Simplify your answer.

Answer:

Part 1) The measure of angle x is 24°

Part 2) The measure of angle y is 66°

Step-by-step explanation:

step 1

Find the measure of angle m∠IKL

we know that

m∠JKI+m∠IKL=180° ----> supplementary angles (form a linear pair)

we have

m∠JKI=48°

substitute

48°+m∠IKL=180°

m∠IKL=180°-48°=132°

step 2

Find the measure of angle x

we know that

The triangle IKL is an isosceles triangle

so

m∠KIL=m∠KLI=x

Remember that

The sum of the interior angles of a triangle must be equal to 180 degrees

m∠IKL+2x=180°

132°+2x=180°

2x=180°-132°

x=24°

step 3

In the right triangle JIL

Angles x and y are complementary

so

x+y=90°

24°+y=90°

y=90°-24°

y=66°

Answer:

there are 3.3399 moles in 318 grams! ✔️

Step-by-step explanation:

So we know that 100 grams MgCl2 to mol = 1.0503 mol.

Therefore, to find the number of moles in 318g of the compound, we use the rule of three:

if 1.0503 mol -------------> 100 grams

       X            <------------- 318 grams

The solution is: X = (318*1.0503)/100 = 3.3399 mol.

Summarizing, there are 3.3399 moles in 318 grams! ✔️

I believe the answer is B. I apologize if this is incorrect

Answer:

B) 168.8

Step-by-step explanation:

Amongst all the options given, B is the correct answer.

!!

Answer:

A. 7 in.

Step-by-step explanation:

We have been given that the perimeter of a rectangle is 16 inches. The equation that represents the perimeter of the rectangle is , where l represents the length of the rectangle and w represents the width of the rectangle.

We know that perimeter of rectangle is 2 times the sum of width and length of rectangle.

[tex]\text{Perimeter}=2(l+w)[/tex]

[tex]\text{16 in}=2(l+w)[/tex]

[tex]\frac{\text{16 in}}{2}=\frac{2(l+w)}{2}[/tex]

[tex]\text{8 in}=l+w[/tex]

To be a rectangle length cannot be 8 as length and width of the rectangle is 8 inches.

Therefore, 7 inches the possible value for the length of the rectangle.

Answer:

A

Step-by-step explanation:

Answer:

The mean of the combined group of 30 students is equal to 56.67

Step-by-step explanation:

Let

x ----> The sum of the notes of the 20 papers

y ----> The sum of the notes of the 10 papers

we know that

60=x/20 -----> x=60*20=1,200

50=y/10 -----> y=50*10=500

The mean of the combined group of 30 students is equal to

(x+y)/30

substitute

(1,200+500)/30=56.67

Step-by-step explanation:

To find the equation of the line, start by finding the slope. You can do this by using the slope formula below.

m(slope) = (y2 - y1)/(x2 - x1)

m = (2 - -1)/(-5 - 10)

m = 3/-15

m = -1/5

Now that we have the slope, we can use it along with either point in point-slope form to get the equation.

y - y1 = m(x - x1)

y - 2 = -1/5(x + 5)

y - 2 = -1/5x - 1

y = -1/5x + 1

Answer: In slope intercept formula it is y=-1/5x+3

Step-by-step explanation:

Answer:

B) Find the ratio of minutes to miles, 4:1. Multiply 7.5 by 4

Step-by-step explanation:

A bicyclist rides the same number of miles every minute. The ratio table below shows the number of miles she rides during certain amounts of time.

Biking Times and Distances        

Number of Minutes         Number of Miles

10                                             2.5

16                                              4

?                                              7.5

48                                              12

Which statement explains how to find the number of minutes it takes to bike 7.5 miles?

B) Find the ratio of minutes to miles, 4:1. Multiply 7.5 by 4....

Answer:

Option B.

Step-by-step explanation:

A bicyclist rides the same number of miles in one minute.

Ratio table is given as

Number of minutes    Distances (miles)

       10                                   2.5

        16                                   4

        x                                    7.5

       48                                  12

We have to find the number of minutes taken by a biker to bike 7.5 miles

So the ratio between minutes to the distance biked will be = [tex]\frac{10}{2.5}=4:1[/tex]

Now this ratio will be similar to the ratio = [tex]\frac{x}{7.5}=x:7.5[/tex]

Now [tex]\frac{4}{1}=\frac{x}{7.5}[/tex]

x = 7.5×4 = 30 minutes

Therefore, Option B will be the answer.

We know that after a dreary day of rain, the sun peeks through the clouds and a rainbow forms. So you notice the rainbow is the shape of a parabola as shown in the first figure. This parabola has the following equation:

[tex]y=-x^2+36[/tex]

On the other hand, in the distance you notice that an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. So let's choose two points on the graph of the parabola to build up the equation of the line:

[tex]\bullet \ If \ x=-5, then: \\ \\ y=-(-5)^2+36=11 \\ \\ So: \\ \\ P_{1}(-5,11) \\ \\ \\ \bullet \ If \ x=4, then: \\ \\ y=-(4)^2+36=20 \\ \\ So: \\ \\ P_{2}(4,20)[/tex]

Therefore, the equation of the line using these two points is:

[tex]y-20=\frac{20-11}{4-(-5)}(x-4) \\ \\ y-20=\frac{9}{9}(x-4) \\ \\ y-20=x-4 \\ \\ y=x+20-4 \\ \\ y=x+16[/tex]

FOR THE PARABOLA, THE TABLE IS:

[tex]Other \ two \ points: \\ \\ \bullet \ If \ x=0, then: \\ \\ y=-(0)^2+36=36 \\ \\ So: \\ \\ P_{3}(0,36) \\ \\ \\ \bullet \ If \ x=1, then: \\ \\ y=-(1)^2+36=35 \\ \\ So: \\ \\ P_{4}(1,35)[/tex]

So the table is:

[tex]\left[\begin{array}{cc}x & y\\-5 & 11\\4 & 20\\0 & 36\\1 & 35\end{array}\right][/tex]

FOR THE LINE, THE TABLE IS:

[tex]Other \ two \ points: \\ \\ \bullet \ If \ x=0, then: \\ \\ y=x+16=0+16=16 \\ \\ So: \\ \\ P_{3}(0,16) \\ \\ \\ \bullet \ If \ x=1, then: \\ \\ y=x+16=1+17=17 \\ \\ So: \\ \\ P_{4}(1,17)[/tex]

So the table is:

[tex]\left[\begin{array}{cc}x & y\\-5 & 11\\4 & 20\\0 & 16\\1 & 17\end{array}\right][/tex]

The domain represents the horizontal distance while the range represents the height. In this situation, all values don't make sense. First, the rainbow starts in a point on the earth's crust. Also, the airplane starts at a point on the runway, so this doesn't include all the real numbers. A similar thing happens to the height since the airplane turns into an horizontal way at a moment of its trip and this doesn't include all the real numbers.

x-intercepts:

The x intercepts are the points at which the graph passes through the x-axis, that is, when [tex]y=0[/tex]. So:

[tex]-x^2 + 36=0 \\ \\ x^2=36 \\ \\ x=\pm\sqrt{36} \\ \\ x=\pm 6[/tex]

So the x intercepts are [tex]x_{1}=6 \ and \ x_{2}=-6[/tex]

y-intercepts:

The y-intercept is the point at which the graph passes through the y-axis, that is, when [tex]x=0[/tex]. So:

[tex]y=-x^2+36 \\ \\ y=-(0)^2+36 \\ \\ y=36[/tex]

So the y-intercept is [tex]b=36[/tex]

In conclusion, if we take the x-axis as the ground, the x-intercepts represent the beginning and the end of the rainbow while the y-intercept represent its maximum height.

The equation of this line is:

[tex]y=x+16[/tex]

As you can see, the slope [tex]m=1[/tex] is positive, therefore the line I've created is positive. This means as x increases y increases, but how do x and y increase? Well, they increase as the airplane is taking off, so this means the horizontal distance and the height increase.

The system of equations we created is:

[tex]\left\{ \begin{array}{c}y=x+16\\y=-x^{2}+36\end{array}\right.[/tex]

Remember that in Part 1, chose two points on the graph of the parabola to build up the equation of the line, so the solutions to this system is indeed those two points:

[tex]P_{1}(-5,11) \ and \ P_{2}(4,20)[/tex]

They represents that the airplane cuts through the rainbow at those two points.

A piecesewise function is a function defined by two or more equations over a domain. Our piecewise function is shown in the second figure below and is defined by:

[tex]f(x)=\left\{ \begin{array}{c}x+16\quad if\quad-16\le x\le-5\\-x^{2}+36\quad if\quad-5\le x\le4\\x+16\ \quad if\quad4\le x\le24\\40\quad if\quad x\ge24\end{array}\right.[/tex]

To graph this function, let's follows these steps:

STEP 1: Graph [tex]y=x+16[/tex] from -16 to -5. This represents the graph of the trajectory of the airplane before touching the rainbow.

STEP 2: Graph [tex]y=-x^2+36[/tex] from -5 to 4. This is represents the graph of the rainbow as the airplane passes under its path.

STEP 3: Graph [tex]y=x+16[/tex] from 4 to 24. This is represents the graph of the trajectory of the airplane after touching the second point of the rainbow.

STEP 4: Graph [tex]y=x+16[/tex] from 24 and forward. This is represents the graph of the trajectory of the airplane when turning into an horizontal way.

The type of tessellation used to cover a surface completely using one type of regular polygon is regular tessellation.

Tessellation is defined as the process of covering of a surface or a plane using the geometric shapes.

One geometric shape will not overlap with the other and there will not be any gaps in between.

Regular tessellation is the tiling which uses one type of regular polygon to form a pattern.

In semi-regular tessellation, two or more regular polygons are used such that each vertex is the same.

Here, it is only used one type of regular polygon. No other polygons are used.

So it can't be semi-regular tessellation.+

So it is regular tessellation.

Hence the tessellation is regular tessellation.

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Answer:

D. In step 1, 12! divided by 10! is not equivalent to 6! divided by 5!.

F. There are sixty-six ways to choose ten items from twelve.  

Step-by-step explanation:

The expressions that determine Lorelei's solution include in step 1, 12! divided by 10! is not equivalent to 6! divided by 5! as well option F.

From the information given, Lorelei evaluates the expression to determine how many different groups of ten she can make out of twelve items.

In this case, the expressions that determine Lorelei's solution include in step 1, 12! divided by 10! is not equivalent to 6! divided by 5! and that there are sixty-six ways to choose ten items from twelve.

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Answer:

A.) Figure A

Step-by-step explanation:

because the first part "If..." always goes on the inside of the 2 circles

Step-by-step explanation:

The elevator is descending, so its velocity is -5 m/min.  After 1 hour (or 60 minutes), the position is:

x = (-5 m/min) (60 min)

x = -300 m

It's position after one hour is -300 meters.

Answer:

1/4

Step-by-step explanation:

Let the fraction be x/y

(x + 1)/y = 1/2

x/(y - 1) = 1/3          Cross multiply both equations.

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

2*(x + 1) = y           Remove the brackets

2x + 2 = y

################

3x = y - 1               Add 1 to both sides.

3x + 1=y - 1+ 1

3x + 1 = y

#################

Equate both ys

3x + 1 = 2x + 2        Subtract 1 from both sides.

3x + 1-1 = 2x + 2 -1

3x = 2x + 1              Subtract 2x from both sides.

3x-2x = 2x-2x +1    Simplify

x = 1

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

y = 3x + 1

y = 3(1) + 1

y = 3 + 1

y = 4

The original fraction was 1/4

Answer:

The pen costs $5.05, and the pencil costs $0.05

Step-by-step explanation:

First, we define 2 variables for the two prices.

Let x = price of the pen.

Let y = price of the pencil.

Now we use the given information to write two equations.

"A pen and a pencil together cost $5.10. "

x + y = 5.1

"The pen cost $5 more than the pencil. "

y = x + 5

The system of equations is:

x + y = 5.1

y = x + 5

Since the second equation is already solved for y, we will use the substitution method to solve the system of equations.

Substitute y of the first equation by x + 5.

x + x + 5 = 5.1

2x + 5 = 5.1

2x = 0.1

x = 0.05   (price of the pencil)

Now substitute 0.05 for x in the second equation.

y = 0.05 + 5

y = 5.05     (price of the pen)

The pen costs $5.05, and the pencil costs $0.05

Final answer:

The pencil costs $0.05 and the pen costs $5.05, with the pen being $5 more expensive than the pencil and the total cost for both being $5.10.

Explanation:

To solve this problem, we need to create equations based on the information given. Let's assign x as the cost of the pencil and x + $5.00 as the cost of the pen, since the pen costs $5 more than the pencil.

According to the problem, the total cost of both items is $5.10, so we can write the equation as follows:

Combining the like terms, we get:

Subtracting $5.00 from both sides, we find:

Dividing both sides by 2 to solve for x:

Thus, the pencil costs $0.05, and the pen, which costs $5 more, is $5.05.

:

starting value

-- :

the y-intercept is the starting value of the coin after no time has passed. :)

Answer:

Answer:

The solutions for the equation are:

x = 2  

x = − 4

Step-by-step explanation:

Answer:

x = - 4, x = 2

Step-by-step explanation:

Given

x² + 2x - 8 = 0

Consider the factors of the constant term ( - 8) which sum to give the coefficient of the x- term ( + 2)

The factors are + 4 and - 2, since

4 × - 2 = - 8 and 4 - 2 = + 2, hence

(x + 4)x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 2 = 0 ⇒ x = 2

Answer:

10

Step-by-step explanation:

Each term is the sum of the two after it:

a_n = a_n+1 + a_n+2

The next term is:

a₄ = a₅ + a₆

31 = 21 + a₆

a₆ = 10

Answer:

b = 101.52

Step-by-step explanation:

b^2 = a^2 + c^2 - 2ac CosB

b^2 = 105^2 + 9^2 - 2(105)(9) Cos 65°

b^2 = 11 106 - 798.75

b^2 = 10 307.25

b = 101.52

Answer:101.52

Step-by-step explanation:

Given

a=105

c=9

[tex]B=65^{\circ}[/tex]

using cosine rule

[tex]2acCosB=a^2+c^2-b^2 [/tex]

[tex]2(105)(9)Cos65=105^2+9^2-b^2[/tex]

[tex] b^2=11025+81-798.7485[/tex]

b=101.524

-2xy+3x-2xy+3x ( original equation)

-2xy-2xy+3x+3x ( just rearranging)

-4xy+6x

Answer :-4xy+6x- D.

Answer:

The correct answer is option D.  -4xy + 6x

Step-by-step explanation:

It is given an expression, −2xy + 3x − 2xy + 3x  

To simplify the given expression

Let the expression be −2xy + 3x − 2xy + 3x

−2xy + 3x − 2xy + 3x   = -2xy - 2xy + 3x + 3x     [write similar terms together]

 = -4xy + 6x

Therefore the correct answer is option D.

-4xy + 6x

Answer:

Option C [tex]1,102\ in^{2}[/tex]

Step-by-step explanation:

we know that

The lateral surface area of a cylinder is equal to

[tex]LA=2\pi rh[/tex]

we have

[tex]r=13.6\ in[/tex]

[tex]h=12.9\ in[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]LA=2(3.14)(13.6)(12.9)[/tex]

[tex]LA=1,101.76\ in^{2}[/tex]

Round to the nearest square inch

[tex]LA=1,102\ in^{2}[/tex]

Answer:

54°

Step-by-step explanation:

Corn made up 15 % of the vegetables, so

Corn makes up 15 % of the degrees in the circle.

There are 360 degrees in a circle, so

15/100 × 360° = 54 °

The measure of the central angle for corn is 54°.

Answer:

6

Step-by-step explanation:

m = 3

n = 1

Equation

m(m - n)     Substitute the givens

Solution

3(3 -1 )        Evaluate what is inside the brackets.

3(2)      multiply

6

Answer:

m=3 and n-1 ,find m2- mn

Step-by-step explanation:

Answer: D. Y=3/2x

Step-by-step explanation: When going from left to right, the line is going up. This means that the slope is positive. We can eliminate answers C and E because they are negative numbers. The slope is rise over run. From the bottom point, the line goes up 3 and to the right 2. Therefore, the answer is D. Y=3/2x.

Answer:

(f*g)(0)=-2

f(g(0))=5  I think you meant this one based on your answer. Please read lower half of explanation for this answer.  Please ask me any question on this that you have.

Step-by-step explanation:

(f*g)(0) means f(0)*g(0).

f(0) means to replace x with 0 in x^2+1 (since g(x)=x^2+1).

g(0) means to replace x with 0 in x-1 (since g(x)=x-2).

f(0)=0^2+1=0+1=1

g(0)=0-2=-2

So (f*g)(0)=f(0)g(0)=(1)(-2)=-2.

But I guess you didn't mean this because you said the answer is 5...

Oh maybe you mean

[tex](f \circ g)(0)[/tex]?

[tex](f \circ g)(0)[/tex] means [tex]f(g(0))[/tex].

So f(g(0))...we start with the inside first... that is g(0)?

g(0)=-2 (we found this above)

f(g(0))

f(-2)           ->I replaced g(0) with -2

Now f(-2) means to replace x with (-2) in x^2+1 (since f(x)=x^2+1)

So let's do that:

(-2)^2+1

4+1

5

Answer:

Shortest side=5, Largest side=13, Other side=12

Step-by-step explanation:

Let's define the shortest side of the triangle as x, since the other two sides are defined in terms of this one.

The longest side is 2 less than 3 times the shortest side, then it is 3 * x - 2.

The other side is 2 more than twice the shortest side, then it is 2 * x + 2.

By the problem directions, we know that the perimeter or sum of sides is 30.

x + 3x - 2 +  2*x + 2 = 30

Adding all the terms "with x" together and all terms "without x" together, we get...

6*x = 30

Solving for x (dividing both sides by 6), we get...

x = 30/6 = 5

Finally,

Shortest side: 5

Largest side: 3 * 5 - 2 = 13

Other side: 2 * 5 + 2 = 12

The length of each side of the triangle are 5 in, 12 in and 13 in respectively

Given:

Perimeter of the triangle = 30 in

let

shortest side = x

other side = 2x + 2

Longest side = 3x - 2

Perimeter of the triangle = shortest side + other side + Longest side

30 = x + (2x + 2) + (3x - 2)

30 = x + 2x + 2 + 3x - 2

30 = 6x

divide both sides by 6

x = 30 / 6

x = 5

Therefore,

shortest side = x

= 5 in

other side = 2x + 2

= 2(5) + 2

= 10 + 2

= 12 in

Longest side = 3x - 2

= 3(5) - 2

= 15 - 2

= 13 in

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Question 1:

In this question, it's asking you if the decreasing rate is linear or exponential.

The decreasing rate would be linear, due to the fact that it is decreasing at a constant rate of 11%. The decreasing rate doesn't change, which makes this linear.

Question 2:

In this question, it's asking you what would the component's cost be in 3 years if it started off at $120.

To find this, we're going to need multiply the price by -.11, and then subtract to get the price. We would repeat this until we reach 3 years.

Work:

[tex]120*-0.11=-13.2\\\\120-13.2=106.8\ \text{(Year 1)}\\\\106.8*-0.11= -11.748\\\\106.8-11.748=95.05\ \text{(Year 2)}\\\\95.05*-0.11=-10.4555\\\\95.05-10.4555=84.59\ \text{(Year 3)}\\\\\text{In year 3, the cost of the component would be \$84.59}[/tex]

Question 3:

In this question, it asks if the decline in price is linear or exponential.

The decline in price would be exponential, due to the fact that the decrease in price is not always the same, since it changes every year. The price doesn't decrease at the same price each year. As you see from question 2, the change in price is not the same each year.

The price decrease of the computer component is exponential. By using the exponential decay formula, the cost of the component that is $120 today will be approximately $84.96 in three years.

The decline in the price of a computer component that decreases at a rate of 11% per year is an exponential decline. This is because the price reduction each year is based on the current price of the component, not a fixed amount. To calculate the cost three years from now, we can use the formula for exponential decay:

New Value = Original Value × (1 - Rate of Decrease)^Number of Periods

If today's price is $120, the cost after three years would be:

New Price = $120 × (1 - 0.11)^3

New Price = $120 × (0.89)^3

New Price = $120 × 0.708

New Price = $84.96 (rounded to two decimal places)

Therefore, if the component costs $120 today, it will cost approximately $84.96 in three years.

Answer:

A. is less than the radius.

Step-by-step explanation:

If a point is inside a circle, the distance from the center of the circle to that point is option (A) is less than the radius is the correct answer.

A circle is a collection of all points in a plane which are at a constant distance from a fixed point. A circle is a round-shaped figure that has no corners or edges.

For the given situation,

The distance from the center of the circle to any point on it's circumference is called radius.

So, when we consider the distance from the center of the circle, then the term should be related to radius.

Hence we can conclude that if a point is inside a circle, the distance from the center of the circle to that point is option (A) is less than the radius is the correct answer.

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Answer:

D.) 27 * ( 1/3) ^ (x-1)

Step-by-step explanation:

This is because the first value, 27, indicates the rest state, or the y intercept.  The second value, 1/3, is derived from the pattern of the values decreasing by the previous value being divided by 3, or technically multiplied by (1/3).  The (x-1) is derived from the original formula for the geometric series.

f(x) = x * r ^ (n-1)

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For any questions or more information, please comment below and I'll respond as soon as possible.

The explicit formula for the geometric sequence is:[tex]a_n = 27 \cdot \left(\frac{1}{3}\right)^{(n-1)}[/tex]

To find the explicit formula for the geometric sequence 27, 9, 3, 1, ..., we first need to identify key components of a geometric sequence.

First Term (a): The first term of this sequence, denoted as [tex]a[/tex], is 27.

Common Ratio (r): The common ratio [tex]r[/tex] is found by dividing the second term by the first term:
[tex]r = \frac{9}{27} = \frac{1}{3}[/tex]
We can check this by calculating further:
[tex]\frac{3}{9} = \frac{1}{3} \quad \text{and} \quad \frac{1}{3} = \frac{1}{3}[/tex]
Thus, the common ratio is consistent at [tex]r = \frac{1}{3}[/tex].

Explicit Formula: The explicit formula for a geometric sequence is given by:
[tex]a_n = a \cdot r^{(n-1)}[/tex]
where [tex]a_n[/tex] is the [tex]n[/tex]-th term, [tex]a[/tex] is the first term, and [tex]r[/tex] is the common ratio.

Substituting in our values:
[tex]a_n = 27 \cdot \left(\frac{1}{3}\right)^{(n-1)}[/tex]

Answer:

Unknown number, x=-4

Step-by-step explanation:

Forming the equation from the information provided above.  

9=2x+17

If we solve for the unknown number, we first collect like terms together.

2x=9-17

2x=-8

Divide both sides of the equal sign by 2 the coefficient of x

x=-4

Answer:

x = -4

Explanation:

We are given the following statement which we are to translate into a mathematical equation and then solve it:

'nine is seventeen more than two times a number'

Assuming [tex] x [/tex] to be the unknown number, this can be written as:

[tex] 9 = 2 x + 1 7 [/tex]

Solving for x:

[tex] 2 x = 9 - 1 7 [/tex]

[tex] 2 x = - 8 [/tex]

[tex]x=\frac{-8}{2}[/tex]

[tex]x=-4[/tex]

Therefore, the unknown number is -4.