Rhea is solving a math puzzle. To find the solution of the puzzle, she must find the product of two numbers. The first number is the sum of 23 and x, and the second number is 18 less than two times the first number. Which of the following functions represents the product of these two numbers?

Opions are:

A.
P(x) = 2x^2 + 74x + 644
B.
P(x) = 2x^2 + 28x - 414
C.
P(x) = 2x^2 + 102x + 1,288
D.
P(x) = 2x^2 + 110x + 1,472

[tex]x+40=3x\\2x=40\\x=20[/tex]

For this case we have by definition of angles between secant lines that:

[tex]x + 40 = 3x[/tex]

Also, the angle between T and V is equal to the angle between S and W.

Returning to the question, we have to:

[tex]x + 40 = 3x[/tex]

We must know the value of "x":

Subtracting 3x on both sides of the equation we have:

[tex]x-3x + 40 = 0[/tex]

Subtracting 40 from both sides of the equation:

[tex]-2x = -40[/tex]

Dividing between -2 on both sides of the equation:

[tex]x = \frac {-40} {- 2}\\x = 20[/tex]

So, the value of x is 20

Answer:

[tex]x = 20[/tex]

Answer:

An average of 661 people per day.

Step-by-step explanation:

1. 365-7= 358

2. 236,758/ 358= 661.3351

3. Round to 661

Answer:

A. 3,1,1/3,1/9,1/27 because you are multiplying by 1/3 every time to get new term.

C. 1,6,36,216,1296 because you are multiplying by 6 every time to get new term.

The other sequences you are not multiplying repeatedly to get new terms..

Step-by-step explanation:

The sequence is geometric sequence is 3, 1, 1/3, 1/9, and 1/27.

The sequence is a geometric sequence that is 1, 6, 36, 216, 1, 296.

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

If the common ratio between the two successive terms must be constant. Then the sequence is called a geometric sequence.

The sequences are given below;

3, 1, 1/3, 1/9, 1/27

The common ratio between the terms are;

[tex]\rm \dfrac{a_2}{a_1}=\dfrac{1}{3}\\\\\dfrac{a_3}{a_2}=\dfrac{\dfrac{1}{3}}{1}= \dfrac{1}{3} \times \dfrac{1}{1}=\dfrac{1}{3}\\\\\dfrac{a_4}{a_3}=\dfrac{\dfrac{1}{9}}{\dfrac{1}{3}}=\dfrac{3}{9}=\dfrac{1}{3}[/tex]

The sequence is a geometric sequence.

The sequences are given below;

1, 6, 36, 216, 1, 296.

The common ratio between the terms are;

[tex]\rm \dfrac{a_2}{a_1}=\dfrac{6}{1}=6\\\\\dfrac{a_3}{a_2}=\dfrac{36}{6}=6\\\\ \dfrac{a_4}{a_3}=\dfrac{216}{36}=6\\[/tex]

The sequence is a geometric sequence.

More about the sequence link is given below.

brainly.com/question/21961097

#SPJ2

Answer:

Option C is correct.

Step-by-step explanation:

Slope of line JK

J (1,-6) K (0,4)

slope of JK = y₂ - y₁ / x₂ - x₁

Slope of JK = 4-1/0-(-6) = 3/6 = 1/2

so slope of JK = 1/2

Slope of line LM

L (-5,-3) and M(0,3)

slope of LM = y₂ - y₁ / x₂ - x₁

slope of LM = 3-(-5)/0-(-3) = 3+5/3 = 8/3

Slope of line NO

N(-6,-5) and 0 (0,0)

slope of NO = y₂ - y₁ / x₂ - x₁

slope of NO = 0-(-6)/0-(-5) = 6/5

So, slope of line NO = 6/5

Slope of PQ

P(-5,4) Q(0,-2)

slope of PQ = y₂ - y₁ / x₂ - x₁

slope of PQ = -2-4/0-(-5) = -2/5

so slope of line PQ = -2/5

the two lines are perpendicular if slope of one line is m then slope of other line is -1/m

The slope of given line =m= -5/6

The slope of line perpendicular to the given line = -1/m = 6/5

So, line NO is perpendicular to the given line as its slope is 6/5

Option C is correct.

The answer is [tex]\( 24xy^2 \)[/tex].

To solve the expression [tex]\( 3x \cdot 8y^4 \)[/tex], we first multiply the coefficients and the variables separately. The coefficients are 3 and 8, and when multiplied, they give us 24. For the variables, we multiply x by [tex]\( y^4 \)[/tex], keeping in mind that when multiplying exponents with the same base, we add the exponents. Therefore, [tex]\( x \cdot y^4 \)[/tex] remains [tex]\( xy^4 \)[/tex].

Combining the coefficient and the variables, we get \( 24xy^4 \). However, we can simplify this further by recognizing that any variable raised to the power of 1 is simply the variable itself. Thus, [tex]\( xy^4 \)[/tex] is equivalent to [tex]\( xy^2 \)[/tex] because [tex]\( y^1 \)[/tex] is just [tex]\( y \)[/tex].

So the final simplified expression is [tex]\( 24xy^2 \)[/tex].

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y=-\left|x\right|+2[/tex]

we know that

The graph is inverted V-shaped.

The x-intercepts are the points (-2,0) and (2,0)

The vertex is the point (0,2)

The domain is all real numbers

The range is all real numbers less than or equal to 2

using a graphing tool

The graph in the attached figure

Answer:

[tex]\large\boxed{y=2\pm\sqrt{28+4x}}[/tex]

Step-by-step explanation:

[tex]2(x-2)^2=8(7+y)\\\\\text{exchange x to y, and vice versa:}\\\\2(y-2)^2=8(7+x)\\\\\text{solve for y:}\\\\2(y-2)^2=(8)(7)+(8)(x)\\\\2(y-2)^2=56+8x\qquad\text{divide both sides by 2}\\\\(y-2)^2=28+4x\iff y-2=\pm\sqrt{28+4x}\qquad\text{add 2 to both sides}\\\\y=2\pm\sqrt{28+4x}[/tex]

Answer:

y is inverse:  2 ±[tex]\sqrt{28+ 4x}[/tex] .

Step-by-step explanation:

Given: 2(x - 2)²=8(7+y)​.

To find: Find inverse.

Solution : We have given

2(x - 2)²=8(7+y)​.

Step 1: inter change the x and y.

2(y - 2)²=8(7+x)​.

Step 2:

Solve for y

On dividing both sides by 2

(y - 2)² = 4 (7+x)​.

Distributes 4 over ( 7 + x)

(y - 2)² =  28 + 4x

Taking square root both sides.

[tex]\sqrt{(y-2)^{2} } = ±\sqrt{28+ 4x}[/tex].

y - 2 =  ±[tex]\sqrt{28+ 4x}[/tex].

On adding both sides by 2

y =  + 2 ±[tex]\sqrt{28+ 4x}[/tex] .

Therefore, y is inverse : 2 ± [tex]\sqrt{28+ 4x}[/tex].

[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-1})~\hspace{10em} slope = m\implies \cfrac{2}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-1)=\cfrac{2}{5}[x-(-3)]\implies y+1=\cfrac{2}{5}(x+3) \\\\\\ y+1=\cfrac{2}{5}x+\cfrac{6}{5}\implies y=\cfrac{2}{5}x+\cfrac{6}{5}-1\implies y=\cfrac{2}{5}x+\cfrac{1}{5}[/tex]

Answer:

Step-by-step explanation:

y - 3 = -4(x - 5)

Add 3 to both sides to isolate y

y = -4 ( x - 5 ) + 3

Distribute

y = -4x +20 + 3

Combine like terms

y = -4x + 23

y = mx + b is standard form for which m is slope

m = -4

Please mark for brainliest!! :D Thanks!!

If you have any questions or need more information, please comment below and I'll respond asap!!

Answer:

-4

Step-by-step explanation:

Distribute -4 into the parenthesis and get -4x + 20. The number paired with x is the slope, usually represented by m in y = mx + b. So, the slope is -4. For the full slope intercept format, move the -3 on left side to the right by adding 3. The new equation is y = -4x + 23.

Answer:

[tex]24\sqrt{5}\ yards[/tex]

Step-by-step explanation:

Let A1 be the area of one square and A2 be the area of second square

So,

A1 = s^2

where s is side of square

[tex]s^2=125\\\sqrt{s^2}=\sqrt{125}\\s=\sqrt{25*5}\\ s= \sqrt{5^2 * 5}\\ s= 5\sqrt{5}[/tex]

So side of one square is [tex]5\sqrt{5}[/tex]

To calculate the length of fence we need to find the perimeter of the square

So,

P1 = 4 * s

[tex]=4*5\sqrt{5} \\=20\sqrt{5}[/tex]

For second square:

[tex]A_2=s^2\\5=s^2\\\sqrt{s^2}=5\\{s}=\sqrt{5}[/tex]

The perimeter will be:

[tex]P_2 = 4*s\\=4 * \sqrt{5} \\=4\sqrt{5}[/tex]

So the total fence will be: P1+P2

[tex]= 20\sqrt{5}+4\sqrt{5} \\= 24\sqrt{5}\ yards[/tex]

Answer:

The fifth term is 620

Step-by-step explanation:

y=40×(-2)^(n-1)​

The 5th terms means n=5

y = 40 * (-2) ^ (5-1)

  = 40 * (-2) ^4

  = 40 * (16)

  = 640

[tex]x(x-3)=x\\x^2-3x-x=0\\x^2-4x=0\\x(x-4)=0\\x=0\vee x=4[/tex]

[tex]\text{Hey there!}[/tex]

[tex]\text{In order for you can do the distributive property then work from there}[/tex]

[tex]\text{x(x - 4) = x}\\\\\text{x(x)=x}^2\\\\\text{x(-3)= -3x}[/tex]

[tex]\text{Subtract by the value of x on your sides!}[/tex]

[tex]\text{Your new equation becomes: x}^2\text{- 3x = x}[/tex]

[tex]\text{Like}\downarrow[/tex]

[tex]\text{x}^2\text{- 3x - x = x - x}[/tex]

[tex]\text{x - x = 0 }[/tex]

[tex]\text{-3x + (-1x) = -4x}[/tex]

[tex]\text{Our equation becomes: x}^2\text{- 4x = 0}[/tex]

[tex]\text{Next, we have to FACTOR on the LEFT side of your equation}[/tex]

[tex]\text{x(x - 4) = 0}[/tex]

[tex]\text{Set the numbers to FACTOR out to 0}[/tex]

[tex]\text{Like: x = 0 or x - 4 = 0}\text{ (solve that and you SHOULD have the x-values)}[/tex]

[tex]\boxed{\boxed{\bf{Answer: x = 0\ or \ x =4}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirt:)}[/tex]

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

3 times the square root of 2 +2 times the square root of 3 =3sqrt2+2sqrt3

We need to simplify the above expression.

In addition and subtraction, there is a rule of adding or subtracting of like terms is possible only.

But, here, √2 ad √3 are unlike term.

so, we cannot simplified it.

Hence, Option 'D' is correct.

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

Step-by-step explanation:

3√2 + 2√3 is as simple an expression as you'll get for this quantity.

Answer:

-9

Step-by-step explanation:

find the value of i2, which is -9, find the value of i7, which is 6

Then, add them together and multiply by the number of terms in the sequence divided by 2 (6/2=3)

Answer:

0.50

Step-by-step explanation:

we know that

Observing the graph

we have the following points

(1,3),(2,4),(3,9),(4,7),(5,2),(6,18)

Using a Excel tool (Correl function)

The correlation coefficient is equal to r=0.605639

see the attached table

therefore

The correlation coefficient that best matches the data plotted on the graph is 0.50

Answer:

11

Step-by-step explanation:

In this problem we have the following expression

[tex]a + b^2[/tex]

Note that it depends on two variables a and b

Evaluating the expression for a = 2 and b = 3 means that you must replace the variable "a" with the number 2, and you must replace the variable "b" with the number 3

So we have that:

[tex]a + b^2 = 2 + 3^2[/tex]

[tex]a + b^2 = 2 +9[/tex]

[tex]a + b^2 = 11[/tex]

Finally the answer is 11

Answer:

Step-by-step explanation:

Since it's a division we need to look for a common factor to cancel

so first we try to break the numbers to there prime factors

[tex]\frac{\sqrt{10} }{4\sqrt{8} } = \frac{\sqrt{2.5} }{4\sqrt{2.2.2} }[/tex]

So , now we try to factors that are common in top and bottom

[tex]= \frac{\sqrt{2} \sqrt{5}}{4\sqrt{2}\sqrt{4} }[/tex]

common factor is sqrt 2 so lets cancel it

we get

[tex]\frac{\sqrt{5} }{4\sqrt{4} }[/tex]

[tex]\frac{\sqrt{5} }{8}[/tex]

Answer:

y=2

x=5

Step-by-step explanation:

[tex]a_n=3n-10[/tex]

Answer:

an = -7 + (n - 1) 3

Step-by-step explanation:

Answer:

AAS

Step-by-step explanation:

Given one pair of congruent angles and one pair of congruent sides.

When two lines intersect they form a pair of congruent angles (vertical angles are equal)

So the two triangles are congruent by AAS.

Answer: AAS

Step-by-step explanation:

By the figure we can say that the have one side equal. Now for the angles we have that in the part of the triangles are touching we have an oposite angles then these two angles have to be equals. Finally the two triangles have two equal angles and ones equal side. we can conclude that the correct method is AAS.

Answer:

32

Step-by-step explanation:

Substitute n = 4 into the formula

[tex]a_{4}[/tex] = 2 × [tex]4^{4-2}[/tex] = 2 × 4² = 2 × 16 = 32

Answer:

Answer is [tex]\sqrt{13}-\sqrt{11}[/tex]

Step-by-step explanation:

We need to divide

[tex]\frac{2}{\sqrt{13}+\sqrt{11}}[/tex]

For solving this, we need to multiply and divide the given term with the conjugate of [tex]{\sqrt{13}+\sqrt{11}[/tex]

The conjugate is: [tex]{\sqrt{13}-\sqrt{11}[/tex]

Solving

[tex]=\frac{2}{\sqrt{13}+\sqrt{11}} *\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}} \\=\frac{2(\sqrt{13}-\sqrt{11})}{(\sqrt{13}+\sqrt{11})(\sqrt{13}-\sqrt{11})}\\We\,\, know\,\, that\,\, (a+b)(a-b) = a^2-b^2\\=\frac{2(\sqrt{13}-\sqrt{11})}{(\sqrt{13})^2-(\sqrt{11})^2}\\=\frac{2(\sqrt{13}-\sqrt{11})}{13-11}\\=\frac{2(\sqrt{13}-\sqrt{11})}{2}\\=\sqrt{13}-\sqrt{11}[/tex]

So answer is [tex]\sqrt{13}-\sqrt{11}[/tex]

Answer:

The correct Answer is D[tex]\sqrt{13} - \sqrt{11}[/tex]

Step-by-step explanation:

Answer:

The vertex is: [tex](\frac{3}{2},\ \frac{7}{2})[/tex]

The axis of symmetry is:

[tex]x=\frac{3}{2}[/tex]

Step-by-step explanation:

For a quadratic equation of the form:

[tex]y=ax^2 + bx +c[/tex]

The vertex of the parabola will be the point: [tex](-\frac{b}{2a},\ f(-\frac{b}{2a}))[/tex]

In this case we have the following equation:

[tex]y= -2x^2+6x-1[/tex]

Note that:

[tex]a=-2\\b=6\\c=-1[/tex]

Then the x coordinate of the vertex is:

[tex]x=-\frac{b}{2a}[/tex]

[tex]x=-\frac{6}{2(-2)}[/tex]

[tex]x=\frac{3}{2}[/tex]

Then the y coordinate of the vertex is:

[tex]y= -2(\frac{3}{2})^2+6(\frac{3}{2})-1[/tex]

[tex]y=\frac{7}{2}[/tex]

The vertex is: [tex](\frac{3}{2},\ \frac{7}{2})[/tex]

For a quadratic function the axis of symmetry is always a vertical line that passes through the vertex of the function.

Then the axis of symmetry is:

[tex]x=\frac{3}{2}[/tex]

Step-by-step explanation:

All three sides are equal, so this is an equilateral triangle.

Answer:

This is an equilateral triangle

Step-by-step explanation:

All three sides are equal, making it equilateral

Answer:

Center of the circle= (-9,6)

Radius = 5 units

Step-by-step explanation:

Once the equation of the circle has been written in the format

(x-h)²+(y-k)²=r² , (h,k) is the center while r is the radius of the circle.

From the given equation, -h=9 therefore h= -9.

-k = -6 therefore k = 6. r² = 25 therefore r= √25=5

Center of the circle= (-9,6) radius = 5 units

Answer:

One globe costs $60.79

Step-by-step explanation:

The area of the globe is

A = 4.π.r^2

Since the radius is 11 inches

A = 4*(3.14)*(11 in)^2 = 1519.76 in^2

We apply a rule of three

1 in^2  --------------------------------- $0.04

1519.76 in^2 ------------------------- x

x = (1519.76 in^2/ 1 in^2)*$0.04

x = (1519.76)*$0.04

x = $60.79

x ≈ $60.8

Answer: Second Option

$60.79

Step-by-step explanation:

To solve this problem let's suppose that the balloons are spherical

Then the surface area of a sphere is given by the formula:

[tex]SA=4\pi r^2[/tex]

Where r is the radius of the sphere

In this case we know that the radius of each globes is 11 inches, then:

[tex]SA=4(3.14) (11)^2[/tex]

[tex]SA=4(3.14)(121)[/tex]

[tex]SA=1519.76\ in^2[/tex]

If the material to make globes costs $ 0.04 per square inch then the cost of a globes is:

[tex]C=1519.76*0.04[/tex]

[tex]C=\$60.79[/tex]

Answer:

The area is 0.015m²

Step-by-step explanation:

Step one

Given that the expression for area of the circle is A = π r²

Step two

Now our raduis r= 7cm - - - meter =7/100= 0.07

And Pi = 3.142

Step three

Substituting r in the formula for area we have

A= 3.142*(0.07)²

A=3.142*0.0049

A= 0.015m²

Answer:

The coordinates of the point in question is (1, 3).

Step-by-step explanation:

Point (-1, 7) is above and to the left of the point (4, -3). The point in question is to the right and below the point (-1, 7).

What will be the horizontal distance between the point (-1, 7) and the point in question?

The horizontal distance between the point (-1, 7) and (4, -3) is 5. Let the horizontal distance between the point (-1, 7) and the point in question be [tex]a[/tex]. Let the horizontal distance between the point in question and point (4, -3) be [tex]b[/tex].  

[tex]\displaystyle \frac{a}{b} = \frac{2}{3}[/tex].

[tex]\displaystyle a = \frac{2}{3} \; b[/tex].

[tex]\displaystyle b = \frac{3}{2}\; a[/tex].

However,

[tex]a + b = 5[/tex].

[tex]\displaystyle a + \frac{3}{2}\; a = 5[/tex].

[tex]\displaystyle \frac{5}{2}\; x= 5[/tex].

[tex]a = 2[/tex].

In other words, the point in question is 2 units to the right of the point (-1, 7). The x-coordinate of this point shall be [tex]-1 + 2 = 1[/tex].

The vertical distance between the point (-1, 7) and the point (4, -3) is 10. Similarly, the point in question is [tex](2/5) \times 10 = 4[/tex] units below the point (-1, 7). The y-coordinate of this point will be [tex]7 - 4 = 3[/tex].

Thus, the point in question is (1, 3).

Answer:

To solve our given problem we will use section formula :]

Section Formula states that, when a point divides a line segment internally in the ratio m:n, So the coordinates are :]

[tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{m. {x}_{2} +n. {x}_{1} }{m + n} ,y= \frac{m. {y}_{2} +n. {y}_{1} }{m + n} \bigg \rgroup \\ \\ \\ [/tex]

Let

(-1 , 7) = (x₁ , y₁)

(4 , -3) = (x₂ , y₂)

m = 2

n = 3

[tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{2 \times 4 +3 \times - 1 }{2 + 3} ,y= \frac{2 \times - 3 +3 \times 7}{2 + 3} \bigg \rgroup \\ \\ \\ [/tex]

[tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{8 - 3 }{2 + 3} ,y= \frac{ - 6 +21}{2 + 3} \bigg \rgroup \\ \\ \\ [/tex]

[tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{5 }{5} ,y= \frac{15}{5} \bigg \rgroup \\ \\ \\ [/tex]

[tex]\tiny: \implies (x,y) = \bigg \lgroup x = 1,y= 3 \bigg \rgroup \\ \\ [/tex]

Answer:

x =3

Step-by-step explanation:

5(x + 1) = 4x + 8

Distribute the 5

5x+5 = 4x+8

Subtract 4x from each side

5x-4x+5 = 4x-4x+8

x+5 =8

Subtract 5 from each side

x+5-5 = 8-5

x =3

Answer:B

f(0)=0

Step-by-step explanation:

when 0 is squared it’s just 0

Answer: option b.

Step-by-step explanation:

Given the function f(x):

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

In order to find [tex](fof)(x)[/tex], the first thing you must do is to substitute the function f(x) into the same  function f(x). Observe the procedure:

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

Now, you need to simplify:

[tex](fof)(x)=x^4[/tex]

Finally, to find  [tex](fof)(0)[/tex] you need to substitute  [tex]x=0[/tex] into  [tex](fof)(x)=x^4[/tex], then you get:

 [tex](fof)(0)=(0)^4[/tex]

 [tex](fof)(0)=0[/tex]