The coordinates of PQR are P(1, 1), Q(2, 2), and R(3, 1). If PQR is rotated 90° about the origin, what are the vertices of P'Q'R'?

B is the correct answer , it is incorrect.

Answer:

(b) is incorrect

Step-by-step explanation:

Applying Pythagoras' theorem to the right triangle.

The square on the hypotenuse (t ) is equal to the sum of the squares on the other 2 sides, that is

t² = r² + s² ( subtract r² from both sides )

t² - r² = s² ← is a correct equation → (a)

Answer:

Part A : 9x^2 - x - 3

Part B : 5x^2 - 9x + 9

Part C : -5x^2 + 9x - 9

Answer:

number of hours  Alexander family ‘s sprinkler work = 20

number of hours  Morgan family ‘s sprinkler work = 30

Step-by-step explanation:

Given in the question,

water output rate for the Alexander family ‘s sprinkler = 40 L  

water output rate for the Morgan family ‘s sprinkler = 20 L

Suppose, number of hours  Alexander family ‘s sprinkler work = x

Suppose, number of hours  Morgan family ‘s sprinkler work = y

Equation1

x + y = 50

Equation 2

40x + 20y = 1400

x = 50 - y

Put this value of x in equation 2

40(50-y) + 20y = 1400

2000 - 40y + 20y = 1400

-20y = 1400 - 2000

-20y = -600

y = 30

Put this value of y in equation 1 to get the value of x

x + 30 = 50

x = 50 - 30

x = 20

Answer:

A. $7,764.62

Step-by-step explanation:

The amount you will have after 10 years if you invest $2,500 into an account that pays 12% per year, compounded annually is given by

[tex]A=P(1+r\%)^t[/tex]

where [tex]t=10[/tex] years

[tex]r\%=0.12[/tex]

and P=$2,500

We substitute these values into the formula to obtain;

[tex]A=2500(1+0.12)^{10}[/tex]

This will give us;

[tex]A=2500(1.12)^{10}[/tex]

[tex]A=7764.6205[/tex]

We round to the nearest hundredth to obtain;

[tex]A=7,764.62[/tex]

The correct choice is A.

Answer:

Option A

Step-by-step explanation:

We must use the compound interest formula:

[tex]A = P(1 + r)^t[/tex]

Where

P is the initial amount = 2500

r is the annual interest rate =0.12

t is time in years = 10

A is the final amount

Then we substitute these values in the formula:

[tex]A = P(1 + r)^t\\\\A = 2500(1+0.12)^10\\\\A = 7,764.62[/tex]

Answer:

3 meters

Step-by-step explanation:

We assume the storage room is a rectangle, like most rooms, no indication it is otherwise.

We know it's a rectangle and not a square because it is longer than wide.

We have the perimeter measurement (16 meters).

So, we can make the following equation:

2x + 2y = 16

x being the width of the room, y being it's length.  A perimeter is the sum of all sides.

We also know the room is 2 meters longer than wide... so:

y = x + 2

If we replace y in the first equation by its value relative to x, we get:

2x + 2(x + 2) = 16 which becomes

2x + 2x + 4 = 16

4x =12

thus x = 3

Width: 3 meters

Length: 5 meters.

Confirms the 16 meters perimeter.

Answer:

Width = 3 meters

Step-by-step explanation:

We are given that for an equipment storage room, it is 2 meters longer than its width and the perimeter of this room is 16 meters.

Given the above information, we are to find the width of the room.

Perimeter = [tex]2l+2w[/tex]

Supposing [tex]x[/tex] to be the width and [tex]x+2[/tex] to the length, we can write it as:

[tex]16=2(x)+2(x+2)[/tex]

[tex]16=2x+2x+4[/tex]

[tex]12=4x[/tex]

[tex]x=\frac{12}{4}[/tex]

x = 3

Therefore, the width = 3 meters.

Answer:

53 degree angle

Step-by-step explanation:

Two angles are said to be complementary if they add up to 90 degrees. Let the complementary angle of 37 degrees is x. These two angles must add up to 90 degrees. So we can set up the equation as:

37 + x  = 90

Subtracting 37 from both sides, we get:

x = 90 - 37

x = 53 degree angle

From the above solution we can see that if we want to find the complementary angle of any angle, we can subtract the given measure from 90 degrees to get our answer.

Answer:53

Step-by-step explanation:

90-37=53

Answer:

Hence choice A is correct

Step-by-step explanation:

Given equations are [tex]f(x)=\sqrt{x^2-1}[/tex] and [tex]g(x)=\sqrt{x-1}[/tex]

Now we need to find the value of [tex]\left(\frac{f}{g}\right)\left(x\right)[/tex]. Then select correct matching choice from the given choices.

Now let's find  [tex](fof)(3)[/tex]

[tex]\left(\frac{f}{g}\right)\left(x\right)[/tex]

[tex]\left(\frac{f}{g}\right)\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}[/tex]

[tex]\left(\frac{f}{g}\right)\left(x\right)=\frac{\sqrt{x^2-1}}{\sqrt{x-1}}[/tex]

[tex]\left(\frac{f}{g}\right)\left(x\right)=\frac{\sqrt{\left(x+1\right)\left(x-1\right)}}{\sqrt{x-1}}[/tex]

[tex]\left(\frac{f}{g}\right)\left(x\right)=\sqrt{x+1}[/tex]

Hence choice A is correct

Answer:

a. (f/g)(x) =  √x+1

Step-by-step explanation:

We have given two function.

f(x)  = √x²-1

g(x)  = √x-1

We have to find the quotient of f(x) and g(x).

(f/g)(x) = ?

The formula to find (f/g)(x) is :

(f/g)(x) = f(x) / g(x)

simplifying f(x) , we have

f(x)  = √(x-1)(x+1)

f(x)  = (√x-1)(√x+1)

Putting values in above formula, we have

(f/g)(x) = (√x-1)(√x+1) / √x-1

(f/g)(x) =  √x+1 which is the answer.

Answer:

It is 1/3 throughout the line.

Step-by-step explanation:

It is 1/3 throughout the line.

Answer: 2 cans.

Step-by-step explanation:

Calculate the volume of the go cart tank, which has the form of a rectangular prism. You can use the following formula:

[tex]V=l*w*h[/tex]

Where:

l: is the lenght.

w: is the width.

h: is the height.

In this case:

[tex]l=15.4in\\w=10in\\h=3in[/tex]

Substitute values into the formula. Then:

[tex]V=(15.4in)(10in)(3in)=462in^3[/tex]

If a gas can holds 1 gallon of gas and [tex]1\ gallon=231\ in^3[/tex], then the number of full gas cans that will take to fill the go cart's tank (whose volume is 462 in³) is:

[tex]gas\ cans=\frac{(462in^3)(1can)}{(231in^3)}=2\ cans[/tex]

Answer:

8 full cans

Step-by-step explanation:

It will take 8 full cans of gas to fill the go cart's gas tank.

An atom containing two more electrons than protons has a net charge of negative two (-2), as determined by the difference in number of positive protons and negative electrons.

An atom which has two more electrons than protons has a charge of -2. The charge of an atom is determined by the difference between the number of protons and electrons. Protons have a charge of +1 and electrons have a charge of -1. Hence, if the atom has two more electrons than protons, it will have a charge of -2 because electrons contribute a negative charge. For instance, for an atom with 2 protons (+2 charge) and 4 electrons (-4 charge), the overall charge would be -2.

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An atom with 2 more electrons than protons will have a net charge of -2.

An atom is the basic unit of matter, consisting of a nucleus containing protons and neutrons, surrounded by electrons. Elements are defined by the number of protons in their atoms. An atom's charge is determined by the difference between the number of electrons and the number of protons. If an atom has 2 more electrons than protons, it will have a net charge of -2.

For example, let's consider the element oxygen (O). Oxygen normally has 8 protons and 8 electrons, resulting in a neutral charge. If we add 2 more electrons to oxygen, it will then have 10 electrons and still 8 protons, giving it a net charge of -2.

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Answer:

the third graph

The correct graph is Graph 3.

We are given a modulus function f(x) by:

       [tex]f(x)=2|x|[/tex]

We will go through the following graphs by checking the value of the graph at some value of x and see whether the value on the graph at that x matches the value of f(x) at that particular x.

when x=1 we have:

[tex]f(x)=2\times |1|\\\\f(x)=2[/tex]

Graph 1:

When x=1

we have:

[tex]f(x)=0.5\neq 2[/tex]

Hence, Graph 1 does not represent the given function.

Graph 2:

when x=1 we have:

[tex]f(x)=1\neq 2[/tex]

Hence, Graph 2 is not the answer.

Graph 4:

when x=1 we have:

[tex]f(x)<2[/tex]

Hence, graph 4 is not the correct graph to represent f(x).

Hence, we are left with Graph 3.

When we plot the function f(x) we see that it matches the graph 3.

Answer:

C. [tex]g(x)=(x-2)^2[/tex]

Step-by-step explanation:

Remember the rules for function transformations:

- [tex]f(x+a)[/tex] shifts the function, [tex]f(x)[/tex], [tex]a[/tex] units to the left

- [tex]f(x-a)[/tex] shifts the function, [tex]f(x)[/tex], [tex]a[/tex] units to the right

We can infer from the picture that the blue graph is shifted 2 units to the right of the red graph, so we should apply the second rule:

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

[tex]g(x-2)=(x-2)^2[/tex]

[tex]g(x)=(x-2)^2[/tex]

We can conclude that the correct answer is C. [tex]g(x)=(x-2)^2[/tex]

You can deduct that the height of the first box is 5cm. Since the next box is 3x the size, that means it’s height is 15. So 30*30*15= 13500.

Your answer is 13500 cm^3

Have a blessed day,

Jrodt

Answer:

13500 cm³

Step-by-step explanation:

The linear ratio = 10 : 30 = 1 : 3

The volume ratio = 1³ : 3³ = 1 : 27

Thus the volume of the larger box is 27 times larger than the volume of the smaller box

volume = 500 × 27 = 13500 cm³

Answer:

Multiply by 2

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

A circle can be circumscribed around the four vertices of a quadrilateral if and only if,

both pair of opposite angles inscribed in the quadrilateral are supplementary to each other. By supplementary to each other we mean that their sum is equal to 180°.

In this case we have opposite interior angles supplementary to each other hence we can circumscribe a circle around it. Such Quadrilateral are called cyclic quadrilateral.

Answer:

The answer is True

Step-by-step explanation:

I just got it correct.

Answer:

38 units  

Step-by-step explanation:

Triangle ABC is a right triangle.  To find the missing side, AB (which is the hypotenuse), we use the Pythagorean theorem:

a²+b² = c²

10²+24² = c²

100+576 = c²

676 = c²

Take the square root of both sides:

√(676) = √(c²)

26 = c

AB is a diameter; this means the radius is 26/2 = 13.  This means that OB = 13 and OE = 13.

BD and DE are congruent; this means that BD = 6.

This makes the perimeter

13+13+6+6 = 38 units.

The perimeter of kite OBDE is 38 units.

Pythagoras theorem states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

Perimeter is the distance around the edge of a shape.

A kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.

According to the given question.

We have a circle with center o and diameter AB.

Triangle ABC is a right triangle.  

To find the missing side, AB (which is the hypotenuse), we use the Pythagoras theorem.

So,

[tex](AB)^{2} = (10)^{2} +(24)^{2}[/tex]

[tex]\implies (AB)^{2} = 100+ 576\\\implies (AB)^{2} = 676\\\implies AB = \sqrt{676} \\\implies AB = 26[/tex]

Since, AB is the diameter of the circle. Therefore,

[tex]OB = \frac{AB}{2} \\\implies OB = \frac{26}{2} = 13[/tex]

Also, OBDE is a kite and we know that the adjacent sides of a kite are congruent.

[tex]\implies OB = BD = 13 \\\And,\ OE = ED = 6[/tex]

Therefore,

the perimeter of kite OBDE

= Length of sides (OB + BD + DE + EO )

= 13 + 13 + 6 + 6

= 26 + 12

= 38 units.

Hence, the perimeter of kite OBDE is 38 units.

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Answer:

[tex]EF=7.6\ units[/tex]

[tex]EG=15.9\ units[/tex]

[tex]m<G=28.6\°[/tex]

Step-by-step explanation:

step 1

Find the measure of side EF

we know that

In the right triangle EFG

[tex]tan(61.4\°)=\frac{FG}{EF}[/tex]

[tex]EF=\frac{FG}{tan(61.4\°)}[/tex]

[tex]EF=\frac{14}{tan(61.4\°)}[/tex]

[tex]EF=7.6\ units[/tex]

step 2

Find the measure of side EG

we know that

In the right triangle EFG

[tex]sin(61.4\°)=\frac{FG}{EG}[/tex]

[tex]EG=\frac{FG}{sin(61.4\°)}[/tex]

[tex]EG=\frac{14}{sin(61.4\°)}[/tex]

[tex]EG=15.9\ units[/tex]

step 3

Find the measure of angle G

wee know that

[tex]m>E+m<G=90\°[/tex] -----> by complementary angles

we have

[tex]m<E=61.4\°[/tex]

substitute

[tex]61.4\°+m<G=90\°[/tex]

[tex]m<G=90\°-61.4\°=28.6\°[/tex]

Answer:

23

Step-by-step explanation:

For this case we have that the order of algebraic operations must be carried out in the following way, according to the PEMDAS method:

P

Parenthesis first

E

Exponents (powers and square roots, etc.)

MD

Multiplication and Division (from left to right)

AS

Addition and Subtraction (from left to right)

We have two expressions:

[tex]8 * 3 ^ 2 + 3 =\\8 * 9 + 3 =\\72 + 3 =\\75[/tex]

The second expression is:

2^2 * 8÷2 + 2 =

4 * 8÷2 + 2 =

32÷2 + 2 =

16 + 2 =

18

ANswer:

75 and 18

Answer:

1100 in²

Step-by-step explanation:

Find the area of the boxes separately and add them

[tex]1.6 \times {10}^{8} = 160000000[/tex]

[tex]5.8 \times {10}^{6} = 5800000[/tex]

[tex]4 \times {10}^{6} = 400000[/tex]

Answer:

Step-by-step explanation:

Twenty-seven minus of a number (x) is not more than 36

27 - x ≤ 36           subtract 27 from both sides

27 - 27 - x ≤ 36 - 27

-x ≤ 9           change the signs

x ≥ - 9

Answer:

x ≥ -6

Step-by-step explanation:

got it right

Answer:

The Rate of Change between two points on a line

Answer:

horizontal

Step-by-step explanation:

The measure of one interior angle of a 42 sided regular polygon is given by A = 171.428°

The sum of the interior angles of a polygon is given by the formula

Sum of Interior angles of a polygon with n sides is

nθ = 180 ( n - 2 )

where n is the number of sides

θ = angle in degrees

Given data ,

Let the interior angle of the polygon be represented as A

Now , let the number of sides of the polygon be n = 42 sides

So , Sum of Interior angles of a polygon with n sides is

nθ = 180 ( n - 2 )

On simplifying , we get

42θ = 180 ( 42 - 2 )

42θ = 180 ( 40 )

Divide by 42 on both sides , we get

A = 180 ( 40 ) / 42

A = 171.428°

Therefore , the value of A is 171.428°

Hence , the measure of one angle is  171.428°

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None of the provided numbers are directly equivalent to 243. Depending on the context like exponents or probability distribution, 243 could arise from such mathematical constructs.

From the numbers provided, it seems like none of them are directly equivalent to 243. However, if you are referring to a possible mathematical equation, there could be several combinations of numbers that can equate to 243. For instance, one could add several numbers to total 243. In context of

exponents

or

powers

, 3 raised to the power of 5 (3^5) equals 243. In the world of

binomial probability distribution

, 243 could be a possible result based on specific conditions. Without more context, it's hard to provide a specific equivalence to 243.

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Answer:

A:  6x - 7

Step-by-step explanation:

You may find it helpful to rearrange these two quantities vertically:

Add:

  (4x-3)

 +(2x-4)

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

    6x - 7

This corresponds to the first possible answer listed:  A.

The simplified expression is 6x - 7.

Hence the correct option is A.

Given is an expression (4x-3) + (2x-4), we need to perform addition operation to simplify the expression.

You must combine like terms in the provided expression, (4x-3) + (2x-4), to make it simpler.

Similar terms are those that share a variable and an exponent.

Group terms that are similar together.

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

Add the like terms' coefficients.

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

Add the coefficients together.

6x - 7

Therefore, the simplified expression is 6x - 7.

Hence the correct option is A.

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Answer:

-3 143/1000

Step-by-step explanation:

To write -3.143 in its equivalent fraction form, multiply the whole number part by the place value of the decimal and add it to the decimal part multiplied by the place value. The resulting fraction is -3143/1000.

To write the decimal number -3.143 in its equivalent fraction form, we first need to determine the place value of each digit. The number -3.143 has three digits after the decimal point, so the fraction's denominator will be ten, raised to the power of three, which is 1000. The fraction's numerator will be the whole number part of the decimal (in this case, -3) multiplied by 1000, plus the decimal part (0.143) multiplied by 1000.

Therefore, the equivalent fraction form of -3.143 is:

-3.143 = (-3 * 1000 + 0.143 * 1000) / 1000 = -3143 / 1000

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Answer:

45 mph ≠ 40 mph

Step-by-step explanation:

Answer:

2.0*10^(-7) meters

Step-by-step explanation:

We'll need to move the decimal point 7 places to the right, obtaining 2.0, and then multiply this 2.0 by 10^(-7).

This diameter is 2.0*10^(-7) meters.

Answer:

2x2^10m

Step-by-step explanation:

0.0000002

Answer:

B) x = 1

C) x = 4

Step-by-step explanation:

Given:

f(x) = 2x

g(x) = 2^x

We have to find at what value of x, the above two functions are equal in value.

Now we have to check with the each options.

When x = 0, f(0) = 2(0) = 0 ; g(0) = 2^0 = 1 [Anything power 0, is 1]

When x = 1, f(1) = 2(1) = 2 ; g(1) = 2^1 = 2.

when x = 2, f(2) = 2(2) = 4; g(2) = 2^2 = 4

when x = 3, f(3) = 2(3) = 6, g(3) = 2^3 = 8

when x = 4, f(4) = 2(4) = 8, g(4) = 2^4 = 16

The two functions are equal in value when x = 1 and x = 2.

Final answer:

The value(s) of x for which the equation f(x) = 2x and g(x) = 2ˣ are equal are x = 1 and x = 2, as those are the points where the two functions have the same value.

Explanation:

The student seems to be asking for which value(s) of x the equations f(x) = 2x and g(x) = 2ˣ are equal. To find the solution, we need to identify the point where the two functions intersect, by setting them equal to each other and solving for x.

So we set up the equation 2x = 2ˣ and look for solutions. At first glance, it seems there are two obvious solutions:

When x = 1, f(x) = 2 x 1 = 2 and g(x) = 2¹ = 2, so the statement f(x) = g(x) is true.

When x = 0, f(x) = 2 x 0 = 0 and g(x) = 2⁰ = 1, so the statement f(x) = g(x) is not true.

Testing the other provided options similarly, you'll find that:

For x = 2, f(x) = 4 and g(x) = 4, hence f(x) = g(x) is true.

For x = 3, f(x) = 6 and g(x) = 8, hence f(x) = g(x) is not true.

For x = 4, f(x) = 8 and g(x) = 16, hence f(x) = g(x) is not true.

The correct answers are x = 1 and x = 2, where the equation f(x) = g(x) holds true.