Find the distance of a line with endpoints (1, 2) and (7, 4). Round to the nearest tenth.
Distance Formula:
d=√√(x₂-x₁)² + (y₁ - y₁)²

The equation for plan (2) is y = 10x.

Two or more expressions with an equal sign are defined as an equation.

Given that, the second plan costs $10 for each bowling visit.

Therefore, the total cost, y, for x bowling visit is:

y = 10x

Hence, the equation for the plan (2) is y = 10x.

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Answer:

36

Step-by-step explanation:

[tex]m\angle TSU=36^{\circ}[/tex] using the definition of an isosceles triangle. By CPCTC, [tex]m\angle USR=36^{\circ}[/tex].

Answer: A gym membership cost 3 dollars a month. There is an initial fee of $5. How many months would you need to be paying for the membership to have spent 20 dollars?

Step-by-step explanation:

3x+5=20

3x=15

x=5

5 Months

Step-by-step explanation:

always remember Pythagoras for right-angled triangles (90°) :

c² = a² + b²

c is the Hypotenuse (the baseline opposite of the 90° angle), a and b are the legs.

so, in our case

ramp² = 11² + 60² = 121 + 3600 = 3721

ramp = sqrt(3721) = 61 ft

Answer:

61 feet

Step-by-step explanation:

Because the triangle is a right triangle we can use the Pythagorean theorem to solve for the length of the ramp.

The Pythagorean theorem is a² + b² = c²

Where, a and b = leg lengths and c = hypotenuse (longest side)

Here, the length of the ramp represents the hypotenuse as it is the longest side. We are also given the length of the legs. The lengths being 60 ft and 11 ft.

This means that a and b = 11 and 60

We can plug these lengths in and then solve for c or the length of the ramp

a² + b² = c²

==> plug in a = 11 and b = 60

11² + 60² = c²

==> simplify exponents

121 + 3600 = c²

==> add 121 and 3600

3721 = c²

==> take the square root of both sides

61 = c

So the length of the ramp is 61 feet

Answer:

-3/14

Step-by-step explanation:

Step 1) Convert into -7/14 + 4/14

Step 2) -7/14 + 4/14= -3/14

The value of quotient will be;

⇒ 60

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The expression is,

⇒   15 ) 900 (

Now,

Solve the expression by dividing, we get;

⇒   15 ) 900 ( 60

          - 90

          --------

            × 0

Thus, The value of quotient will be;

⇒ 60

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line k and second line h are not parallel lines because the have different slopes.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Where x₁ - x coordinate

y₁ - y coordinate

m - slope

A line k passes through the points ​(−5​,−5​) and ​(1,37​).

Then Slope m = 37 + 5/ 1 + 5

m = 7

Now Write the equation as;

y + 5 = 7(x + 5)

y = 7x + 30

A second line h passes through the points ​(−3​,−33​) and ​(3​,9​).

Then Slope m = 9 + 3/ 3 + 33

m = 0.33

Now Write the equation as;

y + 33 = 0.33(x + 3)

Hence, line k and second line h are not parallel lines because the have different slopes.

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Answer:

½

Step-by-step explanation:

The coefficient of x is 1 but the equation is not in the form of y = mx + b

x - 2y = 4

-2y = 4 - x

2y = x - 4

y = ½x - 2

Therefore, the gradient is ½

The largest number of matches she could have won before are 164 matches.

A ratio shows the relation between two amounts. For example, the ratio of apples to pears in a basket or the ratio of women to men in a town.

First represent the matches she had won, using n as a reference. This means:

[tex]\frac{n}{2n} = \frac{1}{2}[/tex]

Then, based on this let's add the current ratio:

[tex]\frac{n+3}{2n+4} = \frac{503}{1000}[/tex]

Based on this, let's solve this inequality to find out the number of matches the player won before. Follow these steps:

Based on the previous process, the number of matches the player could have won before the weekend began was 164 matches.

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Jamal's estimate of the distance across the gorge is 1424.56 ft

What is Pythagorean Theorem ?

The Pythagorean Theorem is a well-known geometric principle that states that the squares on the hypotenuse of a right triangle, which is the side opposite the right angle, equal the total of the squares on the legs.

First, he can draw a diagram to represent the situation. He can label points Y, X, A, and B on the diagram and draw the lines YX and AB to represent the locations of the tree and the points he marked.

Next, he can use the Pythagorean Theorem to find the distance AC. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the side AC is the hypotenuse, and the sides YA and YC are the other two sides. Therefore, he can use the theorem to find AC as follows:

AC^2 = YA^2 + YC^2

He knows the values of YA (500ft) and YC (327ft), so he can substitute these values into the equation and solve for AC:

AC^2 = 500^2 + 327^2

AC^2 = 250000 + 107649

AC^2 = 357659

AC = √357659

AC ≈ 597.56 ft

Finally, he can use the distance AC to estimate the distance across the gorge. The distance across the gorge is equal to the distance from X to Y, which is equal to the sum of the distances from X to A and A to Y. Therefore, he can estimate the distance across the gorge as follows:

distance across gorge = XA + AY

distance across gorge = AC + YA + YC

distance across gorge = 597.56 ft + 500 ft + 327 ft

distance across gorge ≈ 1424.56 ft

This is Jamal's estimate of the distance across the gorge.

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The option that is not a polynomial is d 2/y

An equation made up of variables, exponents, and coefficients along with operations and the equal sign is known as a polynomial equation.

Sums of terms of the form kxⁿ, where k is any number and n is a positive integer, make up polynomials.

a. -4x + 3y this is a polynomial

k = -4 and 3

n = 1

b. p^2q - 3pq^2 this is a polynomial

k = 1 and 3

n = 2

c. 4 - x this is a polynomial

k = -1

n = 1

d 2/y this is not a polynomial

= 2y^-1

A polynomial does not have a variable in the denominator or have a negative exponents. Hence this is not a polynomial

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Answer:

Yes

Step-by-step explanation:

[tex]6[/tex] × [tex]5 = 30[/tex]

[tex]4[/tex] × [tex]5 = 20[/tex]

[tex]30 + 20 = 50[/tex]

[tex]84-50=34[/tex]

Yolanda can purchase 5 pairs of mittens and 5 scarves and still have $34 leftover.

Hello,

I hope you and your family are doing well!

If the potatoes in the bag are split equally among 5 people, each person will get 25 potatoes / 5 people

= 25/5

=5 potatoes.

Therefore, each person will receive 5 potatoes.

----

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Happy Holidays!

The five rational numbers between - 4 / 7 and - 3 / 8 by discretizing the set of rational numbers are - 181 / 336, - 85 / 168, - 53 / 112, - 37 / 84, - 137 / 336.

Rational numbers are real numbers of the form m / n, where m and n are integers and n is a non-zero number. In this case, we need to determine five numbers between two given rational numbers: - 4 / 7, - 3 / 8.

Since there is an infinite set of rational numbers, we must create an additional criterion to discretize that set and find the five required numbers more easily. This can be done by means of the following formula:

y = a + (b - a) · [x / (n + 1)]

Where:

If we know that a = - 4 / 7, b = - 3 / 8 and n = 5, then the five rational numbers are:

n = 1

y = - 4 / 7 + [- 3 / 8 + 4 / 7] · (1 / 6)

y = - 181 / 336

n = 2

y = - 4 / 7 + [- 3 / 8 + 4 / 7] · (2 / 6)

y = - 85 / 168

n = 3

y = - 4 / 7 + [- 3 / 8 + 4 / 7] · (3 / 6)

y = - 53 / 112

n = 4

y = - 4 / 7 + [- 3 / 8 + 4 / 7] · (4 / 6)

y = - 37 / 84

n = 5

y = - 4 / 7 + [- 3 / 8 + 4 / 7] · (5 / 6)

y = - 137 / 336

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The evaluation of the function would be f(x) = 7.

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

The number of subscribers of the third-ranked Magazine is  1116,279.

What is algebra?

One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.

Here, we have

Given

Number of digital subscribers = 2.4 million

Percentage increment = 1150%

Let x represent the number of subscribers the third-ranked magazine

The relationship between the number of subscribers of the top-ranked and third-ranked magazines is defined as follows;

2.4 million = x + 1150% of x

Convert to digits only

2,400,000 = x + 1150% * x ------- By reordering

x + 1150% * x = 2,400,000

x + 1150/100 * x = 2,400,000

x + 1.15 * x = 2,400,000

Now we Factorize

x(1 + 1.15) = 2,400,000

x (2.15) = 2,400,000  

Now we Divide through by 2.15

x = 2,400,000/2.15

x = 1116,279.07

x = 1116,279

Hence, the number of subscribers of the third-ranked Magazine is  1116,279.

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Answer:

32

Step-by-step explanation:

we have to find the side of the bigger triangle by making a ratio

5/8=7/x

cross multiply

5x=7(8)

5x=56

/5.  /5

x=11.2

now for the other side

5/8=8/x

5x=8(8)

5x=64

/5. /5

x=12.8

we know all three sides 11.2, 12.8 and 8 so we add them

11.2+12.8+8

24+8

32

hopes this helps

It would cost $25.05 to buy 5 small and 4 large cards.

What is Total cost?

The total cost is the sum total of costs of individual items.

Given,

Cost of small card = $2.05

Cost of large card = $3.70

Therefore,

Total cost = total cost of small card + total cost of large cards

                 = 5*(2.05) + 4*(3.70)

                 = 10.25 + 14.8

                 = 25.05

Hence, It would cost $25.05 to buy 5 small and 4 large cards.

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Therefore the solution of this question is the velocity of roller coaster  after 3 second is 22 m/s

The rate at which an object's position is changing as perceived from a given point of view and as described by a certain unit of time is known as its velocity.

Here,

The speed of  roller coaster is 4m/s

The acceleration of  roller coaster is 6m/s2

So,

we have to find the velocity after 3 second

thus we use the formula v=u + at

Putting values

=> v = 4 +6*3

=> v = 4 + 18

=> v = 22 m/s

Therefore the velocity of roller coaster  after 3 second is 22 m/s

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Answer:

The sales tax is 13.72

Step-by-step explanation:

Answer:

The function rule for g(x) can be obtained by performing the transformations described on the function f(x) = -6x.

First, we need to stretch the graph of f(x) vertically by a factor of 7. This means that the y-values of the points on the graph of g(x) will be 7 times the y-values of the points on the graph of f(x). We can achieve this by multiplying the y-values of the function f(x) by 7.

Next, we need to reflect the graph of g(x) in the x-axis. This means that the y-values of the points on the graph of g(x) will be the negative of the y-values of the points on the graph of f(x). We can achieve this by multiplying the y-values of the function f(x) by -1.

Applying these transformations to the function f(x) = -6x, we get the function rule for g(x) as follows:

g(x) = (-1) * (7) * (-6x)

= (-1) * (-42x)

= 42x

Therefore, the function rule for g(x) is g(x) = 42x.

If ABCD is a parallelogram and  ∠D=57° then ∠BCD =123°

What is a parallelogram ?

A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base (one of the parallel sides) and height (the distance from top to bottom) of the parallelogram determine its area. A parallelogram's perimeter is determined by the lengths of its four sides.

Using corresponding angle property int he parallelogram we can se that the ∠D is equal to exterior ∠C (57° ) because side AD and BC are parallel

and we know ∠C + exterior ∠C will be 180°

∠BCD=180° - 57°

∠BCD =123°

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Answer:

5

Step-by-step explanation:

12x - 3y

------------

4x - z

Input the values provided:

12(3) - 3(1/3)

------------------

4(3) - 5

Start by simplifying the numerator and denominator expressions:

-numerator;

12(3) = 36

3(1/3) = 1

36 - 1 = 35

-denominator:

4(3) = 12

12 - 5 = 7

Then divide:

35

----

7

This will equal to 5, which is your final answer.

Hope this helps! :D

The required point at which point is the object accelerating toward the right is Z.

A  force following up on a moving body at a point to the bearing of movement, having a tendency to cause the body to follow a round or ended way. The power of gravity following up on a satellite in circle is an illustration of a centripetal power; the rubbing of the tires of a vehicle making a turn comparatively gives centripetal  force on the vehicle.

The item in the guide is moving by round movement: consequently, there is a force (called centripetal force ) that pulls the item towards the center point of the circle.

As indicated by Newton's law motion,

F = ma

a power on the item relates to a speed increase, and this speed increase (called centripetal speed increase) has a similar course of the power. Thus, since the speed increase is towards the focal point of the circle also, the main place of the direction where the speed increase is towards the right is at point Z.

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The function r ( m ) $12 more than the salary of someone who has worked for m months.

What is function?

A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would say that y is a function of x.

If we have S(m) represents salary after m months i.e. y=S(m) will be the graph of salary Corresponding to the number of months m.

So, we have [tex]m+12 \geqslant 12$,[/tex]

[tex]$\Rightarrow S(m+12)$[/tex] will give us the value of Salary after 12 months of the Job.

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The cost of each small package of cookies is $7 and the cost of each large package of cookies is $11.

What is a variable?

Any qualities, quantity, or number that can be gauged or tallied qualifies as a variable. A data item is another name for a variable. Examples of variables include age, sex, company income and expenses, country of birth, capital expenditures, class grades, eye colour, and vehicle kind.

Given that the total cost of  3 small packages of cookies and 14 large packages of cookies is $203.

The total cost of  11 small packages of cookies and 11 large packages of cookies is $220.

Assume that the cost small packages of cookies is x and large packages of cookies y.

Then the cost of 3 small packages of cookies and 14 large packages of cookies is (3x + 14y).

The cost 11 small packages of cookies and 11 large packages of cookies is (11x + 11y).

The system of linear equation is

3x + 14y = 203  .....(i)

11x + 11y = 220  .....(ii)

Multiply equation (i) by 11 and equation (ii) by 3

33x + 154y = 2233

33x + 33y = 660

______________

        121y = 1573

Divide both sides by 121:

y = 13

Putting y = 13 in equation (i)

3x + 14 × 13 = 203

3x = 21

x = 7

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Answer:

x = 3

Step-by-step explanation:

CD is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides, that is

[tex]\frac{BD}{AD}[/tex] = [tex]\frac{BC}{AC}[/tex] ( substitute values )

[tex]\frac{x}{2.25}[/tex] = [tex]\frac{4}{3}[/tex] ( cross- multiply )

3x = 4 × 2.25 = 9 ( divide both sides by 3 )

x = 3

Noah is using the 50/30/20 budgeting strategy because he is using 50% of his income for his basic needs, 30% for entertainment, and 20% for savings and debt repayment.

Money management in mathematics is the application of mathematical principles and techniques to the management of personal or corporate money. It entails the use of mathematical tools like equations, graphs, and statistics to analyse financial data and make educated decisions about budgeting, saving, investing, and spending. Mathematicians also use probability and risk analysis to manage money by estimating the likelihood of different financial events and making decisions based on the benefits and dangers of various financial options. Overall, mathematicians' understanding of money management enables people and organisations to better manage their financial resources and reach their financial objectives.

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Answer:

One possible decomposition of h(x) is:

h(x) = (1/x²) * (1/(1 + 3/x))

This decomposition can be obtained by applying the identity (a/b) * (1/c) = a/(b*c).

Another possible decomposition of h(x) is:

h(x) = 1/((x+3)*(x+3))

This decomposition can be obtained by applying the identity (a/b) * (c/d) = (ac)/(bd).

Note that these are just two possible decompositions of h(x) and there may be other ways to decompose the function as well. The choice of decomposition will depend on the specific context and the intended use of the function.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The normal distribution is defined by its mean and standard deviation, so if we know that the heights of the seedlings are normally distributed and we know certain percentiles of the distribution, we can find the mean and standard deviation.

We are given that 10% of the seedlings are taller than 15 cm, which means that 90% of the seedlings are shorter than or equal to 15 cm. This tells us that the 90th percentile of the distribution is 15 cm.

Similarly, we are given that 5% of the seedlings are shorter than 4 cm, which means that 95% of the seedlings are taller than or equal to 4 cm. This tells us that the 95th percentile of the distribution is 4 cm.

Since the normal distribution is symmetrical, the mean of the distribution is the value that separates the upper and lower halves of the distribution. In this case, the mean is the value that separates the lower 95% from the upper 5%, which means it is the value that is exactly halfway between the 95th and 90th percentiles.

To find the mean, we can add the 95th percentile (4 cm) and the 90th percentile (15 cm) and divide by 2:

mean = (4 + 15) / 2

= 19 / 2

= 9.5 cm

To find the standard deviation, we can use the fact that the normal distribution has the property that approximately 68% of the values fall within one standard deviation of the mean, approximately 95% fall within two standard deviations, and approximately 99.7% fall within three standard deviations.

Since we know that the 95th percentile (4 cm) is 2 standard deviations below the mean and the 90th percentile (15 cm) is 2 standard deviations above the mean, we can set up the equation:

4 cm = mean - 2 * standard deviation

15 cm = mean + 2 * standard deviation

Solving for standard deviation, we get:

standard deviation = (15 cm - 4 cm) / (2 * 2)

= 11 cm / 4

= 2.75 cm

So, the mean height of the seedlings is 9.5 cm and the standard deviation is 2.75 cm.

Answer:

There are many possible ranges, including  (−∞,15.051464)

 and  (15.051464,18.6844845)

 as well as  31.5±0.6270678

 (centered on the mean). Observe, in R:

> pnorm(15.051464, 31.5, 10) - pnorm(-Inf, 31.5, 10)

[1] 0.05

> pnorm(18.6844845, 31.5, 10) - pnorm(15.051464, 31.5, 10)

[1] 0.05

> pnorm(32.1270678, 31.5, 10) - pnorm(30.8729322, 31.5, 10)

[1] 0.05

In general, if you are given a small enough but otherwise arbitrary number  a∈R

 you can find a unique  b

 such that  b>a

 and

∫baϕ(x,31.5,10)dx=0.05,

where  ϕ

 is the normal density. For example, if  a=10

, then  b≈16.42

. Again in R:

> qnorm(pnorm(10, 31.5, 10) + 0.05, 31.5, 10)

[1] 16.42003

So your question doesn’t determine the answer uniquely: I’m free to choose the upper or lower bound of the interval or any particular point relative to those (e.g. the midpoint) arbitrarily.

If you had asked for a 95% interval, it would have been a reasonable assumption (but an assumption nonetheless) that you want an interval centered on the mode, median, or mean. But for a 5% interval, it’s not obvious that you want that — in practice it’s more likely that you want the upper tail or the lower tail.

That said, at a fundamental level, the answer is the same: use the cumulative distribution function and/or its inverse, as appropriate.