What is the length of OP’ if the scale factor of the dilated segment is 2.5?

A. 10cm
B. 2.5cm
C. 6.5 cm
D. 7.5 cm

Answer:

93.2° (nearest tenth)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]

From inspection of the given triangle:

Substitute the values into the sine rule to find the measure of angle C:

[tex]\implies \dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

[tex]\implies \dfrac{\sin 38^{\circ}}{9}=\dfrac{\sin C}{11}[/tex]

[tex]\implies \sin C=\dfrac{11\sin 38^{\circ}}{9}[/tex]

[tex]\implies C=\sin ^{-1} \left(\dfrac{11\sin 38^{\circ}}{9}\right)[/tex]

[tex]\implies C=48.80523914...^{\circ}[/tex]

Interior angles of a triangle sum to 180°.

[tex]\implies A+B+C=180^{\circ}[/tex]

[tex]\implies A+38^{\circ}+48.80523914...^{\circ}=180^{\circ}[/tex]

[tex]\implies A=93.19476086...^{\circ}[/tex]

Therefore, the size of angle A is 93.2° (nearest tenth).

255 biology and 192 sociology textbooks were sold in a week.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

While the graph of a linear equation with two variables, x and y, creates a straight line, the graph of a linear equation with just one variable, x, forms a vertical line that is parallel to the y-axis.

Step 1:

Let x be the number of biology textbooks and y be number of sociology textbooks.

x + y = 447 ------(1)

x - y = 63 ------(2)

Step 2:

Adding (1) and (2), we get

2x = 510

x = 255

Step 3:

Subtracting (1) from (2), we get

2y = 384

y = 192

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Answer:

  (x, y) = (4 7/9, 1 2/3)

Step-by-step explanation:

You want to solve this system of equations using the elimination method.

First of all, take a look at the coefficients of the variables:

  x: 3 and 3. Subtracting one from the other will eliminate x

  y: 4 and -2. Adding twice the second to the first will eliminate y.

The easiest elimination is accomplished by subtracting the second equation from the first:

  (3x +4y) -(3x -2y) = (21) -(11)

  6y = 10 . . . . . . . . . . simplify

  y = 10/6 = 5/3 = 1 2/3 . . . . divide by the coefficient of y

Substitute for y to find x.

  3x +4(5/3) = 21

  x +20/9 = 7 . . . . . . divide by 3

  x = 7 -(2 2/9) = 4 7/9

The solution is (x, y) = (4 7/9, 1 2/3).

__

Additional comment

A graphing calculator confirms this solution.

12: This one if fairy simple: all you need is a line that is not parallel to the line provided, and combined with it, it will provide a solution that's on that line. For example:

y = 2x

x - y = 10

13: Just find two lines that cross (6, -4).

You can use point-slope form:

y - y1 = m(x-x1)

y + 4 = m(x - 6)

then choose two equations with different m's

y = 2(x-6) - 4

y = 3(x-6) - 4

14:

Line one has a slope of two and an intercept at y=0 so it is y = 2x

Line two has a slope of one and an intercept at y=-1 so it is y = x - 1

To find the solution of the system, substitute y:

2x = x - 1

x = -1

Then plug back in:

y = 2 * -1 = -2

So the solution is: (-1, -2)

None of the option are correct for the solution to inequality.

For the given inequality:

4 > 102/z + 11

Subtract both side by 11

4 - 11 > 102/z + 11 - 11

-7 > 102/z

Divide both sides by 102

-7/102 > 1/z

Taking reciprocal of each;

z < -102/7

z < -14.5

Thus, none of the option are correct for the solution to the inequality.

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The required expression will be 2/x+15 as the problem says "the sum of 2 divided by x and 15".

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases. A phrase in language may contain an action on its own, but it does not constitute a complete sentence.

Here,

2 divided by x,

=2/x

sum of 2/x and 15,

2/x+15

The conclusion is "the sum of 2 divided by x and 15," hence the necessary equation will be "2/x+15."

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Answer:

The answer is 45

Step-by-step explanation:

the way to find this answer is by, first, knowing that each angle of a triangle adds up to 180. So, we must first add the 85 and 50 which will give us 135. After, you subtract it all from 180, which gives you 45.

In the triangle, the value of x is,

⇒ x = 45°

We have to given that;

In triangle;

The angles are 85 degree, 50 degree and x.

Since, We know that;

Sum of all interior angle of a triangle are 180 degree.

Hence, We get;

⇒ x + 85 + 50 = 180

⇒ x + 135 = 180

⇒ x = 180 - 135

⇒ x = 45°

Thus, the value of x is,

⇒ x = 45°

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Answer:

$84.50

Step-by-step explanation:

Add the amounts:

$63.48 + $52.02 = $115.50

Two $100 bills add to $200.

To find the change, subtract the total cost from the amount of money handed over.

$200 - $115.50 = $84.50

Molly should give him $84.50. Thus option B is the correct answer.

The change given must be equal to the balance left after deducting the price of the goods from the total money received.

In this case,  

Price of goods = Price of DVD player + Price of five DVDs

                         = $63.48 + $52.02

                         =$115.50

Total Money Received = 2 x $100 = $200

Therefore, Change = Total Money Received - Price of goods

                                = $200 - $115.50

                                = $84.50

The 3 to the power of three halves equal to square root of 27 sqrt(27).

What is the square root?

A square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4² = ² = 16.

A square root is a number that can be multiplied by itself to give the original number.

3 to the power of 3/2 is equal to the square root of 3 to the power of 3, which is equal to the square root of 27. The square root of 27 is approximately 3.872983346207417.

To calculate this value, you can use a calculator or you can use the following formula:

3^(3/2) = sqrt(3^3) = sqrt(27) = 3.872983346207417

Hence, the 3 to the power of three halves equal to square root of 27 sqrt(27).

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Answer: This is where the answer is undefined

Step-by-step explanation:

Edge 2022 :)

Answer: 5th option

Step-by-step explanation:

edge 2023

The Elimination equations: 3s = 33, s = 11.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, etc

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.

According to our question-

5s+3t=30

-1(2s+3t=-3)

which will eventually

5s+3t=30

-2s-3t=3

which then becomes

3s = 33, s=11

Hence, The Elimination equations: 3s = 33, s = 11.

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The inverse of the function g(x) = ∛(2x + 4) is equal to: D. g(x)⁻¹ = 1/2(x³) - 2.

The domain of the function shown in the graph is: B. [-2, 1].

In Mathematics, an inverse function can be defined as a type of function that is obtained by reversing (undoing) the operation of a given function (f(x)).

In order to determine the inverse of the given function, we would interchange input value (x) and the output value (y) as follows:

g(x) = ∛(2x + 4)

x = ∛(2y + 4)

Next, we would take the cube root of both sides of the function;

x³ = 2y + 4

2y = x³ - 4

y = (x³ - 4)/2

y = x³/2 - 2

g(x)⁻¹ = 1/2(x³) - 2

In Mathematics, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right as follows;

Domain = [-2, 1].

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The slope that needs to be programmed into the computer to accomplish the delivery is x=3441/100.

A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem or Pythagoras theorem in mathematics. It is believed that the area of the square with the hypotenuse equals the sum of the areas of the squares on the other two sides.

Pythagoras, a Greek philosopher who was born around 570 BC, is honored in the name of the theorem. Perhaps more than any other mathematical theorem, the theorem has been demonstrated several times using a variety of techniques. There are many different types of proofs, some of which go back thousands of years, including both geometric proofs and algebraic proofs.

By using Pythagorean theorem,

x²=20²+28²

x²=400+784

x²=1184

x=34.41

x=3441/100

Therefore, the slope that needs to be programmed into the computer to accomplish the delivery is x=3441/100.

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The solution to the expression 2 1/2 + 3 1/5 x 5 5/8 is 223/2

fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

2 1/2 + 3 1/5 x 5 5/8 can be solved by converting all the mixed fraction to improper fraction

2 1/2 = 5/2

3 1/5 = 16/5

5 5/8 = 45/8

which reduces it to

5/2 + 45/8 x 16/5

using BODMAS we taking care of the multiplication section first

45/8 x 16/5 = 18

5/2 + 18

18 can be writen as a fraction which is 36/2

5/2 + 36/2 = 41/2

in conclusion the simplified form of the expression is 41/2

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The speed represents the rate of the plane is 250 miles/ hour.

What is speed?

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

An object is considered to be moving at constant speed when it travels an equal distance in an equal amount of time.

When an object travels a different distance at equal intervals of time, it is said to be moving at variable speed.

Average speed is the constant speed determined by the ratio of the total distance travelled by an object to the total amount of time it took to travel that distance.

Immediately speed is When an object is travelling at a variable pace, its speed at every given moment

Speed =distance/ time taken

= 100/0.4

= 250 miles/ hour

Hence, the speed represents the rate of the plane is 250 miles/ hour.

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Answer: Ariana uses 85% drink mix, and Andres uses 90% drink mix. Therefore, Andres's drink will taste more lemony.

Step-by-step explanation:

Ariana uses 17 cups of mix out of the 20 total cups which is 85%

Andres uses 10 cups of mix out of the 11 total cups which is around 90%

Answer:

Step-by-step explanation:

You want the percent of powdered lemon mix in two recipes:

The desired percent can be found from ...

  (lemon mix)/(water + lemon mix) × 100%

For Ariana, this is ...

  17/(3 +17) × 100% = 17/20 × 100% = 85%

For Andres, this is ...

  10/(1 +10) × 100% = 10/11 × 100% ≈ 91%

__

Additional comment

There aren't many powders that will dissolve 10 cups of powder in 1 cup of water. Even if there were, the resulting combination would not have a volume of 11 cups. This might be a mildly interesting math problem, but it has little relevance to any real-world lemonade recipe.

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Yes , the confidence interval still valid because the sample size is large ( n = 100 is greater than 30 ).

Given :

Monica delivers pizza. She takes a simple random sample of 100 of her deliveries from the first 11 months of 2020 and finds that her tips average $3.66 with an SD of $2.19.The 90% confidence interval for Monica’s average tip size for these months has the form A + - B * C .

if the histogram of monica's tips does not follow the normal curve, is the confidence interval still valid .

Here

sample size n = 100

The sample size is a term used in market research for defining the number of subjects included in a sample size.

here

n > 30

Hence the confidence interval is still valid .

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Full question:

Monica delivers pizza. She takes a simple random sample of 100 of her deliveries from the first 11 months of 2020 and finds that her tips average $3.66 with an SD of $2.19.The 90% confidence interval for Monica’s average tip size for these months has the form A + - B * C .

if the histogram of monica's tips does not follow the normal curve, is the confidence interval still valid?

Answer: 6:11

Step-by-step explanation:

Find the total by 6 + 5 =11

He bought 6 videotapes so ratio is 6:11

Answer:

5.2

Step-by-step explanation:

Construct an altitude. Using the Pythagorean theorem, the height is [tex]\sqrt{6^2-3^2} \approx 5.2[/tex]

The number of floors of windows that the window cleaner cleans will be 10.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A window cleaner has cleaned 467 windows of a high rise. He cleans some more. Presently there are 967 clean windows. Each floor of the high rise has 100 windows.

The number of floors of windows that the window cleaner cleans will be given as,

⇒ 967 / 100

⇒ 9.67

⇒ 10 floors

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The point-slope form with a slope of 5/2 and a point of (4,-7) is 5x-2y=34.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10. Linear equations are classified into three types: point-slope, standard, and slope-intercept.

Here,

The slope of line perpendicular to the line y +6=-2/5(x-1)

m1=5/2

point=(4,-7)

y-y1=m(x-x1)

y+7=5/2(x-4)

2y+14=5x-20

5x-2y=34

The point-slope form for slope given as 5/2 and point as (4,-7) will be 5x-2y=34.

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The number of jars that are fully filled is 5 and one jar filled partially is 8 out of 23 parts.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Song has 123 pounds of beans. She fills containers by placing 23 pounds of beans into each container.

⇒ 123 / 23

⇒ 5 ⁸/₂₃

The number of jars that are fully filled is 5 and one jar filled partially is 8 out of 23 parts.

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At 55 seconds , both the plane A and plane B will have same altitude.

According to the question,

The altitude of plane A = 1500m

The altitude of plane B = 1115m

Altitude plane A gained = 19m/s

Altitude plane B gained = 26m/s

Let "x" be the number of second

Let the equation of plan A and plane B is

a(x) = m₁ x + 1500

b(x) = m₂ x + 1115

We know how fast they are gaining altitude. The are the m values

m₁ = 19

m₂ = 26

So, now we have

a(x) = 19 x + 1500

b(x) = 26 x + 1115

So , to have same altitude ,

a(x) = b(x)

=> 19 x + 1500 = 26 x + 1115

Solving for x,

=> 26x-19x = 1500 - 1115

=> 17x = 385

=> x = 55 seconds

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The print is 35.41 cm tall.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

The original painting is 120 cm wide and 85 cm tall.

and, the print is 50 cm wide.

let the print is x cm tall

So, x/ 50 = 85 / 120

120x = 4250

x= 35.41 cm

Hence, the print is 35.41 cm tall.

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Answer: 6.1

Step-by-step explanation:

The sine rule states that the length of one side of a triangle divided by the sine of the angle opposing the side will be equal to the length of the other side divided by the sine of its opposing angle and the same for the last side.

This means [tex]\frac{14}{sin (90)}[/tex] = [tex]\frac{x}{sin(180-90-64)}[/tex]

14 = [tex]\frac{x}{sin(26)}[/tex]

x = 14sin(26) ≈ 6.1

The best estimate of the average change in mood rating linked with an additional hour spent playing sports is 1.5 points, according to the presented linear function.

Modeling a linear function involves:

y = mx + b

The slope, or m, measures how quickly y changes when x changes by one.

The value of y at x = 0 is represented by the y-intercept, or b.

In the given problem

The amount of time they invested in sports is x.

Their mood score is y.

The required equation is ,

y =1.5 + 5

Given that the slope is m = 1.5, the best estimate of the average change in mood rating resulting from an extra hour spent playing sports is 1.5 points.

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Answer: -20<12<=2

Step-by-step explanation:

First, you simplify the expression.

-20<2*6<=2

And then perform any multiplication or division, from left to right...

-20<2*6<=2

-20<12<=2

And there you have it!

I hope this helped!

Have a great rest of your day and Merry Christmas (and Happy New Year)!

Answer: x ≤ -2

Option C is correct

Answer:

x ≤ -2 then it is C) -2

Step-by-step explanation:

7 ≤ −2x + 3

2x+7 ≤ + 3

2x ≤ 3-7

2x ≤ -4

x ≤ -4/2

x ≤ -2