What is the name of this angle?



A.
acute

B.
right

C.
obtuse

D.
straight

The sentence 'The quotient of 2 and the sum of a number and 1' can be represented as an algebraic expression 2 / (x + 1).

To convert the given statement into an algebraic expression, let's first identify the components of the statement. 'A number' is represented as x. 'The sum of a number and 1' can be written as (x + 1). 'The quotient of 2 and...' signifies division by 2.

Therefore, based on the above definitions, we can represent 'The quotient of 2 and the sum of a number and 1' as 2 / (x + 1).

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To solve the system of equations xy = 6x + 12 and yy = x + 47, we can rearrange the equations, isolate one variable, and substitute it into the other equation. Then, solve for the variables. The solution is x = 282 / (270 - y) and y = (270 - xy) / 6.

To solve the given system of equations,

xy = 6x + 12
yy = x + 47

We can start by rearranging the equations:

xy - 6x = 12
yy - x = 47

Next, we can isolate one variable in terms of the other variable and substitute it into the other equation:

x = (yy - 47)
xy - 6(yy - 47) = 12

Simplifying the equation:

xy - 6yy + 282 = 12

Combining like terms:

-6yy + xy = -270

Now, we can solve this equation for y in terms of x:

y = (270 - xy) / 6

Re-substituting the value of y back into one of the original equations:

(270 - xy) / 6 * x = 47

Simplifying and solving for x:

270x - xy = 282

x(270 - y) = 282

x = 282 / (270 - y)

So, the solution to the system of equations is:

x = 282 / (270 - y)
y = (270 - xy) / 6

Each person would get 1/9 lb of pasta if 6 people were to share 2/3 lb of pasta equally.

In the given question, 6 people are sharing 2/3 lb of pasta equally. This implies that we are performing an operation of division. You would divide 2/3 by 6 to find out how much each person gets. Here's how you can do it:

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We are given the incomplete expression:

x^2 + b x

Now to complete the square, we need to add the square of the half of b, that is:

(b / 2)^2

or

b^2 / 4

Therefore the complete expression is:

x^2 + b x + (b^2 / 4)

difference between -5 and 25 is

25 + 5 = 30 degrees

answer is C.

Answer:

[tex]\frac 15[/tex]

Step-by-step explanation:

Hello!

We can convert it into slope intercept form: [tex]y = mx + b[/tex]

The slope is [tex]\frac15[/tex].

Finding the slope of a line from its equation depends on the equation's form. If it's already in slope-intercept form (y = mx + b), the coefficient of x (m) is the slope. If not, rewrite it to that form by isolating y. Alternatively, use the point-slope form (y - y1 = m(x - x1)) with a known point on the line and solve for m. Remember, the slope tells you how much the line rises/falls per unit move to the right. For the equation in the image, the slope is 1/5.

• Using the slope-intercept form: This is the most straightforward way to find the slope if the equation is already in slope-intercept form, which is y = mx + b. In this form, the slope (m) is the coefficient of the x term. For example, if the equation is y = 2x + 3, the slope is 2.

• Using the standard form: If the equation is not in slope-intercept form, you can first rewrite it in slope-intercept form. To do this, you need to isolate the y term. For example, if the equation is 3x + 2y = 6, you would first subtract 3x from both sides to get 2y = -3x + 6. Then, you would divide both sides by 2 to get y = -3/2x + 3. Once the equation is in slope-intercept form, you can find the slope as described in the first method.

• Using the point-slope form: The point-slope form of the equation of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. To find the slope using this form, you need to plug in the coordinates of a point on the line. For example, if the equation is y - 2 = 3(x - 1), and you know that the point (3, 7) is on the line, you can plug in x = 3 and y = 7 to get 5 = 3(2). Solving for m, you get m = 5/3.

The slope of a line tells you rise over run, or how much the line goes up or down for every unit it goes to the right. A positive slope means the line goes up as you move to the right, a negative slope means the line goes down as you move to the right, and a zero slope means the line is horizontal.

In the image, the equation is -15 - x = -5y. To find the slope using the slope-intercept form, we need to rewrite the equation so that y is isolated on one side. We can do this by adding x and dividing both sides by -5:

y = (1/5)x + 3

Therefore, the slope of the line is 1/5.

7/3 +3(2/3 -1/3)^2 =

2/3 -1/3 = 1/3 now you have

7/3 +3(1/3)^2

1/3^2 = 1/9

7/3 +3(1/9)

3*1/9 = 1/3

7/3 + 1/3 = 8/3, which can be changed to 2 2/3

Final answer:

In the context of a folding chair, as angle 1 (between the backrest and the seat) increases, the distance between the back of the chair and the front leg correspondingly increases due to the lever-like movement of the backrest.

Explanation:

When considering the geometry of a folding chair and the angles formed by its parts, it's important to visualize the chair as a system of linked levers. As angle 1 increases, which is the angle between the backrest of the chair and the seat, the relationship between the back of the chair and the front leg changes. If we assume that the front leg stays still and the back of the chair moves backward to increase the angle, the distance between the back of the chair and the front leg increases. This movement can be seen as the backrest acting like a lever, where increasing the angle effectively moves the lever away from the pivot point at the front leg.

Therefore, the correct answer in the context of a folding chair is: A. As the measure of angle 1 increases, the distance between the back of the chair and the front leg of the chair increases.

Dimensions are 50 feet by 50 feet.

Let the length = x

the width = y

So the perimeter = 2(x+y)=200

or, x+y=100

or, y=100-x

So the area is = A = xy = x(100-x).

For greatest area A' = 0 and A" < 0.

[tex]A= x(100-x)\\A=100x-x^2\\A'=100-2x\\A''=-2[/tex]

We set A'=0 to find x.

[tex]100-2x=0\\2x=100\\x=50[/tex]

For x=50, A"=2 < 0

It means for x=50, y=100-50=50 the rectangle will have the greatest area.

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Line g is a line of symmetry of this regular polygon.

We have regular polygon as shown in the figure.

We have to determine which line is a line of symmetry for this regular polygon.

A plane figure is symmetric about a line if it is its own image when flipped across the line. The reflection line is the line of symmetry.

According to the question, we have a Regular Polygon.

According to the concept of Symmetry of any plane figure -

if we fold this polygon about the line g then both the sides will overlap.

The lines i and h do not fulfill this condition.

Hence, line g is a line of symmetry of this regular polygon.

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Answer:

170.202 years

Step-by-step explanation:

From the compound interest formula, that has interest rate in times per year but compounds monthly we have

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

A is the amount you want to save, P is the principal (what you put down, in this case 100), r is the anual interest rate, n is 12 i.e the times it compounds, and t is the amount of years it will take. So we have data for all variables but t.

Solving for t we have

[tex]\frac{A}{P}=(1+\frac{r}{n})^{nt}[/tex]

taking logs

[tex]log(\frac{A}{P})=nt \,log(1+\frac{r}{n})[/tex]

finally

[tex]t = \frac {log(\frac{A}{P}) }{ n[log(1 + \frac{r}{n})]}[/tex]

replacing and calculating we get t=170.202

The simplified version of the polynomial 3+4p to the second power -5p - 3p to the second power + 4p - 8 is p to the second power - p - 5 which corresponds to answer choice C.

The problem you're asking about is a simplification of a polynomial. We can combine like terms in the polynomial which is a basic skill in algebra. The polynomial you provided is 3+4p to the second power -5p - 3p to the second power + 4p - 8

To solve this, we combine similar variables and constant separately. So, we add 4p to the second power and - 3p to the second power which will give us p to the second power. Next, we add -5p to +4p which results in -p. Finally, adding the constants 3 and -8 gives us -5. Therefore, the simplified polynomial becomes p to the second power - p - 5. Thus, the correct answer is option C.

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Nonlinear function (A)

The graph of a combination of line segments that passes the vertical line test is a Non Linear function.

The vertical line test states that a graph represents a function if and only if all vertical lines intersect the graph at most once.

The vertical line check is a graphical approach of determining whether or not a curve inside the aircraft represents the graph of a function by means of visually examining the variety of intersections of the curve with vertical lines.A vertical line intersects with them only once, making them features.Parabolas that face upward and downward are capabilities.They may be functions because a vertical line intersects the curve no extra than once.

If a vertical line intersects a curve on an xy-plane greater than once then for one price of x the curve has multiple value of y, and so, the curve does now not represent a function. If all vertical lines intersect a curve at most once then the curve represents a function.

The vertical line take a look at helps to find it a given curve represents a function or now not. If the vertical line cuts the graph of the equation at simplest one factor, then it's miles a characteristic, and if cuts the graph of the characteristic at a couple of point, then it does not constitute a characteristic. A vertical form is a shape with layers stacked on top of every other, with a fixed layer top, for instance a spherical tower where the radius corresponds to the datapoint.

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Answer:

R  ~ D,

S  ~  E,

T  ~  B,  and

Q  ~  C

Answer:

By having or building a good credit history.

Step-by-step explanation:

When an item is to bought by you on credit , for you to have or build a good credit history , Buying something with credit means that you are buying something with money you don't have at that very time

Later on, you will have to give back this money borrowed to a person,an interest will be paid for lending it.

The probability of Mark hitting the bull's-eye on the fourth shot, assuming he misses the first three times, is 8.64%. This is calculated as the product of the probabilities of each event occurring independently.

This is indeed a problem related to probability, particularly, this pertains to the concept of an independent event in statistics. Mark's success in shooting an arrow accurately to the target is an independent event because the outcome of one shot doesn't affect the outcome of other shots.

In Mark's case, he hits the bull's-eye about 40% of the time, i.e. his success rate P(Success) is 0.40 and his failure rate P(Failure) is 0.60. Since the question asked about the probability of him hitting the bull's-eye on the fourth shot, we should look at the first three shots being failures and only the fourth being a success.

This leads us to the calculation: P(FFFH) = P(F) x P(F) x P(F) x P(H) = (0.60)*(0.60)*(0.60)*(0.40) = 0.0864 or 8.64% chance.

So, there's an 8.64% chance that Mark will hit the bull's-eye on the fourth shot given that he misses the first three.

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The probability that Mark hits the bull's-eye on his fourth shot, given he typically hits the bull's-eye 40% of the time, is 0.0864 or 8.64%

The problem is about the probability that Mark hits the bull's-eye on the fourth shot given that he hits the bull's-eye about 40% of the time. In these cases, for the first three shots, he should not hit the bull's-eye (probabilty of 60%) and on the fourth trial, he should hit the bull's-eye (probability of 40%). Therefore, we multiply the individual probabilities together to find the answer.

Step 1: Find the probability that he does not hit the bull's-eye in the first three trials. This is (0.6)*(0.6)*(0.6) = 0.216.

Step 2: Find the probability that he hits the bull's-eye on the fourth trial. This is simply 0.4.

Step 3: Multiply the two probabilities together to find the final answer. This gives us 0.216*0.4 = 0.0864.

So, the probability that Mark hits the bull's-eye on the fourth shot is 0.0864, or 8.64%.

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