1. Solve the system of equations using addition
and/or subtraction with multiplication method.
Select the best answer with the format (x, y).
6x + 4y = 12
-6x+6y=-72
O (6, -6)
O (13, 1)
O (3,5)
(12, 12)
no solution
infinite solutions

[tex]PQ = 2 - (-3) = 2 + 3 = 5 \ cm[/tex]

[tex]RS = PQ \implies RS = 5 \ cm[/tex]

the perimeter of rectangle PQRS is 20 centimeters ⇒

[tex]QR = SP = 5 \ cm[/tex]

⇒ PQRS is square

[tex]x_{R} = x_{Q} - 5 = -1-5 = -6[/tex]

[tex]y_{R} = y_{Q} = 2[/tex]

[tex]\implies R(-6,2)[/tex]

[tex]x_{S} = x_{R} = -6[/tex]

[tex]y_{S} = y_{P} = -3[/tex]

[tex]\implies Q(-6,-3)[/tex]

Answer:

slope is undefined

Step-by-step explanation:

We have 2 coordinates (-4,0) and (-4,1)

Slope m = (y2 - y1)/(x2 - x1) = (1 - 0)/(-4 - -4) = 1/0 or undefined

The undefined slope is the slope of a vertical line

An example of a compound interest problem and the solution problem is:

"Sarah deposits $10,000 into a savings account with a 5% annual interest rate compounded annually. How much will she have in the account after 3 years?"

Solution: Sarah will have $11,576.25 in the account after 3 years.

The compound interest on the same sum at the same rate for the same period, compounded annually, is:

$6,646.34

Sarah deposits $10,000 into a savings account with a 5% annual interest rate compounded annually. How much will she have in the account after 3 years?

To solve this problem, we can use the formula for compound interest: A = P(1 + r)^n, where A is the final amount, P is the principal amount, r is the annual interest rate, and n is the number of years.

To find the compound interest on the same sum at the same rate for the same period, we can use the same formula for compound interest: A = P(1 + r)^n.

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The  (√12 - √3)² = 6 according to the provided assertion.

Why do you use the word "binomial"?

A Binomial is a name for an algebraic equation with only two elements. It is a polynomial with two terms. It is also referred to as the total or difference of two or more binomials. It is a polynomial's most basic shape.

To expand and simplify the expression (√12 - √3)², we can use the formula for the square of a binomial:

(a - b)² = a²  + b² - 2ab

In this case, a = √12 and b = √3, so we have:

(√12 - √3)² = (√12)² - 2(√12)(√3) + (√3)²

To simplifying, we have:

(√12 - √3)² = 12 - 2√36 + 3

Since √36 = 6, we can simplify further:

(√12 - √3)² = 12 - 2(6) + 3 = 6

Therefore, the expanded and simplified equation (√12 - √3)² = 6.

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Answer:

m<BFC= 64°; m<AFB= 116°

Step-by-step explanation:

Using the Vertical Angle Theorem, in which "the opposing angles of two intersecting lines must be congruent, or identical in value"

m<AFE is congruent to m<BFC, therefore m<BFC is 64°

You can also use the straight angle theorem where BE is a straight line, and is therefore 180°. so subtracting 180° from 64° will result in m<AFB being 116°, you second answer. You can take it a step further without using the vertical angle theorem to get our first answer by using the same rules for the straight angle theorem again, knowing that AC is a straight line and that m<AFB is 116°, subtract 180° by 116° to get m<BFC, 64°.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{2\sqrt{41}}\\ a=\stackrel{adjacent}{10}\\ o=opposite \end{cases} \\\\\\ o=\sqrt{ (2\sqrt{41})^2 - 10^2}\implies o=\sqrt{ (2^2)(\sqrt{41})^2 - 100 } \implies o=\sqrt{ (4)(41)-100 } \\\\\\ o=\sqrt{164-100}\implies o=\sqrt{64}\implies o=8[/tex]

The value of 8#(8#8) is (A) 1/2

An operation \# for positive real numbers is defined by the equation a#b=ab/a+b. The value of 8#(8#8) is (A) 1/2. To solve, use the equation given:

8#(8#8) = (8*8)/(8+8)

= 64/16

= 1/2

Hope this helps!

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The length of the arc intercepted by a central angle of 6 radians in a circle of radius 53 is:

Arc length = radius x central angle

Arc length = 53 x 6

Arc length = 318

Therefore, the length of the arc intercepted by a central angle of 6 radians in a circle of radius 53 is 318.

The length of the arc intercepted by a central angle of 97° in a circle of radius 8 is:

First, we need to convert 97° to radians:

97° = (97/180) x π radians

97° = 1.69 radians (rounded to two decimal places)

Arc length = radius x central angle

Arc length = 8 x 1.69

Arc length ≈ 13.52 (rounded to two decimal places)

Therefore, the length of the arc intercepted by a central angle of 97° in a circle of radius 8 is approximately 13.52.

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The proof that ∠B ≅ ∠C is:

D is the midpoint of of BC - Given...................(1)
Thus
BD = DC ................................................................(2)

∠EDC ≅ ∠FDB  - Given......................................(3)

DE ⊥ AB - Given...................................................(4)
DF ⊥ AC - Given ..................................................(5)
∠AED = ∠DEB = 90° - perpendicular bisector theorem  ....(6)

∠AFD = ∠DFC = 90° - perpendicular bisector theorem ....(7)
∠EAF = ∠EDF = 90° - Properties of the angles of a Quadrilateral

Since ∠EDC ≅ ∠FDB, as in   (3) above, and

Both comprise of ∠EDF,

thus,
(∠EDC - ∠EDF) ≅ (∠FDB - ∠EDF)

Since

∠EDB = (∠FDB - ∠EDF); and

∠FDC = (∠EDC - ∠EDF)

Thus,

∠EDB ≅ ∠FDC

thus,
∠EDB = ∠FDC = 45° (Sum of Angles on a Straight line) that is
∠EDB =  ∠FDC = (180° -∠EDF)/2

Since  ∠EDF = 90°
∠EDB =  ∠FDC = (180° -90°)/2

∠EDB =  ∠FDC = 90/2
∠EDB =  ∠FDC = 45°

Since
∠DEB = 90° (5); and

∠DFC = 90° (7)
ΔBED ≅ ΔDFC

Thus, by Sum of Angles in a Triangle,
∠B ≅ ∠C.

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The zero vector [0, 0, 0], the length would be √(0^2 + 0^2 + 0^2) = 0.

Examples of 3 element vectors include:
- [1, 2, 3]
- [-1, 0, 5]
- [3, -2, 1]
- [0, 0, 0]
- [4, 4, 4]
- [-2, -2, -2]

There are infinitely many 3 element vectors that have a length of 0. A vector with a length of 0 is called the zero vector, and it has all of its components equal to 0. In the case of a 3 element vector, the zero vector would be [0, 0, 0].

Examples of 3 element vectors include:
- [1, 2, 3]
- [-1, 0, 5]
- [3, -2, 1]
- [0, 0, 0]
- [4, 4, 4]
- [-2, -2, -2]

Remember that the length of a vector is calculated using the formula √(x1^2 + x2^2 + x3^2), where x1, x2, and x3 are the components of the vector. So, for the zero vector [0, 0, 0], the length would be √(0^2 + 0^2 + 0^2) = 0.

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When lines A and B are cut by a transversal, then ∠1 and ∠4 fοrm a pair οf vertical angles.

In geοmetry, a transversal line intersects twο lines in the same plane at twο different lοcatiοns. In the Euclidean plane, transversals help establish the parallelism οf twο οr mοre οther straight lines. It crοsses twο lines at separate lοcatiοns. Transversal intersectiοn results in numerοus angles.

Twο parallel lines are A and B are drawn.

They are cut by a transversal C.

The angles ∠1 and ∠2 are fοrming a pair οf alternate exteriοr angles.

The angles ∠3 and ∠4 are fοrming a pair οf alternate interiοr angles.

The angles ∠2 and ∠3 are verticals angles.

Similarly, the angles ∠1 and ∠4 fοrm a pair οf vertically οppοsite angles.

Therefοre, the angles fοrm vertical pair.

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The total fluid intake for the meal is 493.04 mL.

We first need to convert the volume of each beverage to ounces, and then to milliliters.

1/3 glass of orange juice = (1/3) x 8 oz = 2.67 oz = 79.01 mL (assuming 1 oz = 29.57 mL)

1/2 cup of tea = (1/2) x 6 oz = 3 oz = 88.72 mL

1/2 pt milk = (1/2) x 16 oz = 8 oz = 236.59 mL (assuming 1 pt = 16 oz and 1 oz = 29.57 mL)

1 popsicle (3oz) = 3 oz = 88.72 mL

The total fluid intake for the meal is

79.01 mL + 88.72 mL + 236.59 mL + 88.72 mL = 493.04 mL

Therefore, the fluid intake for the meal is approximately 493.04 mL.

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Answer is in a picture, so zoom in!

But overall, the answer is  below!

9 people can be seated at a round table is 8! = 40,320.

When people are seated at a round table, the number of arrangements is given by (n-1)!, where n is the number of people. This is because one person can be considered as fixed, and the remaining (n-1) people can be arranged in (n-1)! ways. So for 9 people, the number of arrangements is (9-1)! = 8! = 40,320.

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The daily percent οf decrease is 12.94%.

Sο the cοrrect οptiοn is: 12.94%.

Percentage decrease is the percentage by which a quantity οr value has decreased cοmpared tο its οriginal οr previοus value. It is calculated by taking the difference between the οriginal value and the new value, dividing that difference by the οriginal value, and then multiplying by 100 tο cοnvert the result intο a percentage. The fοrmula fοr percentage decrease is:

Percentage decrease = [(Original value - New value) / Original value] x 100%

The fοrmula fοr the amοunt οf radiοactive element remaining, r, in a 100-mg sample after d days is given as:

[tex]r = 100(1/2)^{(d/5)[/tex]

Tο find the daily percent οf decrease, we need tο find the difference between the amοunt οf the element at the start οf a day and the amοunt at the end οf that day, and then express this as a percentage οf the starting amοunt.

Let's assume that we start with 100 mg οf the radiοactive element. After οne day, the amοunt remaining is:

[tex]r = 100(1/2)^{(1/5)[/tex] ≈ 87.06 mg

The difference between the starting amοunt and the amοunt at the end οf the day is:

100 - 87.06 = 12.94

Tο express this as a percentage οf the starting amοunt, we divide this difference by the starting amοunt and multiply by 100:

12.94/100 * 100% = 12.94%

Therefοre, the daily percent οf decrease is 12.94%.

Sο the cοrrect οptiοn is: 12.94%.

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The simplified expression is 14+a.

Using the commutative and associative properties, we can simplify the expression (7+a)+7.

First, let's use the commutative property to rearrange the terms. The commutative property states that the order of addition or multiplication does not matter. In other words, a+b = b+a and a*b = b*a.

So, we can rearrange the terms in the expression to get:

(7+7)+a

Next, let's use the associative property to simplify the expression. The associative property states that the way we group terms in an addition or multiplication problem does not matter. In other words, (a+b)+c = a+(b+c) and (a*b)*c = a*(b*c).

So, we can group the terms in the expression to get:

14+a

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The LCM of the given polynomials is \[ (x+6y)(x+2y)(x-6y) \].

The LCM (Least Common Multiple) of two polynomials is the smallest polynomial that is a multiple of both of the given polynomials. To find the LCM, we need to factor the given polynomials and then take the product of the highest power of each factor.

Factoring the first polynomial: \[ x^{2}+8 x y+12 y^{2} = (x+6y)(x+2y) \]
Factoring the second polynomial: \[ x^{2}-36 y^{2} = (x+6y)(x-6y) \]

Now, we can take the product of the highest power of each factor to find the LCM:

\[ LCM = (x+6y)(x+2y)(x-6y) \]

So, the LCM of the given polynomials in factored form is \[ (x+6y)(x+2y)(x-6y) \].

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Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

7:6

Step-by-step explanation:

...

Answer:

Below

Step-by-step explanation:

154 : 132      the GCF of these two numbers is 22.   Divide them both by 22

7:6    Done

The leading coefficient of f(x) is positive, which means that the graph will be pointing upwards on both ends. The graph is attached below.

Graphs are a not unusual place technique to visually illustrate relationships within side the statistics. The reason for a graph is to provide statistics that are too severe or complex to be defined appropriately within side the textual content and in much less space.

To sketch the graph of f(x) = x^4 - 3x^3 + x - 3, we can use the information gathered from analyzing the function:

Using this information, we can sketch the graph of f(x) as follows:

Putting all of this information together, we can sketch the graph of f(x) as shown below:

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The fraction of the euro is 8/100

one Euro will cost in 8 rands

When we talk about exchange rates, we're essentially talking about the value of one currency compared to another. In this case, we're comparing the South African rand to the euro.

We know that one South African rand is valued at 0.125 of one euro. To figure out what fraction of the euro one South African rand is worth, we can simply divide the value of one rand by the value of one euro:

1 rand ÷ 0.125 euro = 8/100 euro

So, one South African rand is worth 8/100 or 0.08 (which is equivalent to 8%) of one euro.

To calculate what one euro would cost in rands, we can use the inverse of the exchange rate we were given:

1 euro ÷ 0.125 rand/euro = 8 rand

So, one euro would cost 8 South African rand.

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The statement that explains how the bear population is changing is  A. The population is decreasing by 4% per year.

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

N(t) = 850(0.96)^t

The rate factor of the above function is

Rate factor = 0.96

This is less than 1

So, we have

Rate = 1 - 0.96

Evaluate

Rate = 4%

Hence, the rate is 4%

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Diameter of flu virus particle is 8.1 × 10⁻⁸ meter

Scientific notation is a way of representing numbers that are too large or too small to be easily written in decimal form because they require very long strings of digits to  be written. This is sometimes called scientific or standard exponential format, or British standard format.

Given,

Diameter of water molecule = 2.7 × 10⁻¹⁰ meters

Flu virus particle is 300 times bigger than water molecule

Diameter of flu virus

= 300 × 2.7 × 10⁻¹⁰

= 810 × 10⁻¹⁰

= 8.1 × 10⁻⁸ meter

Hence, 8.1 × 10⁻⁸ meter is the diameter of the Flue virus particle.

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139

because you do 5 dollars times 11 cats equals 55 and 12 dollars times 7 dogs equals 84 add it together is 139

The line of reflection that produces Z′(10, 7) is y - axis.

A triangle is a two - dimensional figure with three sides and three angles.

The sum of the angles of the triangle is equal to 180 degrees.

∠A + ∠B + ∠C = 180°

Given is a Triangle XYZ is drawn with vertices X(−2, 4), Y(−9, 3), Z(−10, 7). Determine the line of reflection that produces Z′(10, 7).

The rule for a reflection over the y -axis is (x, y) → (−x, y). We can write the reflection as -

Z(- 10, 7) → Z'(10, 7)

Therefore, the line of reflection that produces Z′(10, 7) is y - axis.

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The line of reflection that produces Z′(10, 7) is y - axis.

What is a triangle?

A triangle is a two - dimensional figure with three sides and three angles.

The sum of the angles of the triangle is equal to 180 degrees.

∠A + ∠B + ∠C = 180°

Given is a Triangle XYZ is drawn with vertices X(−2, 4), Y(−9, 3), Z(−10, 7). Determine the line of reflection that produces Z′(10, 7).

The rule for a reflection over the y -axis is (x, y) → (−x, y). We can write the reflection as -

Z(- 10, 7) → Z'(10, 7)

Therefore, the line of reflection that produces Z′(10, 7) is y - axis.

Answer: the meeting lasted for an hour and 5 min.

Step-by-step explanation:

Therefore, the meeting lasted for an hour and five minutes.

Answer:

Yes

What is horizontal distance ?

The distance between two points is understood to mean the horizontal distance, regardless of the relative elevation of the two points.

How to calculate horizontal distance?

Horizontal distance can be expressed as x = Vtx = Vtx=Vt. Vertical distance from the ground is described by the formula y = – 1 2 g t 2 y = – \frac{1}{2}g t^2 y=–21gt2, where g is the gravity acceleration, and h is an elevation.

Step by step explanation:

As long as the ramp is no more than .9965 feet high, then yes

If the ramp is .9965 feet high then its horizontal distance is 12 X .9965 feet or 11.958 feet

Using Pythagoras’ Theorem, the actual length of the ramp would be the square root of (11.958 X 11.958 + .9965 X .9965)

Or the square root of (142.9934 + .9930)

Or SQRT (143.987)

= 11.999 feet

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Answer: bro hear me out rq in the explanation

Step-by-step explanation: Jim hands the cashier the $20 bill and, if necessary, provides his identification to purchase the item. The cashier will then record the purchase, give Jim his change, and thank him for his business.

Answer:

x=18

Step-by-step explanation:

Being that the angles are corresponding they are going to equal the same thing.

(7x+7)=133

Now just follow the laws of PEMDAS

7x+7=133

-7 -7

7x=126

÷7 ÷7

x=18