Triangle ABC is to be dilated through point P with a scale factor of 3. How many units away from point A along ray PA will A’ be located?

if we take 72 as the 100%, what is 27 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 72&100\\ 27&x \end{array}\implies \cfrac{72}{27}=\cfrac{100}{x}\implies \cfrac{8}{3}=\cfrac{100}{x}\implies 8x=300 \\\\\\ x=\cfrac{300}{8}\implies x=\cfrac{75}{2}\implies x=37.5[/tex]

To calculate the percentage, divide the part (27) by the whole (72) and multiply by 100, resulting in 37.5%.

Percentage is a way of expressing a portion or fraction of a whole as a value out of 100. It is commonly used to compare relative quantities, represents proportions, or express the relationship between a part and a whole.

The term "percent" comes from the Latin phrase "per centum," which means "per hundred." It signifies that percentages are calculated on a scale of 100.

In practical terms, a percentage represents a fraction of a whole, where the whole is equal to 100%. It allows us to easily compare different quantities and understand their relative sizes or proportions.

To calculate a percentage, you typically divide the part (the specific quantity you want to express as a percentage) by the whole (the total or reference quantity) and then multiply by 100 to obtain the value as a percentage.

To calculate the percentage, you can divide the given number (27) by the total number (72) and then multiply the result by 100. So, to find out what percent 27 is of 72:

(27 ÷ 72) × 100 ≈ 37.5%

Therefore, 27 is approximately 37.5% of 72.

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Answer:

x = 8

Step-by-step explanation:

Step 1: Create an equation

(2+4+x+6) ÷ 4 = 5

Step 2: Solve the equation

(12+x) ÷ 4 = 5

(12+x) = 20

x = 8

The value of the unknown number x is 8.

The given numbers include:

The sum of the given numbers is calculated as follows;

2 + 4 + x + 6 = 12 + x

The mean of the given 4 numbers is calculated as follows;

[tex]\frac{12 + x}{4} = 5\\\\12 + x = 20\\\\x = 20 -12\\\\x = 8[/tex]

Thus, the value of the unknown number x is 8.

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The equation represented by the tape diagram is: 2x + 3 = 5x

This can be solved by subtracting 2x from both sides: 3 = 3x

Dividing both sides by 3 gives the solution: x = 1

Therefore, the equation to solve is: 2x + 3 = 5x

The tape diagram represents the following equation:

2x + 3 = 5x

This can be solved by subtracting 2x from both sides:

2x + 3 - 2x = 5x - 2x

3 = 3x

Dividing both sides by 3 gives the solution:

x = 3 / 3

x = 1

Therefore, the equation to solve is:

2x + 3 = 5x

The solution is:

x = 1

The  equation to solve m is  2/3 = 1/4 + m.

The equation you wrote, 2/3 = 1/4 + m, is indeed correct based on the tape diagram you described.

Here's how to solve it:

Combine fractions:

Get both fractions on the same side of the equation. Subtract 1/4 from both sides:

m = 2/3 - 1/4

Find a common denominator:

The smallest common denominator for 3 and 4 is 12.

Multiply both sides by 12:

12m = 8 - 3

Solve for m: Combine like terms and simplify:

12m = 5

m = 5/12

Therefore, the value of m is 5/12.

Answer:

$11,480

Step-by-step explanation:

1,400 x 0.9 = 1,260

1,260 x 8 = 10,080

1,400 + 10,080 = 11,480

Answer:

400cm2

Step-by-step explanation:

20 • 20 = 400

The answer is 400 cm squared.

Hope this helps!

If it does then I would appreciate it if you could make me brainliest.

A 9

B 10

C 6

Hope this helps;$

Answer:

a. 3:24 = 9:72.

b.  10:18 = 5:9.

c. 6:6 = 36:36.

Step-by-step explanation:

a.  72 / 24 = 3 so we multiply 3 by 3 to give 9.

b.  18/9 = 2  so we multiply 5 by 2 = 10.

c.  The answer is 6.

Answer:

66°

Step-by-step explanation:

Since segments MN and MP are tangent to the circle, then

[tex]\angle MPO=\angle MNO=90^{\circ}[/tex]

The sum of the measures of all interior angles of the quadrilateral is equal to 360°, so

[tex]\angle NOP+\angle MPO+\angle MNO+\angle NMP=360^{\circ}\\ \\114^{\circ}+90^{\circ}+90^{\circ}+x^{\circ}=360^{\circ}\\ \\x^{\circ}=360^{\circ}-114^{\circ}-90^{\circ}-90^{\circ}\\ \\x^{\circ}=66^{\circ}[/tex]

Answer:

The value of x = 66°

Step-by-step explanation:

From the figure we can see that,

PM and MN are the tangent from the point M to the circle with center O

m<PON = 114°

To find the value of x

From the figure we can write,

m<PON + m<PMN = 180°

114 + x = 180

x = 180 - 114 = 66°

Therefore the value of x = 66°

ANSWER

The missing term is 24

EXPLANATION

The given arithmetic sequence is 9,14,19,_29,34

We can observe that:

[tex]14 = 9 + 5[/tex]

[tex]19 = 14 + 5[/tex]

Let the missing term be x, then

[tex]x = 19 + 5[/tex]

[tex]x = 24[/tex]

Therefore the missing term is 24.

Answer:

a =4   b=8 c=-8

y-value of vertex =

ah^2 + bh + c

where h = -b/2a

h= -8/8 =-1

y-value of vertex =

4(-1)^2 + 8*-1 -8

4 -8 -8

y value of vertex = -12

Step-by-step explanation:

Answer: 230ft

Step-by-step explanation:

The perimeter is just all 4 sides added together, so,

75+75+40+40=230

The total distance around the wall is 230ft.

since AC=1/2AB=6 THEREFORE C is the midpoint ofAB

Step-by-step explanation:

Given : AB = 12 , AC = 6

To prove = AB = 2 × AC (C is mid point of AB)

Solution:

AB = 12...[1]

AC = 6.....[2]

[1] ÷ [2]

[tex]\frac{AB}{AC}=\frac{12}{6}[/tex]

[tex]\frac{AB}{AC}=\frac{2}{1}[/tex]

[tex]AB=2\times AC[/tex] (hence, proved)

Answer:

8y+12

Step-by-step explanation:

Explanation:

1. The set of points 5 cm from the nearest point on a circle of radius 2 cm will be a circle with a radius 5 cm larger: a circle with a radius of 7 cm.

__

2. The set of points 6 in from the nearest point on a line will be a cylindrical shell 12 inches in diameter centered on the line.

If AB is a line segment, then the shell will have hollow hemispherical ends of radius 6 inches about the end points.

700-175=525. 525/35=15

Answer:

The distance between points P1 = (4,2) and P2=(8,5)  is 5.

Step-by-step explanation:

Let P1 = (4,2) and P2=(8,5)

The distance between two points can be found using formula:

[tex]d(P,Q), \sqrt{(x_{2}-x_{1})^2+ (y_{2}-y_{1})^2}[/tex]

where x₁ = 4 , x₂=8, y₁= 2 and y₂ = 5

Putting values in the formula

[tex]=\sqrt{(8-4)^2+(5-2)^2} \\=\sqrt{(4)^2+(3)^2} \\=\sqrt{16+9} \\=\sqrt{25} \\=5[/tex]

So, the distance between points P1 = (4,2) and P2=(8,5)  is 5.

Final answer:

The distance between the points (4,2) and (8,5) can be found using the Pythagorean Theorem. After calculating the squares of the differences in the x and y coordinates and adding them, the square root of the sum gives a distance of 5 units.

Explanation:

The distance between two points in a two-dimensional plane can be calculated using the Pythagorean Theorem. The coordinates of the points provided are (4, 2) and (8, 5). To find the distance, we calculate the difference in the x-coordinates and the difference in the y-coordinates, and then square both values before adding them together. This gives us the distance squared.

The formula is as follows:

d² = (x2 - x1)² + (y2 - y1)²

In this scenario:

d² = (8 - 4)² + (5 - 2)²

d² = (4)² + (3)²

d² = 16 + 9

d² = 25

Finally, we take the square root of the distance squared to get the distance:

d = √25

d = 5

The distance between the points (4,2) and (8,5) is 5 units.

For this problem you must do Pythagorean theorem:

[tex]a^{2} + b^{2} =c^{2}[/tex]

In this example 10ft is c and 7ft is a (or it could be b, and you'll be solving for a instead of b. It's the same thing, since a and b are both legs)

Plug what you know into the equation:

[tex]7^{2} +b^{2} = 10^{2}[/tex]

49 +b^{2} = 100

Bring 49 to the right side by subtracting it:

b^{2} = 51

Now you still must isolate b. The opposite of squaring is taking the square root so take the square root of both sides to cancel it from the left side:

[tex]b =\sqrt{51}[/tex]

b = 7.1414

b ≈ 7 ft

Hope this helped!

[tex]\bf x^3=216\implies x=\sqrt[3]{216}\implies x=6[/tex]

Divide 216 by 3 to get your x-value

Answer:

11

Step-by-step explanation:

The x-value -4 is less than 3, so use the first formula for f:  x^2 - 5.

Then f(-4) = (-4)^2 - 5 = 11

Answer:

given

Step-by-step explanation:

The vertically opposite angles, ∠4 and ∠2 are equals.

Vertical angles are angles opposite each other where two lines cross.

A linear pair can be defined as two adjacent angles that add up to 180° or two angles which when combined together form a line or a straight angle.

According to the given question.

On line m, we have

∠4 + ∠1 = 180 degrees ...(i)    (by linear pair)

On line n, we have

∠1 + ∠2 = 180 degrees ...(ii)   (by linear pair)

from equation (i) and (ii)

∠4 + ∠1 = ∠1 + ∠2

⇒ ∠4 = ∠2

Hence, we proved that the vertically opposite angles ∠4 and ∠2 are equals.

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Answer:

$3000 was invested at 11%.

Step-by-step explanation:

The total interest was $426.  This was comprised of interest earned at 8% (represented by e) and (separately) interest earned at 11% (represented by v).

Then e + v = $4200 total investment, and  

i = $426 = e(0.08)(1 year) + v(0.11)(1 year)

We eliminate the variable e as follows:  since e + v = $4200, e = $4200 - v.  Thus,

i = $426 = e(0.08)(1 year) + v(0.11)(1 year) becomes:

i = $426 = ($4200 - v)(0.08)(1 year) + v(0.11)(1 year)  

This is one equation in one unknown, the amount of $ invested at 11%.

Performing the indicated multiplications:

426 = 4200(0.08) - 0.08v + 0.11v.  Simplifying this further, we get:

426 = 336 + 0.03v.

Then 90 = 0.03v, and v = 90 / 0.03 = $3000.

$3000 was invested at 11%.

Answer: OPTION D

Step-by-step explanation:

To complete the table, you need to substitute the values of "x" given in the table into the quadratic equation [tex]y=x^{2}-x-6[/tex] to obtain the corresponding value of "y".

Then:

When [tex]x=-5[/tex] :

[tex]y=(-5)^{2}-(-5)-6[/tex]

[tex]y=24[/tex]

When [tex]x=-3[/tex] :

[tex]y=(-3)^{2}-(-3)-6[/tex]

[tex]y=6[/tex]

When [tex]x=-1[/tex] :

[tex]y=(-1)^{2}-(-1)-6[/tex]

[tex]y=-4[/tex]

When [tex]x=2[/tex] :

[tex]y=(2)^{2}-(2)-6[/tex]

[tex]y=-4[/tex]

Answer:

90

Step-by-step explanation:

Answer:

The answer is 3,589,234

Step-by-step explanation:

Because it basically means addition meaning you just have to add it 3,489,234 + 100,000 gives you the answer

Answer:

(-2, 0), (-3, 0), and (5, 0)

Step-by-step explanation:

The x-intercept is found when y = 0.

So, we have to find x when (x + 2)(x + 3)(x - 5) = 0

We can do that by pulling apart all parts, because if one part = 0, the whole thing will have to be too (multiplication property of identity).

1. When x + 2 = 0, x = -2

2. When x + 3 = 0, x = -3

3. When x - 5 = 0, x = 5

That gives us (-2, 0), (-3, 0), and (5, 0)

Answer:

Step-by-step explanation:

x-intercepts are for

(x + 2)(x + 3)(x - 5) = 0

The product is equal to 0 if one of the factors is equal to 0.

Therefore

x + 2 = 0 or x + 3 = 0 or x - 5 = 9

x + 2 = 0     subtract 2 from both sides

x = -2

x + 3 = 0        subtract 3 from both sides

x = -3

x - 5 = 0              add 5 to both sides

x = 5

If the decimal expansion of pi would end, then it would have to be a rational number, ie pi could be written as a fraction pi = p/q with integers p and q. There are many proofs that this is not the case, but they are all a bit complicated

Pi is an irrational and transcendental number, meaning it never terminates or repeats. Its non-ending and non-repeating nature is reflected in its definition as the ratio of a circle's circumference to its diameter. Pi's transcendence ensures it cannot be expressed by any algebraic equation with rational coefficients.

Understanding the Nature of Pi ( 3.141592653589793237...)

Pi ( 3.14159...) is known to be a non-terminating, non-repeating decimal, which classifies it as an irrational number. This means that no matter how many digits you calculate, Pi will never repeat in a pattern nor end. The number has been calculated to trillions of digits without any repeating pattern emerging.

The non-ending nature of Pi arises from its definition as the ratio of a circle's circumference to its diameter. This ratio is the same for all circles, but it can never be expressed exactly by a fraction or a finite decimal.

Moreover, Ferdinand von Lindemann's proof that Pi is a transcendental number further solidifies that it cannot be the solution of any algebraic equation with rational coefficients, making Pi an essentially complex and infinite entity in mathematics.

Answer:

5, 144°

Step-by-step explanation:

A vector with magnitude v and angle θ can be split into x and y components as:

vx = v cos θ

vy = v sin θ

Here, we're given the components and asked to find the magnitude and direction.  By matching, we can see the magnitude is 5 and the angle is 144°.

So the answer is 5, 144°.

Answer:

Linear Function

[tex]y=4x+18[/tex]

Step-by-step explanation:

Let

x----> the time in hours

y----> the total inches of snow on the ground

we know that

The function that best model this situation is the linear function

so

[tex]y=mx+b[/tex]

In this problem

[tex]m=4\frac{in}{h}[/tex]

[tex]b=18\ in[/tex] ----> the y-intercept

substitute

[tex]y=4x+18[/tex]

Answer:

Linear decreasing function best model this situation and the required function is

f(x)=4x+18

Step-by-step explanation:

It is given that a ski resort has 18 inches of snow on the ground. The snow is falling at a rate of 4 inches per hour.

If a function has constant rate of change, then the it is a linear function.

It the given case the rate of change is constant so linear function best model this situation.

The slope intercept form of linear function is

[tex]f(x)=mx+b[/tex]           ... (1)

where, m is slope and b is y-intercept or initial value.

Ski resort has 18 inches of snow on the ground it means initial value is 18.

The snow is falling at a rate of 4 inches per hour. So, m=4.

Substitute m=4 and b=18 in equation (1).

[tex]f(x)=4x+18[/tex]

Therefore the required function is f(x)=4x+18.

Answer:

Depending of the exact career but measurements are plentiful in the healthcare business.

First, you'll most likely deal with weight and height... since that's part of most health care consultations.

Then, if you deal with medication, you'll use grams, milligrams, milliliters, liters all the time. depending if the medication is in solid or liquid form.

Even as a nutritionist, you'll deal with grams and such for portion sizes.

There are countless of ways you'll use maths and measurements in the healthcare sector.  

Answer:

Measurement can be used in healthcare career also. Like - the doctors and nurses are well trained to give medicines accurately as per measurement of milligrams or nano-gram. High doses can prove fatal with some medicines, so the correct measurement is very necessary.

Similarly, measurement is used in syrups. Like a child can be given upto 5 mg of syrup twice daily.

Answer:

Final answer is 3.

Step-by-step explanation:

Given function is [tex]f\left(x\right)=3x^4-x^2+4x-2[/tex].

Now we need to find about what is the maximum number of relative extremes contained in the graph of the given function [tex]f\left(x\right)=3x^4-x^2+4x-2[/tex].

Degree of the given function = 4.

Because degree is the highest power of variable.

Then relative number of extremas = degree - 1 = 4 - 1 = 3

Hence final answer is 3.

Answer:

The building is [tex]116\ m[/tex] high

Step-by-step explanation:

we know that

Using proportion

Let

x-----> the height of the building

[tex]\frac{2}{6}=\frac{x}{348}\\ \\x=2*348/6\\ \\x=116\ m[/tex]