which point is the image P

Answer:

Part A: x^2 + 6x + 8 = 0 use the factoring the equation method

Part A: x^2 + 6x + 8 = 0 use the quadratic formula

Step-by-step explanation:

Part A;

The equation is  x^2 + 6x + 8 = 0 , looking at this quadratic expression, you notice it is written in a quadratic equation standard form  of ax^2+bx+c=0. Additionally, you notice that can find what multiplied to get the quadratic equation,factor.You can identify two numbers that multiply to get ac and add to give b.In this question;

a=1,b=6,c=8

ac=8

The numbers are 4 and 2. Factoring the equation method will give;

x²+6x+8=0

x²+4x+2x+8=0

x(x+4)+2(x+4)=0

(x+2)+(x+4)=x²+6x+8

x+2=0, x=-2  and x+4=0, x=-4

Part B

The quadratic equation is ;

x²+6x-11=0

You notice that there are no factors that multiply direct to get the quadratic equation like in part 1. When you observe, a=1, b=6 and c=-11

ac=1×-11=-11 and b=6 .You notice there are no factors that multiply to give -11 and add to get 6, hence the factorizing the equation method can not be used.However, you can apply the quadratic formula that requires coefficients. You have a=1, b=c and c=-11 as the coefficients to use in the quadratic formula.

Answer:

Part A  -  use the factor method

Part B - use the quadratic equation

Step-by-step explanation:

Thinking process:

Let's look at the two parts in the problem:

Part A: x^2 + 6x + 8 = 0

This is a quadratic equation. Now, the product of the first and last term produces 8x². This product is a common multiple of 4 x and 2 x. These numbers can be added to get the middle term: 6x. Hence the equation can be solved by factorization.

Part B: x^2 + 6x - 11 = 0

Part B is also a quadratic equation. This equation can be analysed as follows:

The product of the first and last product gives -22x². Two factors are possibe: -11x and 2x or -2x and 11 x. These factors wjhen added or subtracted do not give the middle term (6x). Hence factorization will not work.

The best way to solve the equation is to use the quadratic formula:

[tex]x= \frac{-b+/-\sqrt{b^{2}-4ac } }{2a}[/tex]

Answer:

Step-by-step explanation:

[tex](g-f)(x)=g(x)-f(x)\\\\f(x)=4-x,\ g(x)=6x\\\\(g-f)(x)=6x-(4-x)=6x-4-(-x)=6x-4+x=7x-4\\\\(g-f)(3)-\text{put}\ x=3\ \text{to the expression}\\\\(g-f)(3)=7(3)-4=21-4=17[/tex]

Answer:

The son is 8 years old

The father is 32 years old

Step-by-step explanation:

Let the man age be x

Let the son age = y

Right now the man is four times as older as his son = x=4y

In four years time he will be three times as old. ⇒x+4 =3(y+4)

Now substitute the value x=4y in x+4=3(y+4)

x+4=3(y+4)

4y+4=3(y+4)

4y+4=3y+12

Combine the like terms:

4y-3y =12-4

y=8

If the son is 8 years old than;

x=4y

x=4(8)

x=32

Father will be 32 years old....

Answer:

Present age of son: 8 years.

Present age of father: 32 years.

Step-by-step explanation:

Let x represent present age of the son and y represent present age of father.

We have been given that a man is four times as older as his son. 4 times of age of son would be [tex]4x[/tex].

We can represent this information in an equation as:

[tex]y=4x[/tex]

We are also told that in four years time he will be three times as old.

Age of father in 4 years would be [tex]y+4[/tex].

We can represent this information in an equation as:

[tex]y+4=3(x+4)[/tex]

Upon substituting [tex]y=4x[/tex] in 2nd equation, we will get:

[tex]4x+4=3(x+4)[/tex]

[tex]4x+4=3x+12[/tex]

[tex]4x+4-4=3x+12-4[/tex]

[tex]4x=3x+8[/tex]

[tex]4x-3x=3x-3x+8[/tex]

[tex]x=8[/tex]

Therefore, the present age of son is 8 years.

Upon substituting [tex]x=8[/tex] in equation [tex]y=4x[/tex], we will get:

[tex]y=4x\Rightarrow 4(8)=32[/tex]

Therefore, the present age of father is 32 years.

[tex]\bf \begin{array}{ccll} gallons&minutes\\ \cline{1-2} 4.39&1\\ 280&x \end{array}\implies \cfrac{4.39}{280}=\cfrac{1}{x}\implies 4.39x=280\implies x=\cfrac{280}{4.39} \\\\\\ x\approx \stackrel{\textit{minutes}}{63.78}~\hspace{7em}63.78 ~~\begin{matrix} min \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \cdot \cfrac{hr}{60 ~~\begin{matrix} min \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ } \implies \boxed{1.063~hr}[/tex]

Answer:

B. (x-4)^2 + (y - 3)^2 = 5^2

Step-by-step explanation:

The equation for a circle is given by

(x-h)^2 + (y-k) ^2 = r^2

where (h,k) is the center and r is the radius

We have a center of (4,3) and a radius of 5

(x-4)^2 + (y-3) ^2 = 5^2

Answer:

Step-by-step explanation:

i believe it is 4.

assuming feburary it snowed about 8.5 inches and in november it is at about the 3 in line you would subtract to get about 5.5 inches

Answer:

4) 5.4 inches

Step-by-step explanation:

5.4 inches of snow fell in February 1889 than November 1888.

According to the graph:

Feb '89: 8.5 inches

Nov '88: 3 inches

8.5 - 3 = 5.5 or 5.4.

Answer:

3 + 2i

Step-by-step explanation:

3 + √(-4) = 3 + i√4 = 3 + 2i

Recall that √(-1) = i

Answer:

The correct answer is B⊂A.

Step-by-step explanation:

The sets are:

A={x|x is a polygon}

B={x|x is a triangle}

According to the given sets Option 2 is correct:

The correct option is B⊂A.. We will read it as B is a subset of A.

The reason is that the Set A contains polygon and Set B contains triangle. A triangle is also a simplest form of polygon having 3 sides and 3 angles but a polygon has many other types also. Like hexagon, pentagon, quadrilateral etc. All the triangles are included in the set of polygon.

Thus the correct answer is B⊂A....

For this case we have that by definition of multiplication of powers of the same base, the same base is placed and the exponents are added:

[tex]a ^ n * a ^ m = a ^ {n + m}[/tex]

So, we can rewrite the given expression as:

[tex]8 ^ {3-5 + y} = \frac {1} {8 ^ 2}\\8 ^ {- 2 + y} = \frac {1} {8 ^ 2}[/tex]

So, if [tex]y = 0[/tex]:

[tex]8 ^ {- 2} = \frac {1} {8 ^ 2}\\\frac {1} {8 ^ 2} = \frac {1} {8 ^ 2}[/tex]

Equality is met!

Answer:

[tex]y = 0[/tex]

Answer:

Value of y=0

Step-by-step explanation:

We need to solve

[tex]8^3*8^{-5}*8^y=1/8^2[/tex]

We know that 1/a^2 = a^-2

[tex]8^3*8^{-5}*8^y=8^{-2}[/tex]

[tex]8^y=\frac{8^{-2}}{8^3*8^{-5}}\\8^y=\frac{8^{-2}}{8^{3-5}}\\8^y=\frac{8^{-2}}{8^{-2}}\\8^y=1[/tex]

Taking ln on both sides

[tex]ln(8^y)=ln(1)\\yln(8)=ln(1)\\y= ln(1)/ln(8)\\We\,\,know\,that\,\,ln(1) =0\\y=0[/tex]

So, value of y=0

Answer:

328 pages for the novel

123 pages for the second day

Step-by-step explanation:

Let the number of pages of the novel = x

Raw Equation

(1/4)x + 1/2 (3/4)x + 123 = x

Solution

(1/4)x + (3/8)x+ 123 = x

Change the fractions to common denominators.

(2/8)x + (3/8)x + 123 = x

Add the fractions.

(2/8 + 3/8)x + 123 = x

Subtract (5/8)x from both sides.

(5/8)x + 123 = x

(5/8)x- (5/8)x + 123 = x - (5/8)x

Multiply both sides by 8

123 = (3/8)x  

123 * 8 = 3x

Divide by 3

984 = 3x

984/3 = 3x / 3

328 = x

===================

At the end of the second day, she read 3/8 * 328 = 123 pages.

The novel has 328 pages. By the end of the second day, the student had read 205 pages of the novel.

The student's schoolwork question can be addressed by setting up and solving algebraic equations. Let's denote the total number of pages in the novel as x. On the first day, one-quarter of the novel is read, which is x/4 pages. So, there are 3x/4 pages remaining. On the second day, half of the remaining pages are read, which is (1/2) × (3x/4) = 3x/8 pages. On the third day, the student reads the last 123 pages, which were all the pages that were left. Therefore, the equation to solve for x is:

x - (x/4 + 3x/8) = 123

We can solve this equation to find out the total number of pages in the novel:

First, let's find a common denominator for the fractions. It is 8.

8x/8 - (2x/8 + 3x/8) = 123

8x/8 - 5x/8 = 123

3x/8 = 123

Let's multiply both sides of the equation by 8/3 to solve for x.

x = 123 × (8/3)

x = 328

The novel has 328 pages.

To find out how many pages were read by the end of the second day, we add the amount read on the first and second days:

(x/4) + (3x/8) = (2x/8) + (3x/8) = 5x/8

5x/8 when x = 328 is:

(5 × 328)/8 = 205

By the end of the second day, 205 pages were read.

Answer:

30 square units

Step-by-step explananation:

First of all we need to know the formula to finding the perimeter of a rectangle which is:

P = 2 x L(Length) + 2 x h(Height)

12 and 3 are apart by 12 - 3

12 - 3 = 9

Then, we subtract 9 from 3 ( :

9 - 3 = 6)

To get 6 as our answer.

6 will be the width and 9 will be the length.

Now we solve for the perimeter by plugging in our values into our formula:

P = 2(9) + 2(6)

P = 18 + 12

P = 30 square units

Answer:

y is 90

Step-by-step explanation:

The y/x is proportional per point (x,y) since this is a direct variation.

That is ,

[tex]\frac{30}{-3}=\frac{y}{-9}[/tex].

Cross multiply:

[tex]30(-9)=y(-3)[/tex]

Simplify:

[tex]-270=-3y[/tex]

Divide both sides by -3

[tex]\frac{-270}{-3}=y[/tex]

[tex]90=y[/tex]

Answer:

Look at the picture

Hope it helps ;)

Answer:

The catcher will have to throw roughly 127 feet from home to second base.

Step-by-step explanation:

We have to use the Pythagorean Theorem. This gives us the third side length if we know the other two side lengths.

a² + b² = c²

90² + 90² = c²

8100 + 8100 = c²

16200 = c²

[tex]\sqrt{16200}[/tex] = [tex]\sqrt{c^2}[/tex]

c = 127.28 ft

Answer:

[tex]\displaystyle 256[/tex]

Step-by-step explanation:

PEMDAS

P-parenthesis, E-exponent, M-multiply, D-divide, A-add, and S-subtracting.

Exponent rule: [tex]4^8^-^4[/tex]

Subtract by the exponent from left to right.

[tex]\displaystyle 8-4=4[/tex]

[tex]\displaystyle 4^4=4*4*4*4=256[/tex]

256 is the correct answer.

B. You walk down 10 flights of stairs

The situation that can be represented by the opposite of 10 is B. You walk down 10 flights of stairs. The concept of 'opposite' here refers to the negative version of a number, which, in this case, would be -10. When you climb up 10 flights of stairs, that's a positive movement upward, analogous to a positive 10. However, walking down 10 flights is the opposite direction, corresponding to -10. Similarly, a temperature rise or a plant growing represents an increase, not the opposite of 10.

Answer:

False

Step-by-step explanation:

A counterexample goes against what you said in the conjecture. An example of a counterexample in this case would be that your dog ate a burger, which is not dog food, last night.

Answer and Explanation:

Given : Consider the relationship [tex]3r+2t=18[/tex]

To find :

A.  Write the relationship as a function r=f(t)

B. Evaluate f(-3)

C. Solve f(t)= 2

Solution :

A) To write the relationship as function r=f(t) we separate the r,

[tex]3r+2t=18[/tex]

Subtract 2t both side,

[tex]3r=18-2t[/tex]

Divide by 3 both side,

[tex]r=\frac{18-2t}{3}[/tex]

The function is [tex]f(t)=\frac{18-2t}{3}[/tex]

B) To evaluate f(-3) put t=-3

[tex]f(-3)=\frac{18-2(-3)}{3}[/tex]

[tex]f(-3)=\frac{18+6}{3}[/tex]

[tex]f(-3)=\frac{24}{3}[/tex]

[tex]f(-3)=8[/tex]

C) Solve for f(t)=2

[tex]\frac{18-2t}{3}=2[/tex]

[tex]18-2t=6[/tex]

[tex]2t=12[/tex]

[tex]t=\frac{12}{2}[/tex]

[tex]t=6[/tex]

The value of f(-3), to write the relationship as a function (r = f(t)) and to solve the (f(t) = 2) expression, arithmetic operations can be use. Refer the below calculation for better understanding.

Given :

3r + 2t = 18

A) 3r = 18 - 2t

[tex]r = 6-\dfrac{2t}{3}[/tex]   ---- (1)

where,   [tex]\rm f(t)=6-\dfrac{2t}{3}[/tex]   ----- (2)

B)   [tex]r = 6-\dfrac{2t}{3}[/tex]

Given that f(-3) imply that t = -3. So from equation (2) we get

f(-3) = 8

C) Given that f(t) = 2. So from equation (2) we get,

[tex]2 = 6 -\dfrac{2t}{3}[/tex]

2t = 12

t = 6

The value of f(-3), to write the relationship as a function (r = f(t)) and to solve the (f(t) = 2) expression, arithmetic operations can be use.

For more information, refer to the link given below:

https://brainly.com/question/21114745

Answer:

60 inches squared

Step-by-step explanation:

The formula for the area of a triangle is as follows:

[tex]A=\frac{1}{2} bh[/tex]

Where A=area, b=base, and h=height.

Plug in 15 for your base and 8 for your height and solve.

[tex]A=\frac{1}{2} (15)(8)\\A=7.5(8)\\A=60[/tex]

Answer:

B) 60 squared inches

Step-by-step explanation:

To find the area of a triangle you have to use this equation:

A = 1/2 b*h

Now plug in the numbers,

A = 1/2 15*8

15*8 = 120

1/2 of 120 = 60

A = 60

The area of this triangle is 60 squared inches.

Answer:

32

Step-by-step explanation:

I assume you want to find the pills per month?  You know that you take 8 pills per week, and there are 4 weeks in a month.  So:

8 pills/week × (4 week / month) = 32 pills/month

Answer:

Let x be the number of guest and y be the quantity of meat,

According to the question,

[tex]y\geq \frac{x}{3}-2[/tex]

Since, the related equation of the above inequality,

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

Having x-intercept = (6,0),

y-intercept = (0,-2)

Also,'≥' shows the solid line,

Now, 0 ≥ 0/3 - 2  ( true )

Hence, the shaded region of above inequality will contain the origin,

Therefore, by the above information we can plot the graph of the inequality ( shown below ).

Answer:

Its the 4th graph.

Step-by-step explanation:

Answer:

The surface area of the structure is [tex]SA=2,500\pi\ m^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of a sphere is equal to

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

In this problem we have

[tex]r=50/2=25\ m[/tex] -----The radius is half the diameter

substitute

[tex]SA=4\pi (25)^{2}[/tex]

[tex]SA=2,500\pi\ m^{2}[/tex]

Step-by-step explanation:

Definition:

A pyramid is a polyhedron formed by connecting a one polygonal base and a point, called the apex. Each base edge and apex form a triangle.

A) A pyramid has only one base.   TRUE   (definition)

(look at any photo with the pyramid)

B) The base of a pyramid is a polygon.   TRUE    (definition)

(look at any photo with the pyramid)

C) If the altitude of a right pyramid and the apothem of the base are known, then the Pythagorean theorem can be used to find its slant height.   TRUE

(look at the picture)

D) The slant height is always the same length as the base of the pyramid.

FALSE

E) The lateral faces of a pyramid are rectangles.   FALSE   (definition)

(the lateral faces of a pyramid always are triangles)

F) The slant height is used to calculate the lateral area.   TRUE

(the lateral faces of a pyramid are triangles. The formula of an area of a triangle is A = (bh)/2. Where b - base of triangle, h - height of triangle)

Answer:

A: pyramid has only one base.

B: The base of a pyramid is a polygon.

C: If the altitude of a right pyramid and the apothem of the base are known, then the Pythagorean theorem can be used to find its slant height.

F: The slant height is used to calculate the lateral area.

Answer:

The correct option is Option B.   $1293

Step-by-step explanation:

It is given that,the cost function for Judy’s new clothing store where she sells t-shirts is c=$11.50n + 925.  She sells 32 t-shirts this month

To find the total cost for this month

cost for n shirt , c=$11.50n + 925

 Cost for 32 shirts = 11.50 * 32 + 925

 =  368 + 925

 = 1293

Therefore the total cost = $1293

The correct answer is option B.  $1293

Answer:

a=3

b=24

Step-by-step explanation:

If [tex]x^2+x-12[/tex] is a factor of [tex]x^3+ax^2-10x-b[/tex], then the factors of [tex]x^2+x-12[/tex] must also be factors of [tex]x^3+ax^2-10x-b[/tex].

So what are the factors of [tex]x^2+x-12[/tex]?  Well the cool thing here is the coefficient of [tex]x^2[tex] is 1 so all we have to look for are two numbers that multiply to be -12 and add to be positive 1 which in this case is 4 and -3.

-12=4(-3) while 1=4+(-3).

So the factored form of [tex]x^2+x-12[/tex] is [tex](x+4)(x-3)[/tex].

The zeros of [tex]x^2+x-12[/tex] are therefore x=-4 and x=3.  We know those are zeros of [tex]x^2+x-12[/tex] by the factor theorem.  

So x=-4 and x=3 are also zeros of [tex]x^3+ax^2-10x-b[/tex] because we were told that [tex]x^2+x-12[/tex] was a factor of it.

This means that when we plug in -4, the result will be 0. It also means when we plug in 3, the result will be 0.

Let's do that.

[tex](-4)^3+a(-4)^2-10(-4)-b=0[/tex]  Equation 1.

[tex](3)^3+a(3)^2-10(3)-b=0[/tex]  Equation 2.

Let's simplify Equation 1 a little bit:

[tex](-4)^3+a(-4)^2-10(-4)-b=0[/tex]

[tex]-64+16a+40-b=0[/tex]

[tex]-24+16a-b=0[/tex]

[tex]16a-b=24[/tex]

Let's simplify Equation 2 a little bit:

[tex](3)^3+a(3)^2-10(3)-b=0[/tex]

[tex]27+9a-30-b=0[/tex]

[tex]-3+9a-b=0[/tex]

[tex]9a-b=3[/tex]

So we have a system of equations to solve:

16a-b=24

9a-b=3

---------- This is setup for elimination because the b's are the same. Let's subtract the equations.

16a-b=24

9a-b=   3

------------------Subtracting now!

7a    =21

Divide both sides by 7:

 a   =3

Now use one the equations with a=3 to find b.

How about 9a-b=3 with a=3.

So plug in 3 for a.

9a-b=3

9(3)-b=3

27-b=3

Subtract 27 on both sides:

   -b=-24

Multiply both sides by -1:

    b=24

So a=3 and b=24

[tex]\displaystyle\\\text{Decompose numbers into prime factors.}\\\\32=2^5\\\\48=2^4\times3\\\\64=2^6\\\\\text{greatest common divisor (gcd)~}~=2^4=\boxed{\bf16 m}\\\\\boxed{\text{\bf The maximum possible length of each wire cut is 16 m.}}[/tex]

The maximum possible length for each cut of wire that Mrs. Agustin can make from the 32m, 48m, and 64m wire coils is 16m.

In this problem, Mrs. Agustin is aiming to cut three different lengths of wires into equal parts. Therefore, the maximum possible length of each cut of wire can be calculated by finding the greatest common divisor (GCD) of the lengths of the three wires. The lengths of the wire coils are 32 m, 48 m, and 64 m. The GCD of these numbers is 16 m.

Thus, the maximum possible length of each cut wire would be 16 m.

https://brainly.com/question/23270841

#SPJ3

Answer:

Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3 ⇒ 3rd answer

Step-by-step explanation:

* Lets explain how to solve the problem

- To prove that all circles are similar, a translation and a scale factor

  from a dilation will be found to map one circle onto another

- So we can translate the circles to share the same center and dilated

 one of them by the scale factor of the dilation and the center of

 dilation is the common center of the circles

* Lets solve the problem

∵ Circle X has a radius 6 units

∵ Circle Y has a radius 2 units

- At first we translate the circles to share the same center

∴ Use translation to put the centers of the circles at the same point

- Find the scale factor of the dilation from the radii of the two circles

∵ The radius of circle X is 6 units

∵ The radius of circle Y is 2 units

∴ The scale factor = 6/2 = 3

∴ Dilate circle y by scale factor 3

* The steps would prove the circles are similar are;

  Translate the circles so they share a common center point, and

  dilate circle Y by a scale factor of 3.

Answer:

Answer is C

Step-by-step explanation:

The root is placed in the denominator section, and the exponent is placed in the numerator section. it is a fraction because you are not using the entire exponent, you will only be using part of it as the other part of the exponent is negated by the X

For this case we have that by properties of roots and powers it is fulfilled that:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So, if we have the following expression:

[tex]\sqrt [3] {8 ^ x}[/tex]

According to the given definition, we can rewrite it as:

[tex]8 ^ {\frac {x} {3}}[/tex]

ANswer:

[tex]8 ^ {\frac {x} {3}}[/tex]

Option C

Answer:

A. The center of dilation is point C.

B.  It is a reduction.

E.  The scale factor is 2/5.

Step-by-step explanation:

The center is shown as C.  You can see this from the line segments they drew through C, the image, and the pre-image.

The pre-image is the image before the dialation.  The pre-image here is XYZ.

The image is the image after dialation. The image is X'Y'Z'.

If you look at the pre-image XYZ and then it's image X'Y'Z', ask yourself the image get smaller or larger.  To me I see a larger triangle being reduce to a smaller triangle so this is a reduction.

The scale factor cannot be bigger than 1 because the image shrunk so D is definitely not a possibility.

E. is a possibility but let's actually find the scale factor to see.

We can calculate [tex]\frac{CX'}{CX}[/tex] or [tex]\frac{CY'}{CY}[/tex] or [tex]\frac{CZ'}{CZ}[/tex] to find out what the scale factor is.

[tex]\frac{CX'}{CX}=\frac{2}{5}[/tex]

[tex]\frac{CZ'}{CZ}=\frac{3}{7.5}=\frac{2}{5}[/tex].

The scale factor is 2/5.

Answer:

A, The center of dilation is point C.

B, It is a reduction.

and E, The scale factor is 2/5.

Step-by-step explanation:

Answer:

3√3 = l

√3 = w

Step-by-step explanation:

l = 3w

9 = 3w[w] ↷

9 = 3w² [Divide by 3]

3 = w² [Take the square root]

√3 = w [plug this back into the top equation to get a length of 3√3]

[3√3][√3] = 9 [Area]

I am joyous to assist you anytime.