For the point P(13,
14) and Q(18, 9), find the distance
d(P,Q) and the coordinates of the midpoint M of the
segment PQ

Answer:

12

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Just substitute -3 in for a and 2 in for b

[tex]a^2 + 6b\\-3^2 + 6(2)\\9 + 6(2)\\9 + 12\\21[/tex]

When you square a negative number, the answer is positive. Good luck, and have a great day!

Also, Jesus loves you!!!!

Answer:

x/7+12

Step-by-step explanation:

One seventh refers to 1/7.

Since we do not know what "a number" is it, it is written as "x."

Whenever you see the word "increased" think addition.

So in this case,

x / 7 + 12

Answer: 848000

Step-by-step explanation:

(2 x 10³) x (4 x 106)

⇒2000 * 424
⇒ 848000

7.14 containers ≈7 containers are required to fill gallons containers equally for 25 gallons of gas

Given that Tom has 25 gallons of gas and needs to fill it equally in 3[tex]\frac{1}{2}[/tex]  gallons containers and asked how many gallons containers are required to fill equally.

25 gallons gas are required too put in 3[tex]\frac{1}{2}[/tex] gallons containers.

As a result, Divide 25 with 3[tex]\frac{1}{2}[/tex]  to get how many containers are required to fill equality.

⇒[tex]\frac{25}{3\frac{1}{2} }[/tex]

⇒[tex]\frac{50}{7}[/tex]

⇒7.14 gallons containers ≈7 gallons containers

Therefore,7.14 gallons containers ≈7 gallons containers are required to fill gallons containers equally for 25 gallons of gas

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The values of the piecewise function is g(1) = 3, g(2) = 1 / 2, g(3) = 1 / 4.

Piecewise functions are functions consisting in two or more expression constrained by intervals. In this case, we find a piecewise function formed by three equations. In this exercise we need to evaluate the function, whose expression depends on the x-value to be used. There are three values to be evaluated:

x = 1

g(1) = (1 + 1)² - 1

g(1) = 2² - 1

g(1) = 4 - 1

g(1) = 3

x = 2

g(2) = - (1 / 4) · 2 + 1

g(2) = - (1 / 2) + 1

g(2) = 1 / 2

x = 3

g(3) = - (1 / 4) · (3) + 1

g(3) = - (3 / 4) + 1

g(3) = 1 / 4

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The measure of the each angle is a 45° and 135°.

According to the statement

We have to find that the measure of the each angle.

So, For this purpose, we know that the

A figure which is formed by two rays or lines that shares a common endpoint is called an angle.

From the given information:

Two angles a form a linear pair. The measure of one angle is 1/3 the measure of the other angle.

Then

Since the two angles form a linear pair, the sum of their angles is equal to 180°. The condition given in the problem is that one angle is one-third of the other angle, or simply speaking, one angle is three times more than the other angle. We find the values of the angles by dividing the sum of the angles by 4 and assigning 3 and 1 times the dividend.

180°/4 = 45°

By obtaining the dividend, we obtain the values of the angles to be 45°

Then

the other angle is

Other angle = 180 -45

Other angle = 135.

So, The measure of the each angle is a 45° and 135°.

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Answer: $52 is your new balance

Step-by-step explanation: -12+60=52

A  = p +0.2p

We don't know the value of P, so it stays unknown.

The r is the interest rate as a decimal. we know that r = 0.04 because we're told the interest rate is 4%. Note that 4% = 4/100 = 0.04

The time in years is t = 5

So this means...

A = P + P*r*t

A = P + P*0.04*t ... replace r with 0.04

A = P + P*0.04*5 ... replace t with 5

A = P + P*0.2 ... multiply

A = P + 0.2*P ... swap term

A  = p +0.2p

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Answer: 0

Step-by-step explanation:

-2+-1 = -3

-3+0 = -3

-3+1 = -2

-2+2 = 0

Integer addition is the addition of integers with the same signs, whereas integer subtraction is the addition of integers with the opposite signs.

Are there any consistent rules for adding and subtracting integers?

What in math is an integer?

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The mathematical expression of the statement is x - 15 <= 5

The statement is given as:

Hourly wage of $15 differs from the average by less than or equal to $5

Let the average hourly wage be x

So, we have:

Hourly wage of $15 differs from the average = x - 15

less than or equal to $5 => <=5

So, the expression is

x - 15 <= 5

Hence, the mathematical expression of the statement is x - 15 <= 5

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The height from which any two objects is thrown affects their time of motion, the greater the height, the more time the objects spend in air and vice versa.

The time of motion of an object is the time taken for an object to travel from point of projection to the projection plane or it can be said as the time a projected object spent in air.

The time taken for an object dropped from a certain height is calculated as follows;

h = vt + ¹/₂gt²

where;

when the object is dropped from rest, v = 0

h =  ¹/₂gt²

t = √(2h/g)

Thus, the height from which any two objects is thrown affects their time of motion, the greater the height, the more time the objects spend in air and vice versa.

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Answer's:

27. vertex: (-4, -5) and x-intercept: (√5 - 4, 0) and (-√5 - 4, 0)

28. vertex: (-5, -11) and x-intercept: (√11 - 5, 0) and (-√11 - 5, 0)

29. vertex: (1, 16) and x-intercept: (-3, 0) and (5, 0)

To find vertex, the quadratic function should be in f(x) = a(x - h)² + k form.

where:

27.

g(x) = x² + 8x + 11

completing square:

g(x) = (x² + 8x) + 11

g(x) = (x + 4)² + 11 - (4)²

g(x) = (x + 4)² - 5

g(x) = (x - (-4))² - 5

To find x-intercept: set y = 0

[tex]\sf (x + 4)^2 - 5 = 0[/tex]

[tex]\sf (x + 4)^2 = 5[/tex]

[tex]\sf x + 4 = \pm \sqrt{5}[/tex]

[tex]\sf x= \sqrt{5}-4, \ - \sqrt{5}-4[/tex]

Hence, the vertex is (-4, -5) and x intercepts (√5 - 4, 0) and (-√5 - 4, 0).

28.

f(x) = x² + 10x + 14

completing square:

f(x) = (x² + 10x) + 14

f(x) = (x + 5)² + 14 - (5)²

f(x) = (x + 5)² - 11

Find x intercept, so y = 0:

[tex]\sf (x + 5)^2 - 11 = 0[/tex]

[tex]\sf (x + 5)^2 = 11[/tex]

[tex]\sf x + 5 = \pm\sqrt{11}[/tex]

[tex]\sf x = \sqrt{11} -5, \ -\sqrt{11} -5[/tex]

Hence, the vertex is (-5, -11) and x intercepts (√11 - 5, 0) and (-√11 - 5, 0).

29.

f(x) = -(x² - 2x - 15)

f(x) = -((x² - 2x)) + 15

f(x) = -(x - 1)² + 15 + (-1)²

f(x) = -(x - 1)² + 16

Find the x-intercept's:

[tex]\sf -(x - 1)^2 + 16 = 0[/tex]

[tex]\sf -(x - 1)^2 = -16[/tex]

[tex]\sf (x - 1)^2 = 16[/tex]

[tex]\sf x - 1 = \pm\sqrt{16}[/tex]

[tex]\sf x - 1 = \pm4[/tex]

[tex]\sf x = -3, \ 5[/tex]

Hence, the vertex is (1, 16) and x intercepts (-3, 0) and (5, 0).

Answer:

[tex]\textsf{27.} \quad \textsf{Vertex}:(-4,-5) \quad \textsf{$x$-intercepts}: x=-4+\sqrt{5}, \:\:x=-4-\sqrt{5}[/tex]

[tex]\textsf{28.} \quad \textsf{Vertex}:(-5,-11) \quad \textsf{$x$-intercepts}: x = -5+\sqrt{11}, \:\:x=-5-\sqrt{11}[/tex]

[tex]\textsf{29.} \quad \textsf{Vertex}:(1,16) \quad \textsf{$x$-intercepts}: x = 5, \:\:x=-3[/tex]

Step-by-step explanation:

Vertex form of a quadratic function:

[tex]\boxed{y=a(x-h)^2+k}[/tex]

where:

Given function:

[tex]g(x)=x^2+8x+11[/tex]

Change to vertex form by completing the square.

Add and subtract the square of half the coefficient of x:

[tex]\implies g(x)=x^2+8x+11 +\left(\dfrac{8}{2}\right)^2-\left(\dfrac{8}{2}\right)^2[/tex]

[tex]\implies g(x)=x^2+8x+11 +16-16[/tex]

[tex]\implies g(x)=x^2+8x+16+11-16[/tex]

[tex]\implies g(x)=x^2+8x+16-5[/tex]

Factor the perfect trinomial:

[tex]\implies g(x)=(x+4)^2-5[/tex]

Therefore, the vertex is (-4, -5).

To find the x-intercepts, set the function to zero and solve for x:

[tex]\begin{aligned}g(x) & = 0\\\implies (x+4)^2 -5 & = 0\\(x+4)^2 & = 5\\\sqrt{(x+4)^2} & = \sqrt{5}\\x+4&=\pm\sqrt{5}\\x+4-4&=-4\pm\sqrt{5}\\x&=-4\pm\sqrt{5}\end{aligned}[/tex]

Therefore, the x-intercepts are:

[tex]x = -4+\sqrt{5}, \quad x = -4-\sqrt{5}[/tex]

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

Given function:

[tex]f(x)=x^2+10x+14[/tex]

Change to vertex form by completing the square.

Add and subtract the square of half the coefficient of x:

[tex]\implies f(x)=x^2+10x+14+\left(\dfrac{10}{2}\right)^2-\left(\dfrac{10}{2}\right)^2[/tex]

[tex]\implies f(x)=x^2+10x+14+25-25[/tex]

[tex]\implies f(x)=x^2+10x+25+14-25[/tex]

[tex]\implies f(x)=x^2+10x+25-11[/tex]

Factor the perfect trinomial:

[tex]\implies f(x)=(x+5)^2-11[/tex]

Therefore, the vertex is (-5, -11).

To find the x-intercepts, set the function to zero and solve for x:

[tex]\begin{aligned}f(x) & = 0\\\implies (x+5)^2 -11 & = 0\\(x+5)^2 & = 11\\\sqrt{(x+5)^2} & = \sqrt{11}\\x+5&=\pm\sqrt{11}\\x+5-5&=-5\pm\sqrt{11}\\x&=-5\pm\sqrt{11}\end{aligned}[/tex]

Therefore, the x-intercepts are:

[tex]x = -5+\sqrt{11}, \quad x = -5-\sqrt{11}[/tex]

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

Given function:

[tex]f(x)=-(x^2-2x-15)[/tex]

Change to vertex form by completing the square.

Add and subtract the square of half the coefficient of x:

[tex]f(x)=-\left(x^2-2x-15+\left(\dfrac{-2}{2}\right)^2-\left(\dfrac{-2}{2}\right)^2\right)[/tex]

[tex]f(x)=-\left(x^2-2x-15+1-1\right)[/tex]

[tex]f(x)=-\left(x^2-2x+1-15-1\right)[/tex]

[tex]f(x)=-\left(x^2-2x+1-16\right)[/tex]

Factor the perfect trinomial:

[tex]f(x)=-\left((x-1)^2-16\right)[/tex]

Simplify:

[tex]f(x)=-(x-1)^2+16[/tex]

Therefore, the vertex is (1, 16).

To find the x-intercepts, set the function to zero and solve for x:

[tex]\begin{aligned}f(x) & = 0\\\implies -(x-1)^2 +16 & = 0\\(x-1)^2 -16 & = 0\\(x-1)^2 & = 16\\\sqrt{(x-1)^2} & = \sqrt{16}\\x-1&=\pm4\\x-1+1&=1\pm4\\x&=5,-3\end{aligned}[/tex]

Therefore, the x-intercepts are:

[tex]x = 5, \quad x=-3[/tex]

The patient should take three-tenths of a tablet every 4 hours and the infusion rate is 0.13 mL per 12 hours.

Given that, a doctor administers a drug to a ​34-kg ​patient, using a dosage formula of ​55mg/kg/day.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of tablets should a 34​-kg patient takes every four​ hours to be x.

Now, 55 × 34 = 1870 mg/day

For every four hours:

1870 × 1 /24 × 4 = 311.666

≈312 mg per 4 hours

So, x=312/4 × 1/300 = 78 × 0.0033

=0.26 tablet

Liquid suspension is for every 12 hours:

So, 312/12 × 1/200 = 26 × 0.005 = 0.13 mL

Hence, the patient should take three-tenths of a tablet every 4 hours and the infusion rate is 0.13 mL per 12 hours.

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Answer:

11

Step-by-step explanation:

2x-3=19

2x=22

x=11

Answer is  f(x)= [tex]\frac{x^{2}+ 2x - 8 }{x - 5}[/tex]

vertical asymptote, the denominator must be contained (x−5)

and for zeros the numerator must be contained (x−2)

then we get,

So far f(x)= f(x)= [tex]\frac{ (x - 2)}{x - 5}[/tex]

​

For slant asymptote, quotient of numerator divided by denominator must be (x+4)

Therefore:

f(x)= [tex]\frac{(x + 4) (x - 2)}{x - 5}[/tex]

after solving this equation we get,

So f(x)= [tex]\frac{x^{2}+ 2x - 8 }{x - 5}[/tex]

​A vertical asymptote is a vertical line that guides the graph of the function but is not part of it. It can never be crossed by the graph because it occurs at the x-value that is not in the domain of the function. A function may have more than one vertical asymptote.

In Mathematics, a slant asymptote, also known as an oblique asymptote, occurs when the degree of the numerator polynomial is greater than the degree of the denominator polynomial. The slant asymptote gives the linear function which is neither parallel to x-axis nor parallel to the y-axis.

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Answer:

1. y= = 0.5 (2, 0.5)

2. y= 0 (4, 0)

3. y= -0.5 (6, 0.5)

Step-by-step explanation:

To get your answer, you would want to plug in the x-coordinates into the equation and solve for y.

=================================================

Explanation:

Point B is at the location (x, y)

The x coordinates of A and B are 3 and x respectively. Add them up, divide in half, and set the result equal to the x coordinate of M which is 5

(3+x)/2 = 5

3+x = 2*5

3+x = 10

x = 10-3

x = 7 which is the x coordinate of point B

Repeat this same idea for the y coordinates.

(8+y)/2 = 6

8+y = 2*6

8+y = 12

y = 12-8

y = 4

Therefore, point B is located at (x,y) = (7, 4)

Visual verification is shown below. You could also use the midpoint formula on segment AB to find that M = (5,6) is the midpoint.

The expression for the perimeter of the rectangle whose  length of a rectangle is nine more than twice the width is 6x + 18.

Let the width of the rectangle be x units.

According to the given question.

The length of a rectangle is nine more than twice the width.

⇒ Length of the rectangle = 9 + 2x

As we know that, the perimeter formula for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width.

Therefore, the expression for the perimeter of the rectangle whose  length of a rectangle is nine more than twice the width

= 2[x + (9 + 2x)]

= 2[ x + 2x + 9]

= 2[ 3x + 9]

= 6x + 18

Hence, the expression for the perimeter of the rectangle whose  length of a rectangle is nine more than twice the width is 6x + 18.

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We need to know about scientific notation to solve the problem. Convert the numbers to same power of ten for addition or subtraction.

When a number is too big or too small we write it with an exponent raised to 10, this makes the number easy to read and understand. Writing a number like this is called scientific notation. Inorder to add or subtract two numbers written in scientific notation we need to first convert the powers of 10 to the same power, so that we can add the decimal numbers with the power of 10 being the common factor. We can convert the power by either multiplying the number to powers of 10 or by dividing it by powers of 10.

Therefore for addition or subtraction of two numbers written in scientific notation we need to have same powers of 10.

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Answer:

no, in a function x can not repeat so points (2,-1) and (2,-2) makes it wrong bc 2 is your x

The function f(x) = |x|, after shifting it down by 4 units and right by 3 units can be written as -

(y - 4) - |x - 3| = 0

The modulus function can be written as follows -

|x| =  x  [for x ≥ 0]  

|x| = - x [for x < 0]

Given that a function f(x) = |x| which is shifted down by 4 units and right by 3 units. Therefore, we can write -

y = f(x) = |x|

Change in y - coordinate = y + 4.

Change in x - coordinate = x - 3.

We will plot the graph of h(x) after the doing the given changes in the coordinates.

Now, we have -

y = |x|

y - |x| = 0

Change in y - coordinate can be written as -

(y + 4) - |x| = 0

Change in x - coordinate can be written as -

(y - 4) - |x - 3| = 0

Now, the graph of both f(x) and and h(x) is attached at the end.

Therefore, the function f(x) = |x|, after shifting it down by 4 units and right by 3 units can be written as -

(y - 4) - |x - 3| = 0

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If the length of one side of Rory's garden is [tex]5^{2}[/tex] then the area of the garden will be equal to 625 [tex]feet^{2}[/tex].

Given that Rory' garden is square in shape and the length of one side of the garden is [tex]5^{2}[/tex] feet.

We are required to find the area of the garden.

Area is basically the quantity that expresses the extent of a region on the plane or on a curved surface.

Area of square=Side*Side

Area=[tex]5^{2}[/tex]*[tex]5^{2}[/tex]

=[tex]5^{4}[/tex]

=625 [tex]feet^{2}[/tex]

Hence if the length of one side of Rory's garden is [tex]5^{2}[/tex] then the area of the garden will be equal to 625 [tex]feet^{2}[/tex].

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Answer:

The answer to your problem is -1/3

Step-by-step explanation:

Let me know if you need the steps. Thanks

Answer:

1.37037037 or 1 10/27

Step-by-step explanation:

What's there to explain?

27/27 + 10/27 = 1 10/27

The age of the boy is 14 years.

Given average age of 8 men, 7 women and 1 boy is 45 years.

Averages are used to condense a vast number of data points into a single value. It is a visual depiction of all the data set's available numbers. By adding up all the data values and dividing them by the total number of data points, the average is calculated.

age of 8 men is 48 years.

age of 7 women is 46 years.

age of the boy is = ?

= (45 ×16 ₋ 48 × 8 ₋ 7 × 46)

= (720 ₋ 324 ₋ 322)

= 14 years.

Hence the age of the boy is 14 years.

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Answer:

1,803.268

Step-by-step explanation:

so thousandths place is three number after the decimal just see the fourth number after the decimal and if it 5 or greater round the (in this case) 8 but since the fourth number was 4 it stays the same but only three numbers

Cube: Rubrics Cube or Dice

Rectangular Prism: Notebook or Gift box

Sphere: Globe or Beach ball

Cone: Carrot or Cone

Cylinder: Barrel or Bucket

Volume Formulas:

Cube = a^3

Rectangular Prism = L x B x H

Sphere = 4/3 pi(r^2)

Cone = 1/3 pi(r^2)h

Cylinder = pi(r^2)h

(pi = 3.14)

Hope this helps.