What is the distance between points P(8, 5) and Q(2,-3) to the nearest tenth?

Answer:

m = -3/4

Step-by-step explanation:

-5 - 1 / 6 - -2 = -6/8 = -3/4

Answer:

Step-by-step explanation:

(-5 - 1)/(6 + 2)= -6/8 = -3/4

Answer:

31

Step-by-step explanation:

Answer:

n = 7

Step-by-step explanation:

Varies directly

w/n² = k

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

when n = 3, W = 117

k =117/3²

k = 117/9

k = 13

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

Find n when W = 637

637/n² = 13

637 /13 = n²

49 = n²

7 = n

The distance between points C and D is given as follows:

5 units.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates \((x_1,y_1)\) and \((x_2,y_2)\).

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The coordinates for this problem are given as follows:

(-4, -6) and (1, -6).

Hence the distance is given as follows:

\(D = \sqrt{(-4 - 1)^2 + (-6 - (-6))^2}\)

D = 5 units.

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The proportion used to find the missing side  is RS/QS = RO/PQ, the value of y = 12ft

First we need to see whether triangle RQS is similar with triangle RPO

Angle QRS = Angle PRQ (common angle)

Angle RSQ = ROP (Given, that they are right angles)

So, triangle RQS is similar with triangle RPO

Now the sides of one triangle is in proportion with the other

RS/RO = RQ/RP = QS/PQ

RS/RO = QS/PQ

RS/QS = RO/PQ

9/12 = y/16

3/4 = y/16

3/y = 4/16

3/y = 1/4

y = 4 x 3

y = 12

To find the missing side the proportion used is RS/QS = RO/PQ, the value of y = 12ft

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Answer:

Since in finding perimeter you add the lengths divide the number and substitute it into the formula for area

Step-by-step explanation:

75 = 3 x 5 x 5    in prime factorization

Answer:

Step-by-step explanation:

3x5x5

Answer: The best problem solving strategy to solve this problem with is a formula. Additionally Brandon had $12.50 before going to the store.

Step-by-step explanation: Formula and Solving it

He Spent $2.50 on pencils.

Amount left after buying a pencil = x - 2.50

Next, he spent half of the amount left in his pocket.

He spent (x - 2.50)/2 on notebook and paper.

So the total amount he spent = 2.50 + (x -2.50)/2

Amount left when he got home =$ 5.00

That means, x - Total amount spent = 5

=> x - (2.50 + (x -2.50)/2 ) = 5

=> x - 2.50 -x/2 + 2.50/2 = 5

=> x/2 - 2.50/2 = 5

=> x/2 = 5 + 2.50/2

=> x/2 = 6.25

=>x = $12.5

Answer:

ecant and Tangent of a Circle

Imagine you are working with a construction crew. A road already exists through a forest that goes over a circular lake. You want to build another road through a forest that connects to this road, but does not go through the lake.

sectanprod1

As it turns out, the road you will be building and the road it will connect to both represent characteristics of a circle that have their own name. The road/bridge that already exists is called a secant of the circular lake, and the road you're going to build is called the tangent of the circular lake.

In general, a secant of a circle is a line that passes through any two points on the edge the circle, and a tangent of a circle is a line that just touches one point on the edge of the circle. Notice how the road that already exists intersects the circular lake at two points along its shoreline (the start and end of the bridge portion of the road), and the road you will be building just touches the circular lake at one point.

Based on this, we call the road that already exists a secant segment of the circular lake, and we call the road you will be building a tangent segment of the circular lake. Furthermore, we call the portion of the road that already exists that is outside of the lake the external secant segment.

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Secant Tangent Product Theorem

Now for your conundrum: you need to know how long the road you're constructing will be in order to know how many supplies you will need. However, you can't measure it, because it is through a forest, so there are trees and such in the way.

You are able to measure the road that already exists, and you find that the bridge portion of the road is 5 kilometers, and the portion of the road from the bridge to where the new road will be is 4 kilometers.

sectanprod3

Oh boy, how are we going to find the distance of this road? Never fear! Math is here! Thankfully, in mathematics, we have a theorem called the Secant-tangent product theorem, which states that for any secant segment and tangent segment of a circle that meet at a common endpoint outside of the circle, it must be the case that

(Length of the whole secant segment)(Length of the external secant segment) = (Length of the tangent segment)2

That is, the product of the length of the whole secant segment and the length of the external segment is equal to the length of the tangent segment squared.

sectanprod4

This is awesome! We can use this

A scenario where the knowledge of tangents, secants, and chords can be used is in the construction of a road over a circular lake.

This refers to the straight line that touches a curve and can be described as very close points on a curve.

Hence, we can see that with the knowledge of tangents and secants and chords, for a construction worker that is working on a road that oversees a circular lake and the degrees and angles would need to be used and calculated.

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Mathematics provides a framework for developing critical thinking, problem-solving, and analytical skills that are valuable in many aspects of life.

What is mathematics?

Mathematics is a fundamental discipline that plays a crucial role in our daily lives and in shaping our understanding of the world.

Mathematics is a field of study that deals with the properties and relationships of numbers, quantities, shapes, and patterns. It involves using logical reasoning, abstraction, and symbolic manipulation to understand and solve problems related to these concepts.

Mathematics is important for many reasons. First and foremost, it is a fundamental tool for understanding and describing the world around us. It plays a crucial role in science, technology, engineering, economics, finance, and many other fields by providing tools for modeling and analyzing complex phenomena.

Mathematics is also essential for making accurate predictions and decisions based on data and evidence, as well as for designing and optimizing systems and processes.

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The average is 40 and  the margin of error is 10.95.

What is margin of error?

The margin of error is a statistic expressing the amount of random sampling in the result of a survey.

Average (A) = sum of all the value/ given set.

A = (51+ 41 + 28)/3 = 40

margin of error = 100/square root of 120 = 10.95.

Therefore, the average is 40 and  the margin of error is 10.95.

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The volume of the composite solid is  452. 160 ft³

First, it is important to note that the formula for calculating the volume of a cone is expressed as;

V = πr²h/3

Such that the parameters of the formula are;

From the information given,

substitute the values

Volume = 3.14 × 6² × 12/3

Divide the values

Volume = 31.4 × 36 × 4

Multiply the values

Volume = 452. 160 ft³

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The true statement about the parking fees in zone A and zone B is A. The fee in zone A is 25 % higher than the fee in zone A.

From the data table below, we can determine that the higher parking fee occurs in zone A instead of zone B.

There is a difference of 1 € in the parking fees between the two zones, which results in a 25% difference.

                                  Zone A     Zone B

Parking fees per hour   4 €            3 €

Difference in fees         +1 €           - 1 €

Percentage difference:

Higher than the other  25%          0%

Less than the other       0%          33%

Thus, we can conclude that A. The fee in zone A is 25 % higher than the fee in zone A.

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Answer:

You just said the answers. 54

Step-by-step explanation:

5

Step-by-step explanation:

the solution is in the picture

Answer: x= 6, z=96°

Step-by-step explanation:

As shown, the angle z and its opposite angle are congruent angles, so it is 96 degrees.

To find x, first find the degree of the angle (13x+6°).

[360-(96×2)]/2=84°

Then, subtract six from it and divide by three to get 6°.

(84-6)/3=6°

Approximation of decimals is a mathematical technique for finding or measuring approximations and minimizing the number of decimal places.

A fractional representation of a real number that comes close to representing it. Any real number a can be represented by an endless number of decimal fractions.

The number of decimal places in a decimal number is the number of digits following the decimal point. A mathematical method for locating or measuring approximations and reducing the number of decimal places is known as approximation of decimals.

Any comparison that is close but not accurate to another entity is called an approximation. By rounding, one can get a good idea of a number. By rounding the values in a computation before performing the operations, a calculation can be approximated.

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The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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Substituting d=12, and b=3 in the given expression we get:

Answer: Option C).

Answer: 3 cans

Step-by-step explanation:

40-28=12

12\4=3

Answer:

90

Step-by-step explanation:

12 x 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Answer:

$\(4.48\) is the total price.

Step-by-step explanation:

Mulitply the total by the percentage.

\(4 * .12 = .48\)

Add those together.

\(4 + .48 = 4.48\)

Total price of mangoes: $\(4.48\)

It takes 64 pounds of seed to completely plant a 7 acre field. How many pounds of seed needed per acre?

64/7 = 9.1429

Answer:

The base of the rectangle is 21 mm.

Step-by-step explanation:

Given that a rectangle's area is 336 mm, and its height is 16 mm, to determine what is the measure of its base, the following calculation must be performed, knowing that the area of a rectangle arises from multiplying its base by its height:

16 x X = 336

X = 336/16

X = 21

Therefore, the base of the rectangle is 21 mm.

Answer:

Following are the solution to the given point:

Step-by-step explanation:

In point a:

\(\to 2ty'=8y\to \frac{1}{y} dy = 4 \frac{1}{t} dt\\\\\to \int \frac{1}{y} dy = 4 \int \frac{1}{t} dt \\\\\to \log y = 4 \log t + \log C\\\\\to \log y = \log ct^4\\\\\to y=ct^4 \\\\\to y(-2)=16 \\\\\to 16= c(-2)^4\\\\\to 16= 16c\\\\\to c= \frac{16}{16}\\\\\to c=1\\\\\to r=4\)

In point b:

\(\to 2ty' = 8y \\\\\to y'- \frac{4}{t} y=0 \\\\here \ p(t) = \frac{1}{t}\) it's a discontinuous point at t=0, and the largest internal containing -2 since \(y=(-2) = 16 \ is\ (-\infty, 0)\)

In point c:

\((-\infty,0 ) \cup (0, \infty)\)

Using the elimination method, we know that s = 11 and d = 7.

To create an equation in one variable using the elimination approach, you can either add or subtract the equations.

To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.

So, we have the equations:

d+s=18 and 4d+2s=50

Now, calculate as follows:

4d+2s=50       4d + 2s = 50

-4(d+s=18) ⇒   -4d - 4s = -72

                    _____________

                           -2s = -22

s = 11

Then,

d + 11 = 18

d = 18 - 11

d = 7

Therefore, using the elimination method, we know that s = 11 and d = 7.

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Answer:

d 88

Step-by-step explanation:

Answer:D

Step-by-step explanation:

88

The original dimensions of the piece of metal were 15 inches by 20 inches.

To solve this problem, we can use the given information to set up an equation. Let's assume that the width of the rectangular piece of metal is x inches. According to the problem, the length of the piece of metal is 5 inches longer than its width, so the length would be (x+5) inches.

When squares with sides 1 inch long are cut from the four corners, the width and length of the resulting box will be reduced by 2 inches each. Therefore, the width of the box will be (x-2) inches and the length will be ((x+5)-2) inches, which simplifies to (x+3) inches.

The height of the box will be 1 inch since the flaps are folded upward.
Now, let's calculate the volume of the box using the formula Volume = length * width * height.

Substituting the values, we have:

234 = (x+3)(x-2)(1)

Simplifying the equation, we get:

234 = x^2 + x - 6

Rearranging the equation, we have:

x^2 + x - 240 = 0

Now, we can solve this quadratic equation either by factoring or by using the quadratic formula. Let's use factoring to find the values of x.

Factoring the equation, we have:
(x+16)(x-15) = 0
Setting each factor equal to zero, we get:
x+16 = 0 or x-15 = 0
Solving for x, we have:
x = -16 or x = 15
Since the width cannot be negative, we take x = 15 as the valid solution.
Therefore, the original dimensions of the piece of metal were 15 inches in width and (15+5) = 20 inches in length.

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The annual interest rate is 7.5%.

What is Simple interest?

Simple interest is a type of interest that is calculated on the principal amount (or the initial amount) of a loan or investment, without taking into account any accumulated interest from previous periods.

The formula for simple interest is:

I = P × r × t

where I is the interest earned, P is the principal (initial amount), r is the annual interest rate as a decimal, and t is the time in years.

In this case, we know I = $562.50, P = $1500, and t = 5 years.

we ca substitute values into the formula,

562.50 = 1500× r ×5

Simplifying, we get:

r = 562.50 / (1500 ×5)

r = 0.075

r = 7.5%

Therefore, the annual interest rate is 7.5%.

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Answer:

10.7

Step-by-step explanation:

Since this is a right triangle, we can use trig functions to calculate the hypotenuse.

We know the opposite side from the angle labeled 59 degrees.

sin 59 = opp side / hypotenuse

sin 59 = 9.2/x

x = 9.2/ sin 59

x = 10.733