Solve 2x^2 + 31 = 17. The solutions are x= and x=

The distance between each pair of points (-1,4) and (1,-1) exists √29 units after utilizing the distance formula.

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

[tex]$\mathrm{d}=\sqrt{\left(\mathrm{x}_2-\mathrm{x}_1\right)^2+\left(\mathrm{y}_2-\mathrm{y}_1\right)^2}[/tex]

It is given that:

The distance between each pair of points (-1,4) and (1,-1)

Two points are (-1,4) and (1,-1)

To estimate the distance between the above two points utilize the distance formula:

[tex]$\mathrm{d}=\sqrt{(1-(-1))^2+(-1-4)^2}$$[/tex]

[tex]$\mathrm{d}=\sqrt{(1+1)^2+(-1-4)^2}$$[/tex]

The arithmetic operation can be described as the operation in which we do the addition of numbers, subtraction, multiplication, and division

d = √[(2)² + (-5)²]

simplifying the above equation, we get

d = √(4 + 25)

d = √29 units

Therefore, the distance between each pair of points (-1,4) and (1,-1) exists √29 units after utilizing the distance formula.

The complete question is:

Find the distance between each pair of points (-1,4) and (1,-1)

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Answer:

b

Step-by-step explanation:

The graph was reflected over the y-axis.

If the range of the data set is 19. Then the maximum value of the set will be 28.

Statistics is the study of collection, analysis, interpretation, and presentation of data or discipline to collect and summarise the data.

The range of the data is the difference between the maximum number to the minimum number. Then the formula is written as,

Range = Maximum value - Minimum value

The range of a set of numbers is 19. And the minimum value is 9.

Then the maximum value of the set is calculated as,

Range = Maximum value - Minimum value

19 = Maximum value - 9

Maximum value = 19 + 9

Maximum value 28

If the range of the data set is 19. Then the maximum value of the set will be 28.

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The president draw 15 lines on map.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

here, it is given that :

there are 6 cities

No three of the cities are collinear that is are not in a straight line.

Now, to find the lines did the president draw use the formulae :

n(n-1)/2

where, n = number of cities

lines did the president draw = 6 x 5/ 2

                                                = 15

Therefore, The president draw 15 lines on map.

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Hence the probability that the spinner will land on something less than 0.75 is 37/50

As we know in between 0 and 1 the decimal numbers are ( 0.1, 0.2, 0.3, 0.4 _ _ _ _ _ 0.95, 0.96, 0.97, 0.98, 0.99, 1.00)

So,

To find the probability = favorable outcomes/ total numbers of outcomes

Favorable outcomes =  0.74 / 1.00

solve the decimal numbers in the simplified form

The probability that the spinner will land on something less than the decimal number 0.75 is 37/50.

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The number of bars of the same color could be used to show the number of hours that Dan studies hence he studied for 2/3 hours in four days.

The term multiplication refers to the number of times that a number is added to itself. For instance, if I add four three times, I could shorten the expression as four multiplied by three.

If we look at the diagram, we can see that in each tile, there are always two bars of the same color out the whole three bars. The bars that are of the same color shows the number of hours that Dan studied.

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Answer:

12

Step-by-step explanation:

Answer:

x = 19

Step-by-step explanation:

Alternate Exterior Angles Theorem

When a transversal line intersects two parallel lines, the resulting alternate exterior angles are congruent.

Therefore:

⇒ 8x + 11 = 5x + 68

⇒ 8x + 11 - 5x = 5x + 68 - 5x

⇒ 3x + 11 = 68

⇒ 3x + 11 - 11 = 68 - 11

⇒ 3x = 57

⇒ 3x ÷ 3 = 57 ÷ 3

⇒ x = 19

Answer:

a) 225 meters

b) -162°C

Step-by-step explanation:

a) 5 meters per second for 45 seconds. 5*45 = 225 meters

b) cooled by 18°C per hour over a 9 hour period. -18*9 = -162°C

Answer:

a) 225 meters.

B) -2 °

Step-by-step explanation:

a If it is moving 5 meters per second, then in one second it moves 5 meters, in 2 seconds it move 10 meters, in 3 seconds it move 15 minters.

So to find how much it moved in 454 seconds we would multiply 45 x 5 = 225

B)  In 9 hours it cooled 18 degrees 18/9 = 2.  This means that is cooled 2 degrees per hour.

No, i don't think she is correct as she didn't rounded-off correctly while measuring the diameter of bacteria.

Rounding off is a type of estimation. Estimation is used in everyday life and also in subjects like Mathematics and Physics. Many physical quantities like the amount of money, distance covered, length measured, etc are estimated by rounding off the actual number to the nearest possible whole number.
According to the picture it shows the diameter of the bacteria is 0.00000025691m

So , [tex]2.5691 * 10^-^7m[/tex]  is rounded off and will be equal to [tex]3*10^-^7m\\[/tex]

As, The digit right to 2 is 5 and which already passed halfway up

So, the number 2 will be rounded off to 3 as it being the nearest digit.

Therefore, Bonnie is wrong as she did mistake while rounding - off measurments.

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The Divisor is 1.5 , the Dividend is 4.5 and the quotient is 3.

As per the question we need to create a division problem where both the divisor and the dividend are decimals and the quotient must be a whole number greater than 1.

So, Let us suppose divisor as 1.5 . Now the dividend must be a decimal number which is greater than 1.5, let's say 5.5.

Now on dividing 5.5 by 1.5,

Divisor = 1.5

Dividend = 4.5

(Dividend/Divisor) = ( 4.5 / 1.5 ) = 3

Quotient = 3

On dividing dividend by divisor the quotient is 3 which is a whole number greater than 1.

So, we can conclude that the Divisor is 1.5 , the Dividend is 4.5 and the quotient is 3.

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Answer:

40

Step-by-step explanation:

140 + x  = 3*(100-x)

140 + x = 300 - 3x

x + 3x = 300 - 140

4x = 160.

x = 40.

In mathematics, a line's slope, also known as its gradient, is numerical representation of line's steepness and direction. The equation will be [tex]y= \frac{-1}{3}x +5[/tex].

In mathematics, a line's slope, also known as its gradient, is numerical representation of  line's steepness and direction. The letter m is the frequently used to represent slope; the reason for this usage is unclear, although it can be found in O'Brien's (1844) and Todhunter's (1888) formulations of the equation for the straight line as "[tex]y = mx + b[/tex]" and "[tex]y = mx + c[/tex]," respectively.

The ratio of "vertical change" to "horizontal change" between the (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which produces the same number for every two distinct points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or design.

Let, x= -3, x1= -2, y= 5, y1= 2

Then,

slope= [tex]\frac{x-x1}{y-y1} = \frac{-3-(-2)}{5-2} =\frac{-1}{3}[/tex]

now,

y= mx+c

y= [tex]\frac{-1}{3}[/tex]x+ 5

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Integers are 3, 4 and 5.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common mathematical symbol for the set of integers. An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043.

Given Data

Let the three consecutive integers are :

x, x+1 and x+2

According to question
3(x+1) = 4 - 2(x+x+2)

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

3x + 3 = 4 - 4x - 4

3 = 4x-3x

x= 3

Integers are 3, 4 and 5.

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We are asked to find the values needed for the length CB

The coordinates of points C and B are given as

C(-a, -5b)

Recall that the distance formula is given by

For the given case,

Let us substitute these coordinates into the above distance formula

Therefore, the required values are

In linear equations, x = 9.5 Paula use the division property of equality.

What is a formula for linear equations?

The Division Property of Equality states that when both sides of an equation are divided by the same nonzero number, both sides remain equal.

That is, if a, b, and c are real numbers such that a = b and c ≠0, then  

a/b = c/d

The equation was -6x = 57

To move to step 5, Paula had to divide both sides by the co-efficient of x (-6) in order to get the value of x. See below

    -6x = 57      ( Divide both sides by -6)

-6x/6  = 57/-6

x = 9.5

Hence, we can conclude that the division property of equality.

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The complete question is -

Paula used these steps to solve an equation:

Step 1: -4(7 + 8) - 21 = 25

Step 2: -4r – 32 - 2x = 25

Step 3: -61 – 32 = 25

Step 4: -6x = 57

Step 5: x = -95

Between which two steps did Paula use the division property of equality?

The value of x if R is the midpoint of QS is 31 units.

The midpoint is the middle point of a line segment.

It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.

The midpoint is halfway between the two end points.

Therefore, R is the midpoint of QS

Hence,

QS = QR + RS

QR = 5x - 15

QS = 100

Therefore, QR and RS are congruent because R is the midpoint of QS

QR = RS

Hence,

100 = 5x - 15 + 5x - 15

100 = 10x - 30

100 + 30 = 10x

130 = 10x

divide both sides by 10

x = 130 / 10

x = 13

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The perimeter and area of each of the composite figure is:

a. Area: 138.6 mm²; Perimeter = 50.27 mm.

b. Area: 120.5 cm²; Perimeter = 42.7 cm

c. Area: 521.1 mm²; Perimeter: 95.8 mm

Area of a circle = πr²

Area of a triangle = 1/2(base)(height).

Area of a rectangle = (length)(width).

The perimeter of a composite figure = the sum of all lengths of the sides surrounding the composite figure.

a. The area of the composite figure = area of rectangle + area of two semicircles

Two semicircles = 1 circle

Area of the rectangle = (15)(5) = 75 mm²

Area of the two semicircles = πr² = π(4.5²) = 63.6 mm²

The area of the composite figure = 75 + 63.6 = 138.6 mm².

Perimeter = 5(2) + 4(3) + (perimeter of 1 circle)

Perimeter = 5(2) + 4(3) + (2πr)

Perimeter = 5(2) + 4(3) + (2π(4.5))

Perimeter = 50.27 mm.

b. Area = area of triangle + area of square + area of half circle

Area = 1/2(base)(height) + s² + 1/2(πr²)

Base = 5 cm

Height = 7 cm

s = √(7² + 5²) = 8.6 cm [Pythagorean theorem]

r = 8.6/2 = 4.3 cm

Area = 1/2(5)(7) + 8.6² + 1/2(π(4.3²))

Area = 120.5 cm²

Perimeter = 5 + 7 + 8.6 + 8.6 + (perimeter of half circle)

Perimeter = 5 + 7 + 8.6 + 8.6 + 1/2(2πr)

Perimeter = 5 + 7 + 8.6 + 8.6 + (2π(4.3))

Perimeter = 42.7 cm

c. Area = area of triangle + area of rectangle + area of half circle

Area = 1/2(base)(height) + (length)(width) + 1/2(πr²)

Base = 32 - 20 = 12 mm

Height = 14 mm

Length = 20 mm

Width = 14 mm

r = 1/2(20) = 10 mm

Area = 1/2(12)(14) + (20)(14) + 1/2(π(10²))

Area = 521.1 mm²

Perimeter = 14 + 32 + hypotenuse of the triangle + (perimeter of half circle)

Hypotenuse = √(12² + 14²) = 18.4 mm

Perimeter of half circle = 1/2(2πr) = 1/2(2π(10)) = 31.4

Perimeter of the composite figure = 14 + 32 + 18.4 + 31.4

Perimeter of the composite figure = 95.8 mm

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Answer - The constant proportionality constant of proportionality between the actual dimensions of the pavers and the model is 9. The proportionality constant for the area is 81.

Step-by-step explanation: To solve this problem, let's transform all quantities to the same units (inches)

The actual dimensions of the pavers are:

Then we divide the real dimensions between those of the model:

Width:

Long =

Then, the constant of proportionality between the actual dimensions of the pavers and the model is 9.

Actual length = model length * (9)

The "A" area of a paver is the product of its width multiplied by its length.

So:

(real width) * (real length) = ((9) Model width) * ((9) model length)

(real width) * (real length) =  * (Model width) * (model length)

(real area) = 81 * (Model area)

The proportionality constant for the area is 81.

Answer: 5 and the power is 2

the power used is 2

Step-by-step explanation:

Answer: y=12

Step-by-step explanation:

Distribute

Add 10 to both sides

Simplify.

Answer: y = 12

Step-by-step explanation:

2 ( [tex]y\\[/tex] - 5 ) = 14

2[tex]y\\[/tex] - 2 · 5 = 14

2[tex]y\\[/tex] - 10 = 14

(2[tex]y\\[/tex] - 10) + 10 = 14 + 10

2[tex]y\\[/tex] = 24

[tex]\frac{2y}{2} = \frac{24}{2}[/tex]

The values for the parabola are found as-

For the given question.

The total horizontal distance covered by water is 10 feet.

The maximum height attained by nozzle of water is 8 feet.

Thus, the vertex of parabola (h, k) = (5, 8)

The nozzle was 4 foot above the ground, a = 4.

The equation of parabola becomes;

y = a(x - h)² + k

y = 4(x - 5)² + 8

Thus, the equation of parabola becomes; y = 4(x - 5)² + 8.

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Answer: The correct answer is the Law of Large Numbers

Step-by-step explanation:

Imagine flipping a coin. There is a 50% likelihood that you would get tails. However, it doesn't happen all the time. If you flipped it just a few times, you could get all tails and have 100% tails.

However, if you experimented a lot of times (a large number), you almost certainly wouldn't get all tails. You would get close to 50%. That is the main point of the law.

The more trials you do, the more likely you will get close to the theoretical value.

___________________
900
___________________

Answer:

ray:

Part of a line, containing one endpoint and extending to infinity in one direction.

line segment

Two points on a line, and all the points between those two points.

Step-by-step explanation:

If water is leaking from the bottom of a conical cup that is 20 inches across and 20 inches deep.  The rate that the water level changes when the water is 8 inches deep is: 3 /32π.

dv/dt = rate of cup  loss water per minutes=0.5

r = radius when the water is 8 inches deep

Hence,

20/10  = 8/r

r = 4

Volume of conical cup

v= 1/3πr²h

dv/dt=1/3πr² dh/dt

0.5 = 1/3π × (4)² dh/dt

dh/dt =3 /32π

Therefore the rate is 3 /32π.

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Yes if there is a positive correlation existing between the paving of streets and the number of registered cars then paving more streets would result in the increase in the registered cars.

This is the term that is used to tell us that there is the presence of a correlation that would make the two variables that we are talking about to move in the same direction. That is when one increases, the other would have to increase as well.

Such that we would have the increase in the number of paved street to cause an increase in the number of registered cars in the place.

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The discriminant of the quadratic equation is 11.1.

The discriminant is the expression that we could use to deduce the kind of roots that a quadratic equation would have. Note that when we say the roots of the equation, we are talking about the solutions of the quadratic equation. We shall now try to obtain the discriminant of this equation as we can see below.

The discriminant is given as;

√b^2 - 4ac

Given;

3x^2 - 10x + 2 = 0

a = 3

b = -10

c = 2

We have;

√(-10)^2 - 4(-3) (2)

√100 + 24

11.1

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The required solution in scientific notation is 2 × 10¹ .

Scientific notation can be used to indicate values that are either too large or too little to be conveniently written in decimal form (typically would result in a long string of digits).

The given expression is (6.4 × 10³) ÷ (3.2 × 10²)

Simplifying we get :

(6.4 × 10³) ÷ (3.2 × 10²) = 20

This can be written in the scientific notation as : 2 × 10¹

Therefore the required solution is 2 × 10¹

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