División de polinomios(a²+3a+2)÷(a+1)

[tex]\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{y}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{y-1}{6-4}=\stackrel{\textit{slope}}{-\cfrac{1}{4}}\implies \cfrac{y-1}{2}=-\cfrac{1}{4} \\\\\\ 4y-4=-2\implies 4y=2\implies y=\cfrac{2}{4}\implies y=\cfrac{1}{2}[/tex]

Answer: The width is 12 feet shorter than the length.

Step-by-step explanation:

The area of a rectangle can be calculated with this formula:

[tex]A=lw[/tex]

Where "l" is the lenght and "w" is the width of the rectangle.

 We know that lenght of Jennie's yard is 30 feet, the width is [tex](30-x)ft[/tex] and the area is 540 square feet. Then:

[tex]l=30\\w=(30-x)\\A=540[/tex]

Substitute these values into the formula and then solve for "x":

[tex]A=lw\\\\540=30(30-x)\\\\540=900-30x\\\\30x=900-540\\\\x=\frac{360}{30}\\\\x=12[/tex]

Therefore, the width is 12 feet shorter than the length.

Answer:

C

Step-by-step explanation:

got it on edge

interval notation wise, yes, because x < 2 means, x less than 2, not equals to 2, but less, so "x" is anything that is less than 2, not 2 itself, but anything less.

[tex]\bf \stackrel{~\hfill \rule[2pt]{8em}{0.25pt}\circ}{\rule[0.35em]{10em}{0.25pt}}2\rule[0.35em]{10em}{0.25pt}[/tex]

Answer:

[tex]\large\boxed{a_n=2\cdot(3)^{n-1}}[/tex]

Step-by-step explanation:

[tex]2,\ 6,\ 18,\ 54,\ 162,\ ...\\\\2\cdot3=6\\6\cdot3=18\\18\cdot3=54\\54\cdot3=162\\\vdots\\\\\text{It's a geometric series with common ratio}\ r=3,\ \text{and the first term}\ a_1=2.\\\\\text{The explicit formula of a geometric sequence:}\ a_n=a_1r^{n-1}.\\\\\text{Substitute:}\\\\a_n=2\cdot(3)^{n-1}[/tex]

Final answer:

The explicit formula for the sequence 2, 6, 18, 54, 162, ... is [tex]an = 2 imes 3^(n-1),[/tex] where an represents the nth term of the sequence.

Explanation:

The sequence given is 2, 6, 18, 54, 162, ..., which can be recognized as a geometric sequence. In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio (r). To find the explicit formula for the nth term of a geometric sequence, we use the formula an = a1  imes r(n-1), where a1 is the first term and r is the common ratio.

Looking at our sequence, the first term a1 is 2. The common ratio r can be found by dividing the second term by the first term (or any term by the previous term), which is 6/2 = 3. Now that we have both the first term and the common ratio, we can plug these values into our formula to get the explicit formula for the nth term of the sequence: an = 2  imes 3(n-1).

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]\frac{3}{8} \div\frac{3}{2}[/tex]

[tex]\frac{3}{8}\times\frac{2}{3}[/tex]

[tex]\textrm{Multiply the numerator and the denominator.}[/tex]

[tex]3 *2 = 6\\ 3*8=24[/tex]

[tex]\frac{6}{24} =\frac{1}{4}[/tex]

The value of the expression 3/8 divided by 1 and 1/2 is calculated by converting the mixed number into an improper fraction, changing the division to multiplication by using the reciprocal, and simplifying the multiplication to get the final answer, which is 1/4.

The question is asking for the value of the mathematical expression 3/8 divided by 1 and 1/2. To solve this problem, first, we need to convert 1 and 1/2 into an improper fraction.  The result is 3/2. Next, we should remember that division by a number is the same as multiplication by its reciprocal. Therefore, we turn the equation into a multiplication problem by multiplying 3/8 by the reciprocal of 3/2, which is 2/3.

Solving this gives us the answer: (3/8) * (2/3) = 1/4. So, the value of the expression 3/8 divided by 1 and 1/2 is 1/4.

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Answer:

18

Step-by-step explanation:

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Answer: [tex]\dfrac{9}{10}[/tex]

Step-by-step explanation:

From the table , the total number of numbers = 10

The group of 5 digits contain less than or equal to 2 even digits = 55170

i.e. The total group of 5 digits contain at least 2 =[tex]10-1=9[/tex]

Now, the probability that a group of 5 random digits will contain at least 2

even digits is given by :-

[tex]=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}=\dfrac{9}{10}[/tex]

Hence, the probability that a group of 5 random digits will contain at least 2  even digits [tex]=\dfrac{9}{10}[/tex]

Answer:

the answer is 9/10

Step-by-step explanation:

Answer:

ALL REAL NUMBERS actually

Step-by-step explanation:

Any exponential function like this, is ALWAYS R.

Answer:

B. ΔABD, ΔADC, ΔDBC

Step-by-step explanation

Step -1 In ΔABD and ΔADC (from figure).

∠DAB=∠CAD (common in both triangles) ,

∠DBA=∠CDA =90 degree, and

∠BDA=∠DCA (rest angle of the two triangles).

therefore ΔABD similar to ΔADC (by AAA similarity theorem).

Step -2 In ΔDBC and ΔADC (from figure).

∠DCB=∠ACD (common in both triangles) ,

∠DBC=∠ADC =90 degree, and

∠CDB=∠CAD (rest angle of the two triangles).

therefore ΔDBC similar to ΔADC (by AAA similarity theorem).

Step -3 In ΔABD and ΔDBC (from figure).

∠BDA=∠BCD (because , ∠ACD=ADB from stap-1 and ∠ACD=∠BCD from figure) ,

∠DBA=∠CBD =90 degree, and

∠BAC=∠BDC (rest angle of the two triangles).

therefore ΔABD similar to ΔDBC (by AAA similarity theorem).

In the above step- ΔABD similar to ΔADC, ΔDBC similar to ΔADC and ΔABD similar to ΔDBC.

Hence ΔABD, ΔADC, ΔDBC similar to each other in the given figure.

Based on the diagram shown above, the three similar right triangles are: B. ΔABD, ΔADC, ΔDBC.

The Right Triangles Similarity Theorem states that when the altitude of a  triangle is drawn to the hypotenuse of a right angled triangle, then, the two triangles that are formed would be similar to each other, as well as the original triangle.

Based on triangles ABD and ADC, we can logically deduce the following congruent angles;

m∠DAB ≅ m∠CAD

m∠DBA ≅ m∠CDA = 90°

m∠BDA ≅ m∠DCA

ΔABD ~ ΔADC (AAA similarity theorem).

Based on triangles DBC and ADC, we can logically deduce the following congruent angles;

m∠DCB ≅ m∠ACD

m∠DBC ≅ m∠ADC = 90°

m∠CDB ≅ m∠CAD

ΔDBC ~ ΔADC (AAA similarity theorem).

Based on triangles ABD and ΔDBC, we can logically deduce the following congruent angles;

m∠BDA ≅ m∠BCD

m∠DBA ≅ m∠CBD = 90

m∠BAC ≅ m∠BDC

ΔABD ~ ΔDBC (AAA similarity theorem).

Final answer:

The function f(x) = 2x^3 – x^2 – 6x is found by factoring the function, resulting in the zeros at x = 0, x = -3/2, and x = 2.

Explanation:

To find the zeros of the function f(x) = 2x^3 – x^2 – 6x, we must set the function equal to zero and solve for x. If possible, this can be done by factoring the function or using synthetic division. In this case, the function can be factored by taking out a common factor of x:

f(x) = x(2x^2 - x - 6) = 0

Next, we can factor the quadratic equation 2x^2 - x - 6 to find the remaining zeros:

2x^2 - x - 6 = (2x + 3)(x - 2)

This gives us the following zeros for the function:

x = 0

x = -3/2

x = 2

Therefore, f(x) has three zeros: 0, -1.5 (or -3/2), and 2.

Divide the total pieces by the number of kids:

108 pieces / 9 kids = 12 pieces per kid.

Answer:

x= 108/9

Step-by-step explanation:

Answer: D is correct, 18

Step-by-step explanation:

You plug in 5 for x...

4(5)-2=you answer

20-2=your answer

18= your answer

Answer:

(x - 2)² + (y - 3)² = 9

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (2, 3) and r = 3, hence

(x - 2)² + (y - 3)² = 9 ← equation of circle

The ordered pairs (294.5, 61), (364, 70), and (605.5, 88.5) are on the line given by the equation 5x - 2y = 6.

The equation given is 5x - 2y = 6. To determine which group of ordered pairs lies on this line, we can substitute the x and y values of each ordered pair into the equation and check if the equation holds true:

Therefore, all three ordered pairs (294.5, 61), (364, 70), and (605.5, 88.5) lie on the line given by the equation 5x - 2y = 6.

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Answer:

 Multiplicand ;quantity that is to be multiplied by another (the multiplier).

Multiplier ;person or thing that multiplies.a quantity by which a given number (the multiplicand) is to be multiplied.ECONOMICSthe factor by which the return deriving from an expenditure exceeds the expenditure itself.

Product;an article or substance that is manufactured or refined for sale."marketing products and services"2.MATHEMATICSa quantity obtained by multiplying quantities together, or from an analogous algebraic operation.

Step-by-step explanation:

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Answer:

f ^-1 (x) = 2x+28

Step-by-step explanation:

f(x) = 1/2x-14

Replace f(x) with y

y = 1/2 x -14

Exchange x and y

x = 1/2 y -14

Solve for y

Add 14 to each side

x+14 = 1/2 y -14+14

x+14 = 1/2 y

Multiply each side by 2

2(x+14)= 1/2 y*2

2x+28 = y

The inverse function is

f ^-1 (x) = 2x+28

Answer:

2

Step-by-step explanation:

Answer:

The slope of line p is 3.

The slope of line q is -3.

Step-by-step explanation:

Points on line p  = [tex](x_1,y_2),(x_2,y_2):(1,-1), (0.-4)[/tex]

Slope of line p ,m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-4-(-1)}{0-(1)}=3[/tex]

The slope of line p is 3.

Points on line q  = [tex](x_1,y_2),(x_2,y_2): (0,2), (1,-1)[/tex]

Slope of line q ,m'= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m'=\frac{-1-2}{1-0}=-3[/tex]

The slope of line q is -3.

Answer:

(x + 3)(x + 7)

Step-by-step explanation:

Find two numbers that when added up to , they ALSO have to multiply up to 21. This is simple because of the fact that there is no leading coefficient greater than 1⃣.

Answer:

A.) (x+3)(x+7)

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

The totals of the rows and columns of a two way table are not called marginal distributions. They are called conditional distributions.

Answer:

24

Step-by-step explanation:

1/4 * 48 = 12

12 marbles are red.

48 - 12 = 36

36 of the marbles are blue.

Difference = Blue - Red

Difference  = 36 - 12

Difference = 24

Answer:

10

Step-by-step explanation:

Answer: the answer is 10

Step-by-step explanation:  i took the test and got it right

Answer:

Last option

Step-by-step explanation:

Given expression is:

[tex]\sqrt{\frac{128x^5y^6}{2x^7y^5} }[/tex]

The terms can be simplified one by one

[tex]=\sqrt{\frac{64x^5y^6}{x^7y^5} }[/tex]

As the larger power of x is in numerator, the smaller power will be brought to denominator

[tex]=\sqrt{\frac{64y^6}{x^{(7-5)}y^5}}\\=\sqrt{\frac{64y^6}{x^{2}y^5}}[/tex]

Similarly for y,

[tex]=\sqrt{\frac{64y^{(6-5)}}{x^{2}}}\\=\sqrt{\frac{64y}{x^{2}}}[/tex]

Applying the radical

[tex]\sqrt{\frac{8^2*y}{x^{2}}}\\So\ the\ answer\ will\ be\\= \frac{8\sqrt{y}}{x}[/tex]

So, last option is the correct answer ..

Answer: Last option.

Step-by-step explanation:

You need to apply the Quotient of powers property:

[tex]\frac{a^m}{a^n} =a^{(m-n)}[/tex]

Then:

[tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}} =\sqrt{\frac{64y}{x^2}}[/tex]

Remember that:

[tex]64=8*8=8^2[/tex]

Then you can rewrite the expression:

[tex]=\sqrt{\frac{8^2y}{x^2}}[/tex]

Finally, since [tex]\sqrt[n]{a^n}=a[/tex], you get:

[tex]=\frac{8\sqrt{y} }{x}[/tex]

Answer:

C. 10 units

Step-by-step explanation:

The half diagonals of a rhombus are the legs of a right triangle with the hypotenuse being the side of the rhombus.

EG and FH are the diagonals of the rhombus. The half-diagonals measure 8 and 6.

We can use the Pythagorean theorem to find the hypotenuse length with is the length of the side of the rhombus.

a^2 + b^2 = c^2

8^2 + 6^2 = c^2

64 + 36 = c^2

100 = c^2

c^2 = 100

c = 10

Answer: 10 units

The length of one side of the rhombus is 10 units.

A rhombus is a two dimensional shape which consists of four equal sides with opposite side being parallel and opposite angles being equal.

Given that,

EFGH is a rhombus.

Length of the two diagonals are also given.

EG = 16 and FH = 12

In a rhombus, the diagonals bisect each other at right angles.

Let the intersection point of the diagonals be O.

Consider ΔOFG.

Using Pythagoras Theorem,

(FG)² = (OG)² + (OF)²

OG = EG / 2 = 16 / 2 = 8

OF = FH / 2 = 12 / 2 = 6

(FG)² = 8² + 6²

        = 100

FG = √100 = 10

Hence the length of one side of the rhombus is 10 units.

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Answer:

$82,250 < x <= $171,550

Step-by-step explanation:

You didn't provide all the possible answers.  In this case we don't need to see all answers to help you... but because you didn't provide all the choices for answer, we can't give the exact answer, only the possible range of values.

The question asks for a possible taxable income for someone filing under the 28% bracket.

If we look at the table, we see the 28% bracket is for income ranging from $82,250 (exclusively) to $171,550 (inclusively)

So, your answer has to be within the range:

$82,250 < x <= $171,550

It cannot be $82,250 but it can be $171,550 and any number in between.

Since you didn't provide all the answer choices, we can't tell you if it's B, C, D, and so on... but we can tell you it's not A.

Answer:

C

Step-by-step explanation:

The measure of angle BC of the triangle is given by BC = 130°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔBCD , where it is isosceles

And , the measure of BC ≅ BD

where Isosceles triangle C B D has points on the circle.

The measure of arc CD = 100°

Now , arc length is twice the inscribed angle.

2 x ∠B = CD

2 x ∠B = 100

∠B = 100/2

∠B = 50

Now, in an isosceles triangle, the angle opposite to the equal sides must be equal.

The sum of the three angles must be 180.

x + x + 50 = 180°

2x = 180 - 150

2x = 130°

Hence , the measure of angle BC = 130°

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Answer:

D. It is a function

Step-by-step explanation:

When you flip the points of the function, you have:

(2,1) (4,3) (6,5) (8,7)

Each x value has its own y value, so it is a function

Option D is correct. The inverse of the given function is a function since all the element in its co-domain has a unique element in the domain.

For a mapping to be called a function, it must have but the input values called the domain and the output values known as the co-domain.

All the domains must also have a corresponding co-domain, else it is not a function.

From the given mapping, we can see that all the values in the domain have corresponding values in the co-domain and vice versa(in the case of its inverse).

Hence we can conclude that the inverse of the given function is a function making other options incorrect.

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Answer: X=16

Step-by-step explanation: Add 90 and 22 and you will get 112. Since the beginning of the equation is "7x" which is multiplication you use Inverse Operations. So, you divide the sum, 112, by 7. Your answer will be 16.

Answer:

[tex]25 \div 100 \times 12 = 3[/tex]

[tex]12 - 3 = 9[/tex]

[tex] = 9minutes[/tex]

Answer:

9 minutes

Step-by-step explanation:

Step-by-step explanation:

If (p, 0) and (q, 0) are x-intercepts, then p and q are zeros.

The intercept form of an equation of a quadratic function:

y = a(x - p)(x - q)

p, q - x-intercepts (zeros).

We have the equation: y = 2(x + 4)(x - 6) = 2(x - (-4))(x - 6)

Therefore the x-intercepts are -4 and 6.

The zeros are -4 and 6 too.