what are the three rational numbers between -1 and 3​

The slope of the line m is -2 if the line passes through (4, -3) and (0, 5) the answer is -2.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

From the graph:

(4, -3) and (0, 5)

The slope of the line m = (5+3)/(-4)

The slope of the line m = -2

Thus,  the slope of the line m is -2 if the line passes through (4, -3) and (0, 5) the answer is -2.

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Answer:

Step-by-step explanation:

Gallons to liquid quarts

1 gallon = 4 quartes

0.75 gallon = 3 quarts

Answer:

aₙ = 6aₙ - 18

Step-by-step explanation:

a₃ = 0, a₄ = 6, a₅ = 12, a₆ = 18, a₇ = 24...

aₙ = 6aₙ - 18

a₃ = (6 × 3) - 18 = 0

a₄ = (6 × 4) - 18 = 6

a₅ = (6 × 5) - 18 = 12

a₆ = (6 × 6) - 18 = 18

a₇ = (6 × 7) - 18 = 24

I hope this helps!

The expression which is equivalent to; six to the negative power of two as given in the task content is; 1 / 36.

It follows from the task content that the expression which is equivalent to six to the negative power of two is to be determined.

Since the given word phrase can be expressed as; 6^-²; it follows from the laws of indices that we have;

= (1 / 6)²

= 1² / 6²

= 1/36.

Ultimately, the equivalent expression is; 1 / 36.

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Answer:27 cm squared

Step-by-step explanation: we take both numbers(3,4) and multiply them by the scale factor of 1.5 giving you 4.5 and 6, then you find the area of the new colorado by multiplying 4.5 and 6 giving you 27 centimeters squared.

Answer: yes

Step-by-step explanation:

adding 50 40 30 20 10 and 0 gets you 150 so 2nd place gets 40

Answer:

i think its B

Step-bi think iy-step explanation:

2+3+1+2+1= 9

3+1 = 4

4/9 simplified 2/3

By writing and solving a system of equations we will find that the number is 56

So we can write a two-digit number as:

a*10 + b

Where the two digits are a and b.

Here we must have:

a + b = 11

The reversed number is:

b*10 + a

Then we can write the equation:

b*10 + a - a*10 - b = 9

b*9 - a*9 = 9

Then we have a system of two equations:

a + b = 11

b*9 - a*9 = 9

We can divide both sides of the second equation by 9 to get:

b - a = 1

Now we can isolate b to get:

b = 1 + a

Now we can replace this in the other equation.

a + b = a + (1 + a) = 11

2a + 1 = 11

2a = 11 - 1  = 10

a = 10/2 = 5

Now we have the value of a, and we know that:

b = 1 + a = 1 + 5  = 6

Then the two-digit number is:

a*10 + b = 5*10 + 6 = 56

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Answer:

5500m..................

Answer:

0.00863

Step-by-step explanation:

move decimal to the left 3 times!

Answer:

-13 + 25 = 12

Step-by-step explanation:

You get 12 because 13 is a negative so subtract 25 from 13 and that turns 13 into 0 so 0 + 12 = 12

Sorry if my explanation didn't make sense.

The triangle PQR is an equilateral triangle

From the question, we have the following parameters that can be used in our computation:

PQ=QR.

m/P = (2x - 26) and m/R= (x+17)

When two sides of a triangle are congruent, then the triangle is an isosceles triangle

Using the above as a guide, we have the following:

2x - 26 = x + 17 --- base angles of an isosceles triangle

So, we have

x = 43

This gives

m/P = 2 * 43 - 26 = 60

m/R= 43 + 17 = 60

If two angles of a triangle measure 60 degrees, then the third angle is 60 degrees

This implies that the triangle is an equilateral triangle

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The measure of the angle Q is 46.4°

Recall that the sum of the angles of a triangle is equal to 180 degrees

We are told that

PQ = QR

Q = 100°

As PQ and QR are equal so,

By theorem angle opposite to equal sides are equal so,

We can say that angle P = angle R = X

Therefore by angle sum  property of the triangle,

angle P + angle Q + angle R = 180°

X +(2x - 26)+ (2x - 26) = 180°

This implies that 5x-52=180

Collecting like terms

5x=180+52

5X = 232°

X =46.4°

Therefore the measure of R = 40°

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The interest rate on loan is 5.25%.

What is principal amount?

The loan amount that the lender gives to the borrower is referred to as the primary amount. Additionally, it is the factor the lender uses to calculate interest.

What is simple interest?

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. The formula to calculate simple interest is  I=P.r.t

Given, Principal amount=$125,000, time=10years, Interest=$65,625.

Let r be the rate of interest, on applying simplest interest formula

                                               I=P.r.t

Where P=principal amount, r=rate, t=time.

I=125,000 x r x10

65,625=125,000 x r x10

r=\(\frac{65,625}{125,000(10)}\)

r=0.0525

r=5.25%

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is this a real question cause the awnser is fire

Answer:

a) 3x + ky = 8

ky = 8 - 3x

x – 2ky = 5

x - 2(8 - 3x) = 5

x - 16 + 6x = 5

7x = 21

x = 3 (shown)

b) x-2ky = 5

sub x = 3, y = 1/2

3-2k(1/2) = 5

-2k = 2

k = -1

The limit of f(x, y) as (x, y) approaches (0, 0) does not exist. The function f(x, y) is undefined at (0, 0) because the denominator contains |x| and |y| terms, which become zero as (x, y) approaches (0, 0). Therefore, the limit cannot be determined.

To evaluate the limit of f(x, y) as (x, y) approaches (0, 0), we need to analyze the behavior of the function as (x, y) gets arbitrarily close to (0, 0) from all directions.

First, let's consider approaching (0, 0) along the x-axis. When y = 0, the function becomes f(x, 0) = x^2 + 0 + 0/|x| + 0. This simplifies to f(x, 0) = x^2 + 0 + 0 + 0 = x^2. As x approaches 0, f(x, 0) approaches 0.

Next, let's approach (0, 0) along the y-axis. When x = 0, the function becomes f(0, y) = 0 + 0 + y^2/|0| + |y|. Since the denominator contains |0| = 0, the function becomes undefined along the y-axis.

Now, let's examine approaching (0, 0) diagonally, such as along the line y = x. Substituting y = x into the function, we get f(x, x) = x^2 + x^2 + x^2/|x| + |x| = 3x^2 + 2|x|. As x approaches 0, f(x, x) approaches 0.

However, even though f(x, x) approaches 0 along the line y = x, it does not guarantee that the limit exists. The limit requires f(x, y) to approach the same value regardless of the direction of approach.

To demonstrate that the limit does not exist, consider approaching (0, 0) along the line y = -x. Substituting y = -x into the function, we get f(x, -x) = x^2 - x^2 + x^2/|x| + |-x| = x^2 + x^2 + x^2/|x| + x. This simplifies to f(x, -x) = 3x^2 + 2x. As x approaches 0, f(x, -x) approaches 0.

Since f(x, x) approaches 0 along y = x, and f(x, -x) approaches 0 along y = -x, but the function f(x, y) is undefined along the y-axis, the limit of f(x, y) as (x, y) approaches (0, 0) does not exist.

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The event AC describes the scenario in which at least one tail occurs in the five coin flips.The probability of AC is 31/32.

(a) In words, the event AC describes the scenario in which at least one tail occurs in the five coin flips.

Event AC can also be written as {HTTTT, THTTT, TTHTT, TTTHT, TTTTH, HTTTH, HHTTT, THHTT, TTHHT, TTTHH, HTTHH, HHTTH, THHHT, TTHHH, HTHTT, HHTHT, THHTH, HTTHT, THTHT, HTTH, THTTH, TTHTH, TTHHT, THTHH, HTTHH, THHTH, HTHHT, HHTHH, THHH, TTHH, THTH, HTTH, HHTH, THHT}.

(b) The probability of AC can be calculated as follows:

There are two possible outcomes of each coin flip: heads or tails.

Since the coin is fair, both outcomes are equally likely.

Therefore, the probability of getting tails in one flip is 1/2, and the probability of getting heads in one flip is also 1/2.In order to find the probability of AC, we will use the complement rule:Prob(AC) = 1 - Prob(A)Prob(A) = 1/32Prob(AC) = 1 - 1/32Prob(AC) = 31/32

Therefore, the probability of AC is 31/32.

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The number of square units enclosed by the polygon is 18.

First, count the number of dots that are enclosed by the polygon (including those on the boundary). There are 14 such dots.Next, count the number of dots on the boundary of the polygon. There are 8 dots on the boundary.Each of the dots on the boundary corresponds to a line segment of the polygon.

So, the perimeter of the polygon is 8 units (the length of each of these line segments).Now, we can use Pick's theorem to find the area of the polygon. Pick's theorem states that A = i + b/2 - 1, where A is the area of the polygon, i is the number of dots inside the polygon, and b is the number of dots on the boundary of the polygon.

So, plugging in the values we have: A = 14 + (8/2) - 1 = 14 + 4 - 1 = 17

Therefore, the area of the polygon is 17 square units.However, we have to remember that the dots are spaced one unit apart, horizontally and vertically.

Therefore, each square that is enclosed by the polygon has an area of 1 square unit. We counted 17 such squares, so the total area enclosed by the polygon is 17 square units.

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The values of the variables, a, b, and c obtained from the equation of the circle and the coordinates of the point P are;

a) a = 2

b = -2

c = 4

The general equation of a circle is; (x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The coordinates of the radius of the circle

The specified equation of a circle is; x² + y² = 9

The coordinates of the center of the circle, is therefore, O = (0, 0)

a) The coordinates of the points P  and O indicates that the gradient of OP, obtained using the slope formula is; ((3·√3)/4 - 0)/(3/2 - 0) = ((3·√3)/4)/(3/2)

((3·√3)/4)/(3/2) = (√3)/2

The specified form of the gradient is; (√3)/a, therefore;

(√3)/a = (√3)/2

a = 2

The value of a is 2

b) The gradient of the tangent to a line that has a gradient of m is -1/m

The gradient of OP is; (√3)/2, therefore, the gradient of the tangent at P is -2/(√3)

The form of the gradient of the tangent at P is b/(√3), therefore;

-2/(√3) = b/(√3)

b = -2

The value of b is; -2

c) The coordinate of the point on the tangent, (0, (7·√3)/c) indicates

Slope of the tangent = -2/(√3)

((7·√3)/c - ((3·√3)/4))/(0 - (3/2)) = -2/(√3)

((7·√3)/c - ((3·√3)/4)) = (3/2) × 2/(√3) = √3

(7·√3)/c = √3 + ((3·√3)/4) = 7·√3/4

Therefore; c = 4

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To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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Answer:

16.2

Step-by-step explanation:

Add all of them p and divide by the total values. SO there are 9 values, you first add the all up and divide by 9. Easy :)

Answer:

Step-by-step explanation:

(-7 + 4)/2= -3/2

(4 + 20)/2= 24/2= 12

(-3/2, 12) the midpoint

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

\(4y - 12 + 6x + 4y = \)

\(6x + 4y + 4y - 12 = \)

\(6x + 8y - 12\)

If u wanna in factored form :

\(2(3x + 4y - 6)\)

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Answer:

37/18 pie in total, for individual see below

Step-by-step explanation:

kyle has 8/9 apple pie left

bobby has 1/6 of peach pie left

joanie has 2/3 of blueberry pie left

evie has 1/3 of cherry pie left

so in total: 8/9+1/6+2/3+1/3=19/18+1=37/18