equations, so that one of the unknowns disappears. Thus, we obtain an equation with a single unknown.

We're going to subtract the second equation from the first to eliminate the unknown y.

           4x + y = 11

   -  ((-1/2)x + y = 2)

       (9/2)x       =  9 ------>    x= [(2)(9)]/9 ----->  x = 2

Substituing the value x = 2 in [tex]y=\frac{1}{2} x+2[/tex]

y = (1/2)x + 2 ---------> y = (1/2)(2) + 2 -------> y = (2/2) + 2

y = 1 + 2 --------> y = 3

The solution of the system of equations is (2, 3).

The answer will be B

Answer:

The answer is C.

Step-by-step explanation:

The integer form is 60 as the answer

Arranging the given data in ascending order:

1, 2, 2, 3, 3, 4, 7, 7, 7, 9

Meadian is the middle-most observation.

i.e. The Median here is average of 3 and 4.

= (3+4)/2

= 7/2

=3.5

Hope it helps...

Regards;

Leukonov/Olegion

Answer:

110

Step-by-step explanation:

2=80 and 3=30

2+3=ac=110

Answer:

Option B. 110°

Step-by-step explanation:

In the given circle m ∠1 = 100°

m BC = 30°

Then we have to find the measure of m AC

Since ∠1 = 100°

and ∠1 + ∠2 = 180° [supplementary angles]

100 + ∠2 = 180°

∠2 = 180° - 100°

∠2 = 80°

Now we know ∠3 = 15°

and m AC = ∠2 + ∠3

m AC = 80 + 30 = 110°

Therefore, Option B. 110° will be he answer.

Hello There!

The correct answer would be "B" this is because we are taking 6 and multiply it by our x column which is the "in" column and adding 1 to what we get.

Answer:

The Correct answer is (B) or option 2.

Answer:

Step-by-step explanation:

Answer:

Slope

Step-by-step explanation:

Slope is the gradient or steepness of a line.

The term slope defines steepness of a line

Steepness of a line is the the inclination of the line.

Steepness of the line can be defined by the term slope.

Slope is the inclination of the line towards x-axis.

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Answer:

A rigid transformation includes only rotation and translation.

Answer:

Step-by-step explanation:

Answer:

d.

Step-by-step explanation

it is a random variable but is continuos as it doesn't change.

Answer:

Height of 10 years olds

Step-by-step explanation:

A p e x

Answer:

Third Option

[tex]f(x) = 4x,\ g(x)=\frac{1}{4}x[/tex]

Step-by-step explanation:

For a function f(x) it is satisfied that the range of f(x) is equal to the domain of its inverse function. In the same way the domain of f(x) is equal to the range of its inverse.

Therefore, to verify which pair of functions are inverse to each other, perform the composition of both functions and you must obtain

[tex]f(g(x)) = x[/tex]  and   [tex]g(f(x)) = x[/tex]

For the first option we have:

[tex]f(x) = x,\ g(x)=-x[/tex]

Then

[tex]f(g(x)) = (-x) = -x[/tex]  They are not inverse functions

For the second option we have:

[tex]f(x) = 2x,\ g(x)=-\frac{1}{2}x[/tex]

Then

[tex]f(g(x)) = 2(-\frac{1}{2}x) = -x[/tex]  They are not inverse functions

For the third option we have:

[tex]f(x) = 4x,\ g(x)=\frac{1}{4}x[/tex]

Then

[tex]f(g(x)) = 4(\frac{1}{4}x) = x[/tex]

[tex]g(f(x)) = \frac{1}{4}(4x) = x[/tex] They are inverse functions

For the fourth option we have:

[tex]f(x) = -8x,\ g(x)=8x[/tex]

Then

[tex]f(g(x)) = -8(8x) = -64x[/tex]  They are not inverse functions

Answer:

D

Step-by-step explanation:

5/4 can only be greater than 1.

Answer:

Point D is located at 5/4 on the number line. Hope this helps

The expression -4x^2(3x - 7) simplifies to -12x^3 + 28x^2 after distributing -4x^2 across the parentheses and performing the necessary multiplications.

The expression to be simplified is -4x^2(3x - 7).

To simplify the expression, you need to distribute the term -4x^2 across the parentheses. This involves two multiplication steps:

Multiply -4x^2 by -7 to get +28x^2.

After performing these multiplications, the expression simplifies to -12x^3 + 28x^2.

Answer:

The area of the walls is [tex]2,160\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The area of the walls is equal to the perimeter of the conference room multiplied by the height of the ceiling

so

[tex]A=2[40+50](12)=2,160\ ft^{2}[/tex]

Answer:

A. a) 24

A. b) 4

B. a) 40320

B. b) 576

Step-by-step explanation:

General formula for Permutations:

[tex]P(n,r) = \frac{n!}{(n - r)!}[/tex]

A. Concert seats:  2 couple --- total of 4 persons.

a) without restrictions

Since there are no restrictions, but that the order is important (John, Mary, Paul, Michelle isn't the  same as Michelle, Mary, Paul, John), it's a permutation calculation.

Then we calculate the permutations of 4, out of 4, so...

[tex]P(4,4) = \frac{4!}{(4 - 4)!} = 4! = 24[/tex]

24 different ways for them to sit.

b) couples together

Now, we can see the problem as having 2 levels of permutations, first the couples, then inside the couples.

There are 2 ways for the first level or order... couples AB or BA, so 2 possibilities.

Inside each couple, man then woman (MW) or woman then man (WM), so 2 possibilities there too on 2nd level.

Overall 2 * 2 = 4 ways to sit by couple.

B) Single file

a) without restrictions

Again, order is important, so another permutation, not a combination.  And since we have no restriction, it can be any sequence.

We then have to calculate the number of permutations of 8 out of 8...

[tex]P(8,8) = \frac{8!}{(8 - 8)!} = 8! = 40320[/tex]

There are 40,320 ways these 8 kids can pass the door.

b) girls first.

So, the four girls have to enter first.... and these four girls can be in any order.. how many permutations? P(4,4)... so 24 as calculated above.

For the four boys, how many permutations?  Yes, again P(4,4)... so 24 again.

Overall, we need to multiply the two... 24 x 24 = 576 ways if the girls enter first, followed by the boys.

Answer:

17.6 ounces per 500 g

Step-by-step explanation:

Knowing one ounce equals 28.34 g, all we have to do is divide half a kilo (500 g) by the equivalent of an ounce to get the number of ounces in a kg.  So,

O = 500 g / 28.34g/ounce = 17.64 ounces

We round that to the nearest tenth... to get 17.6 ounces per 500 g

Converting between metric and imperial/US system is always complicated.

Answer:

0.5 kilograms (kg) is equal to 17.6 ounces

Step-by-step explanation:

We have

                    1 kg = 35.274 ounces

                   0.5 kg = 0.5 x 35.274 = 17.637 ounces

Rounding to nearest tenth

              0.5 kg = 17.637 ounces   = 17.64 ounces = 17.6 ounces

So we have 0.5 kilograms (kg) is equal to 17.6 ounces    

Answer:

[tex]x_1=4.158[/tex]

[tex]x_2=0.8416[/tex]

Step-by-step explanation:

For an equation of the form [tex]ax^2 +bx +c[/tex]

The quadratic formula is

[tex]\frac{-b\±\sqrt{b^2 -4ac}}{2a}[/tex]

In this case the equation is:

[tex]2x^2 - 10x + 7 = 0[/tex]

Then

[tex]a= 2\\b= -10\\c= 7[/tex]

Therefore, using the quadratic formula we have:

[tex]x=\frac{-(-10)\±\sqrt{(-10)^2 -4(2(7)}}{2(2)}[/tex]

[tex]x=\frac{5\±\sqrt{11}}{2}[/tex]

[tex]x_1=4.158[/tex]

[tex]x_2=0.8416[/tex]

ANSWER

[tex]x = \frac{ 5 }{2} - \frac{\sqrt {11} } {2} \: or \: x = \frac{ 5 }{2} + \frac{\sqrt {11} } {2} [/tex]

EXPLANATION

The given quadratic equation is:

[tex] 2{x}^{2} - 10x + 7 = 0[/tex]

Comparing this equation to

[tex] a{x}^{2} + bx + c = 0[/tex]

we have

a=2, b=-10 and c=7.

The solution is given by the quadratic formula;

[tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

We plug in the values to get,

[tex]x = \frac{ - - 10 \pm \sqrt{ {( - 10)}^{2} - 4(2)(7) } }{2(2)} [/tex]

This implies that

[tex]x = \frac{ 10 \pm \sqrt{ {100} - 56 } }{4} [/tex]

[tex]x = \frac{ 10 \pm \sqrt {44 } }{4} [/tex]

[tex]x = \frac{ 10 \pm 2\sqrt {11 } }{4} [/tex]

[tex]x = \frac{ 5 \pm \sqrt {11 } }{2}[/tex]

[tex]x = \frac{ 5 }{2} - \frac{\sqrt {11} } {2} \: or \: x = \frac{ 5 }{2} + \frac{\sqrt {11} } {2} [/tex]

Answer:

The equation would be:

(X+1)^2 + (y-1)^2 = 9

This is the equation of the circle in general form.  

[tex]\[ x^2 + y^2 + 2x - 2y - 7 = 0 \][/tex]

or

[tex]\[ (x + 1)^2 + (y - 1)^2 = 9 \][/tex]

To write the equation of a circle in general form, you start with the standard form of the circle's equation, which is:

[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]

where \( (h, k) \) is the center of the circle and \( r \) is the radius.

From the information provided:

- The center of the circle is \( (-1, 1) \)

- The radius of the circle is \( 3 \) units

Let's substitute these values into the standard form:

[tex]\[ (x - (-1))^2 + (y - 1)^2 = 3^2 \][/tex]

[tex]\[ (x + 1)^2 + (y - 1)^2 = 9 \][/tex]

Now, to write it in general form, you'll expand the equation and combine like terms:

Step 1: Expand the squares

[tex]\[ (x + 1)^2 = x^2 + 2x(1) + 1^2 \][/tex]

[tex]\[ (y - 1)^2 = y^2 - 2y(1) + 1^2 \][/tex]

Step 2: Write the expanded form

[tex]\[ x^2 + 2x + 1 + y^2 - 2y + 1 = 9 \][/tex]

Step 3: Combine like terms

[tex]\[ x^2 + y^2 + 2x - 2y + 1 + 1 = 9 \][/tex]

Step 4: Move the constant to the right side

[tex]\[ x^2 + y^2 + 2x - 2y = 9 - 2 \][/tex]

Step 5: Final general form

[tex]\[ x^2 + y^2 + 2x - 2y - 7 = 0 \][/tex]

This is the equation of the circle in general form.