My friend is hoping to move to your town but is concerned because she doesn’t have a car. Do you think this will present a big problem for her? Use the distance formula in some way to justify your response.

If a transversal intersects two lines such that a pair of alternate interior angles is equal , then the two lines are parallel.

What do you mean by traversal line?

A transversal is a line that, at two different locations in the geometry, cuts through two lines in the same plane. Various sorts of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.

What do you mean by angle?

An angle is defined as the figure, in which two rays meet at a common point called the vertex. The angle is denoted using the symbol “∠”.

From the figure,

x + 1 = 180°

y + 2 = 180°

Adding above equations,

x + y + 1 + 2 = 360°

Given ,

x + y = 1 +2

x + y + x + y = 360°

2(x + y) = 360°

x + y = 180°

Angles made on same side of transversal is supplementary . So the lines are parallel.

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Answer:

9 days (round up)

Step-by-step explanation:

70 ÷ 8 = 8.75

           ≈ 9 (round up)

The percentage of the cupcakes that had sprinkles if 39 out of the 52 cupcakes had sprinkles on top is 75%.

A division by 100 results in a percentage, often known as a percent. A percentage denotes a component of a total sum and indicates "per 100". For example, 45% represents 45 out of 100. Calculating a percentage is the process of determining a whole's proportion in terms of 100.

Given:

The total no cupcakes = 52,

The no of sprinkled cupcakes = 39,

Percentage of sprinkled cupcakes = The no of sprinkled cupcakes / The total no cupcakes × 100

Percentage of sprinkled cupcakes = 39 / 52 × 100

Percentage of sprinkled cupcakes = 75%

Therefore, the percentage of the cupcakes that had sprinkles if 39 out of the 52 cupcakes had sprinkles on top is 75%.

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The dividend is 35286 and the divisor is 7. The value of the division is $540.8571

When dividing, it's important to note that the number that is being divided in this case 35286 is the dividend.

On the other hand, the number that is being divided by which is in this case 7 is the dividend.

The division will be:

= $35286 ÷ 7

= $540.8571

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Answer:

(4 , 5)

Step-by-step explanation:

midpoint formula: (x1+x2/2 , y1+y2/2)

so

(1+7/2 , 4+6/2)

(8/2 , 10/2)

4 , 5

Answer:

If the coordinates of at least two points in the line are given, the slope (m) may be calculated by,                               m = (y2 - y1) / (x2 - x1

⇒ ∠AEC is the angle vertical opposite to ∠BEC

Answer: the coefficient of the 6th term of (2x - 7)⁹ is -33882912

Step-by-step explanation:

[tex](2x-7)^9[/tex]

In this problem we use the following formula:

                              [tex](a+b)^n=\sum\limits _{k=0}^nC_n^ka^{n-k}b^k[/tex]

a=2x         b=-7        n=9

The 1th term of (2x-7)^9 is k=0

The 2th term of (2x-7)^9 is k=1

The 3th term of (2x-7)^9 is k=2

..........................................................

The 6th term of (2x-7)^9 is k=5

Hence,

[tex]\displaystyle\\C_9^5(2x)^{9-5}(-7)^5=\\\\\frac{9!}{(9-5)!*5!}(2x)^4(-7)^5 =\\\\\frac{9!}{4!*5!} 2^4x^4(-7)^5=\\\\126(16)(-16807)(x^4)=\\\\=-33889212x^4[/tex]

- 33889212x⁴ is the coefficient of the 6th term in  binomial theorem .

What is binomial theorem?

( 2x - 7 )⁹

compare with formula

a = 2x    b = - 7  n = 9

The 1th term of (2x-7)^9 is k=0

The 2th term of (2x-7)^9 is k=1

The 3th term of (2x-7)^9 is k=2

...................................................

The 6th term of (2x-7)^9 is k=5

hence

⁵C₉( 2x )⁹⁻⁵ ( - 7)⁵  = 9!/( 9-5)!* 5! (2x)⁴( -7)⁵

                            = 9!/4! * 5! 2⁴x⁴( -7)⁵

                              = 126(16) ( - 16807 )(x)⁴

                              =  - 33889212x⁴

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The partial fraction is proved.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

=3x²+8x+4/(x²-4)(3x-2)

=3x2+8x+4/(x2-4)(3x-2)

= 3x2+6x+2x+4/(x2-4)(3x-2)

=3x(x+2)+2(x+2)/(x2-4)(3x-2)

Hence proved, l.h.s = r.h.s

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Answer:

7/12

Step-by-step explanation:

12/12 - 5/12 = 7/12

Using the information from the given diagram, the measure of angle x (m ∠x) is 52°

From the question, we are to determine the measure of angle x.

From the given diagram, we can write that

m ∠A + m ∠H + m ∠I = 180° (Sum of angle in a triangle)

Also,

m ∠K = m ∠I (Corresponding angles theorem)

∴ m ∠I = 62°

Thus,

x° + 66° + 62° = 180°

x° + 128° = 180°

x° = 180° - 128°

x° = 52°

Hence, the measure of ∠x 52°

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The expressions (5 + 9 - 2³) and (4² - 6) are not equal (≠) to each other. Then the correct option is B.

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.

The numerical expressions are given below.

(5 + 9 - 2³) and (4² - 6)

Simplify the expression, then we have

(5 + 9 - 2³) = 5 + 9 - 8 = 6

(4² - 6) = 16 - 6 = 10

The expressions (5 + 9 - 2³) and (4² - 6) are not equal (≠) to each other. Then the correct option is B.

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Answer:

1/5

Step-by-step explanation:

equation: 3/5-2/5=x

we can multiply the whole equation by 5 so that we can easily subtract the numbers

3-2=1

now we divide it by 5 so that we get our number in a fraction

after we divide we get 1/5

Answer:

- 90

Step-by-step explanation:

substitute x = - 2 into f(x)

f(- 2) = 3[tex](-2)^{5}[/tex] - [tex](-2)^{4}[/tex] - 6(- 2) + 10

        = 3(- 32) - (16) + 12 + 10

        = - 96 - 16 + 22

        = - 112 + 22

        = - 90

[tex]{ \boxed{ \sf{f( - 2) = - 90}}}[/tex]

Step-by-step explanation:

[tex]{ \red{ \tt{f(x) = {3x}^{5} - {x}^{4} - 6x + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = 3( { - 2})^{5} - ( { - 2})^{4} - 6( - 2) + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = 3( - 32) - 16 + 12 + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = - 96 - 16 + 12 + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = - 112 + 22}}}[/tex]

[tex]{ \green{ \boxed{ \bold{f( - 2) = - 90}}}}[/tex]

Answer:

the answer according to my solution is 06

The other names of AB in the given figure are

Collinear points refers to points that lies on the same plane and on the same straight line.

The figure shows two planes and point A, B and C are collinear points, while points Q and R are collinear

Points A, B and C are non colinear to points Q and R

Points AB are still part of line AC hence can be noted as part of line segment BC.

The line has arrow head and may also be called rays. In this case the are part of an arrow

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The percentages to complete the table for the steaming time are 40 min, 20 min and 100 min respectively

A percentage is a number or ratio that can be expressed as a fraction of 100.

Given: Percentage: 100% of 40 min, 50% of 40 min and 250% of 40 min

100% of 40 min:

100% of 40 min = (100/100) × 40 min = 1 × 40 min = 40 min

50% of 40 min:

50% of 40 min = (50/100) × 40 min = 0.5 × 40 min = 20 min

250% of 40 min:

250% of 40 min = (250/100) × 40 min = 2.5 × 40 min = 100 min

Therefore, the value of the percentages to complete the table for the steaming time are 40 min, 20 min and 100 min for 100% of 40 min, 50% of 40 min and 250% of 40 min respectively.

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A' - (-1,4)

B' - (-1,8)

C' - (-5,4)

hope this helps

We can conclude that (C) Gibbons will live in a building that is similar to the Chimpanzee's rectangular house.

So, observe the given shapes on the graph:

Therefore, we can conclude that (C) Gibbons will live in a building that is similar to the Chimpanzee's rectangular house.

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Answer: x = -135.59

Step-by-step explanation:

20 = 0.694(x + 150)(2)

Step 1: Simplify both sides of the equation.

20 = 0.694 (x + 150)(2)

20 = 1.388x + 208.2 (use the distributive property)

20 = 1.388x + 208.2

Step 2: Flip the equation.

1.388x + 208.2 = 20

Step 3: Subtract 208.2 from both sides of the equation.

1.388x + 208.2 − 208.2 = 20 − 208.2

1.388x = −188.2

Step 4: Divide both sides by 1.388.

1.388x/1.388 = −188.2/1.388

x = −135.590778

Optional: Simplify

x = -135.59

The equation of the line representing the given situation is y = (3/4)x , the graph of the equation is shown below .

In the question ,

it is given that ,

a refreshment stand makes 3 large serving of frozen yogurt from 4 pints .

also given that number of pints is represented by x - axis .

the number of servings is represented by y - axis  .

the equation of the line is represented by y = mx + c .

we get c = 0, because at 0 pint there is no servings

hence , the  equation becomes y [tex]=[/tex] mx .

According to the question ,

3 = m*4

m = 3/4 .

Substituting the value of m in the equation , we get

y = (3/4)x

the graph of the equation is shown below .

Therefore , The equation of the line representing the given situation is y = (3/4)x .

The given question is incomplete , the complete question is

A refreshment stand makes 3 large servings of frozen yogurt from 4 pints. Graph the line and then write its equation. Let the x-axis represent the number of pints and the y-axis represent the number of servings. Use only fractional form, if necessary.

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By using the concept of differentiation, it can be calculated that

value of P is -2 and value of Q is 1

What is differentiation?

Differentiation is the process where  the instantaneous rate of change of function can be calculated based on one variable. Differentiation is a very important tool in calculus

Here differentiation is used

f(x) = [tex]x^2y[/tex]

[tex]df = 2xydx+x^2dy[/tex]

Here P = 2xy, Q = [tex]x^2[/tex]

At x = 1, y = -1

P = 2(1)(-1) = -2

Q = [tex](-1)^2[/tex] = 1

So value of P is -2 and value of Q is 1

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The probability that the proportion of Labradors in a sample of 694 pet dogs would differ from the population proportion by less than 3% is 0.9964

The probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean

The z score is given by the formula

z = (X - μ) / σ

Definition of variables

mean, μ  = p = 8% = 0.08

sample size, n = 694

standard deviation, σ

= √{(p(1 - p)) / n}

= √{(0.08(1 - 0.08)) / 694}

= √{(0.08 * 0.98) / 694}

= 0.0103

The probability

differ from the population proportion by less than 3%

|X - 0.08| < 0.03

X < 0.11 OR X > 0.05

0.05 < X < 0.11

P(z < 0.11) - P(z < 0.05 )

z score for z < 0.05

z = (0.05 - 0.08) / 0.0103

= -2.9126

p value for z < -2.9126 = 0.001792

z score for z < 0.12

z = (0.12 - 0.09) / 0.0102

=  2.9412

p value for z < 2.9412 = 0.9982

The probability required = 0.9982 - 0.0016 = 0.9964 or 99.64%

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The differentiation of [tex]e^x[/tex] is [tex]\frac{d}{dx}(e^x) =e^x[/tex]. Hence, proved,

Given that, [tex]\frac{d}{dx}(e^x) =e^x[/tex].

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

Differentiate using the Exponential Rule which states that [tex]\frac{d}{dx}(a^x)[/tex] is [tex]a^xln(a)[/tex] where [tex]a=e.e^x[/tex]

So, now [tex]\frac{d}{dx}(e^x) =e^x[/tex]

The differentiation of [tex]e^x[/tex] is [tex]\frac{d}{dx}(e^x) =e^x[/tex]. Hence, proved,

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We will need 7 quart package if we want 62 strawberries

What is division?

Division is one of the basic arithmetic computation which divide a value in equal sets of smaller values. The other basic arithmetic computations are addition, subtraction, multiplication. We use long division method to find the quotient and remainder.

We are given that there are 9 strawberries in a quart package

Also we want 62 strawberries

Then how many quart will be required

Now we perform division to find the number of quart

62/9 = we get a value of 8.88

Which is very close to nine

Hence we will need 9 quart packages if we want 62 strawberries

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50 + 20x ≥ 250 is the inequality that can be used to find how many bags of candy Ms. Folk needs to buy to have at least 250 candies​.

How to solve equations in word problems?

Let x be the number of bags she bought:

50 + 20x ≥ 250

3x ≥ 200

x ≥ 200/3

x ≥ 66.67

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The inequality will be represented by p ≥ 33 for at least 15 points.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Mark must score at least 11 points to have an average of 10 points per game.

The average of a set of data is its sum, divided by the number of data points in the set. If p is the number of points Mark scores in his next game, and he wants his average at least 15, then the relation is ...

 (8+14+10+20+5++p)/6 ≥ 15

 57 +p ≥ 90 . . . . . . . . . multiply by 6 and simplify

 p ≥ 33

Mark must score at least 33 points in the next game to average at least 15 points per game.

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