is the grouping method to factor 5x^3+15x^2-2x-6

Answer:

Option D; (x, y) -> (x, -y); A' is at (-5, -1)

.

Step-by-step explanation:

Reflection is one of the linear transformations which reflect any object along the line of reflection. The size of the shape remains the same but the orientation changes.

Reflection along the x-axis means that the sign of y-coordinate changes but the sign of the x-coordinate remains same.

From figure we identified the coordinates of point A:

A (-5,1)

So, A' will be (x,-y)

=> A' = (x,-y) = (-5,-1)

So, Option D (x, y) -> (x, -y); A' is at (-5, -1) is correct.

Answer:

[tex]\large\boxed{x=-6\pm\sqrt{30}}[/tex]

Step-by-step explanation:

[tex](a+b)^2=a^2+2ab+b^2\qquad(*)\\\\\\x^2+12x+6=0\qquad\text{subtract 6 from both sides}\\\\x^2+2(x)(6)=-6\qquad\text{add}\ 6^2\ \text{to both sides}\\\\\underbrace{x^2+2(x)(6)+6^2}_{(*)}=-6+6^2\\\\(x+6)^2=-6+36\\\\(x+6)^2=30\Rightarrow x+6=\pm\sqrt{30}\qquad\text{subtract 6 from both sides}\\\\x=-6\pm\sqrt{30}[/tex]

Answer:

see below

Step-by-step explanation:

395.2

Step-by-step explanation:

Area of a trapezoid is:

A = ½ (a + b) h

where a and b are the top and bottom lengths and h is the height.

If 7.6 refers to the entire side length, then the area is:

A = ½ (2.6 + 7.6) (4)

A = 20.4

If 7.6 refers only to the length right of the right angle, we can use Pythagorean theorem to find the length on the left:

x² + 4² = 5²

x = 3

So the whole side length is 3 + 7.6 = 10.6.  That means the area is:

A = ½ (2.6 + 10.6) (4)

A = 26.4

Answer: D: 672

Step-by-step explanation:

use the equation C = 2πR, where C is circumference and R is radius

re-write the equation with 107 instead of R

C=2*π*107

then solve (use 3.14 for pi and round up)

3.14*2=6.28

6.28*107=671.96

then round up to get 672

I hope this helps!

The circumference of a circular park with a radius of 107 m, calculated with the formula Circumference = 2 * π * radius, is approximately 672 m.

The circumference of a circle is calculated by using the formula: Circumference = 2 * π * radius. In this case, the radius of the circular park is given as 107 m. Substituting the radius into the formula, we obtain: Circumference = 2 * 3.14 * 107 which equals approximately 672 m. So, to the nearest meter, the circumference of the park is 672 m.

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Answer:

0 if the function is [tex]F(x)=\frac{4-x^2}{4-x}[/tex].  Please tell me if this is not the right function.

Step-by-step explanation:

I'm assuming the function is [tex]F(x)=\frac{4-x^2}{4-x}[/tex].  Please tell me if it is not the right assumption.

F(-2) means to use the expression called F and replace x with -2.

Like this:

[tex]F(-2)=\frac{4-(-2)^2}{4-(-2)}=\frac{4-4}{4+2}=\frac{0}{6}=0[/tex]

So the value of F(-2) is 0.

F(-2)=0.

Answer:

15.1792 or 15.18

Step-by-step explanation:

14.32 timex 6% or .06 is 0.8592. You add .8592 to 14.32 and get 15.1792 or 15.18 :)

Answer:

$15.18

Step-by-step explanation:

To find the sales tax, you would multiply $14.32 by 6%.

6% = 0.06

0.06*14.32 =  0.8592

Then add the sales tax to the original price to find how much the total costs.

0.8592 + $14.32 = $15.1792

Round $15.1792 to the nearest cent since its money.

So its $15.18

Answer:

7 high priced speakers

21 Low priced speakers

Step-by-step explanation:

170x7 =1190

90x21=1890

1890+1190=3080

90’s are the low speaker docks, and 170’s are the high speaker docks.

3 times 90 is 270, plus 170 is 440

3080 divided by 440 is 7, the number of 170’s they sold. 7 times 3 is 21, the number of 90’s they sold.

The hexagon is made up of two trapezoids, each having the following dimensions:

[tex]a=12\text{ m}\\b=5\text{ m}\\h=4\text{ m}[/tex]

So, its total area is the sum of the areas of those two trapezoids.

[tex]A_h=2A_t=2\cdot\dfrac{1}{2}(a+b)h=(a+b)h\\A_h=(12+5)\cdot 4=68\text{ m}^2[/tex]

Answer:

[tex]x=-5/7[/tex]

Step-by-step explanation:

we have

[tex]f(x)=7x+5[/tex] ----> The degree of this polynomial is 1 (linear equation)

Remember that

The zero of the polynomial is the value of x when the value of f(x) is zero

so

For f(x)=0

[tex]0=7x+5[/tex]

solve for x

[tex]x=-5/7[/tex] ----> the zero of the polynomial or x-intercept

Answer:

the answer to your question is A.

Answer:

Option A. is correct

Step-by-step explanation:

A rational fraction is an algebraic fraction such that both the numerator and denominator are polynomials.

Here, a graph is given .

We need to find which of the given rational functions is graphed in image.

On x-axis, 1 unit = 2 units

Clearly, we can see the graph is not defined at point x = - 4 and at x = 1.

Corresponding to x = - 4, factor is (x+4) .

Corresponding to x = 1, factor is (x-1) .

So, this graph is of the rational fraction [tex]F(x)=\frac{1}{(x-1)(x+4)}[/tex]

Hence, Option A. is correct

Answer:

Here's one way to do it.

Step-by-step explanation:

-24 ÷ (-4)

-24 is the final number on the number line

-4 means you count by 4s on the number line moving backwards.

Answer: +6 (The sign is + because you are still facing forward).

After modeling the division of [tex]-24[/tex] by [tex]-4[/tex] on the number line, we reach to zero after [tex]6[/tex] steps.

" Number line is defined as a straight line which represents the number at the equal interval on it on the both the side of zero."

According to the question,

Given division,

[tex](-24)[/tex] by [tex](-4)[/tex]

As shown on the model of  number line the given division we have,

Hence, after modeling the division of [tex]-24[/tex] by [tex]-4[/tex] on the number line, we reach to zero after [tex]6[/tex] steps.

Learn more about number line here

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Answer:

40 ft

Step-by-step explanation:

We can use ratios to solve this problem.  Put the scale over the actual size

1/4 inch           2 inches

-------------- = ----------------

5 ft                  x ft

Using cross products

1/4 x = 2 *5

1/4 x = 10

Multiply each side by 4

4*1/4 x = 4 * 10

x = 40

The wall is 40 ft

In the given Angles and Rays question, Based on the given diagram descriptions, the correct answers are ray AB, ∠DCE, and ray CE.  Therefore, the correct options are: B. ∠DCE, C. ray AB, D. ray CE.

The given question seems to be talking about geometric figures involving rays and angles. From the description, we know that there are two diagrams. The first diagram contains a ray namely AB and the second diagram contains two rays namely CD and CE forming angle DCE at common point C.

Based on the given information, Ray AB is correct because it's mentioned explicitly in first diagram. Angle DCE, represented as ∠DCE, is also correct as it has been stated to exist in the problem description within the second diagram. Lastly, ray CE is a legitimate answer as it is a fundamental part of the second figure forming an angle with ray CD at point C.

Learn more about Angles and Rays here:

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Answer:

Option D (4, -5)

Step-by-step explanation:

This question can be solved by various methods. I will be using the hit and trial method. I will plug in all the options in the both the given equations and see if they  balance simultaneously.

Checking Option 1 by plugging (-4, -5) in the first equation:

-2(-4) + 6(-5) = -38 implies 8 - 30 = -38 (not true).

Checking Option 2 by plugging (-5, 4) in the first equation:

-2(-5) + 6(4) = -38 implies 10 + 24 = -38 (not true).

Checking Option 3 by plugging (1, -6) in the second equation:

3(1) - 4(-6) = 32 implies 3 + 24 = 32 (not true).

Since all the options except Option 4 have been ruled out, therefore, (4,-5) is the correct answer!!!

Answer:

[tex]\sin x=1[/tex]

Step-by-step explanation:

The given function is

[tex]\cos^2x+2\sin x-2=0[/tex]

We use the identity: [tex]\sin^2x+\cos^2x=1[/tex] [tex]\implies \cos^2x=1-\sin^2x[/tex]

This implies that:

[tex]1-\sin^2x+2\sin x-2=0[/tex]

[tex]-\sin^2x+2\sin x-1=0[/tex]

[tex]\sin^2x-2\sin x+1=0[/tex]

[tex](\sin x-1)^2=0[/tex]

[tex]\sin x-1=0[/tex]

[tex]\sin x=1[/tex]

Hence the numerical value of one trigonometric function(the sine function) is 1

Answer:

Step-by-step explanation:

From

\cos^2x+2\sin x-2=0

Using the identity, we have: \sin^2x+\cos^2x=1 \implying \cos^2x=1-\sin^2x

Opperating:

1-\sin^2x+2\sin x-2=0

-\sin^2x+2\sin x-1=0

\sin^2x-2\sin x+1=0

(\sin x-1)^2=0

\sin x-1=0

\sin x=1

A numerical value for x would be for example x=90 degrees or pi/2 (radians)

And this answer is valid for every angle x=90+360n (n=0,1,2,3,etc) or x=pi/2+2pi*n (n=0,1,2,3,etc)

Final answer:

The modified surface area of a square pyramid, with the side length tripled and slant height divided by 5, is calculated as 9s^2 + 6sl/5, where 's' is the original side length and 'l' is the original slant height.

Explanation:

To find the modified surface area of the square pyramid when the side length is tripled and the slant height is divided by 5, we need to recall the formula for the surface area of a square pyramid. The original surface area formula for a square pyramid is given by the sum of the area of the base plus the area of the four triangular faces, which can be represented as:

Surface Area = base area + 4 × (1/2 × slant height × side length)

For the modified pyramid, if the original side length is 's' and the slant height is 'l', tripling the side length would make it '3s' and dividing the slant height by 5 would make it 'l/5'. Using these new values, the formula for the modified surface area becomes:

Modified Surface Area = (3s)^2 + 4 × (1/2 × (l/5) × 3s)

Simplifying, we get:

Modified Surface Area = 9s^2 + 6s(l/5)

This accounts for the nine-fold increase in the base area (since area is proportional to the side length squared) and the change in the area of the triangular faces.

Answer:

Step-by-step explanation:

<, > - dotted line

≤, ≥ - solid line

<, ≤ - shaded region below the line

>, ≥ - shaded region above the line

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

[tex]y\leq-2x+10[/tex]

Draw the solid line [tex]y=-2x+10[/tex].

Shade region below the line.

for x = 5

[tex]y=-2(5)+10=-10+10=0\to(5,\ 0)[/tex]

for x = 0

[tex]y=-2(0)+10=0+10=10\to(0,\ 10)[/tex]

[tex]y>\dfrac{1}{2}x-2[/tex]

Draw the dotted line [tex]y=\dfrac{1}{2}x-2[/tex]

Shade region above the line.

for x = 0

[tex]y=\dfrac{1}{2}(0)-2=0-2=-2\to(0,\ -2)[/tex]

for x = 4

[tex]y=\dfrac{1}{2}(4)-2=2-2=0\to(4,\ 0)[/tex]

Look at the picture

The solutions: A, C, D, K

Answer:

Option D is the answer.

Step-by-step explanation:

Volume of sphere is given as:

[tex]\frac{4}{3}\pi r^{3}[/tex]

Case 1:

Lets say the radius is 3 cm.

Volume = [tex]\frac{4}{3}\times3.14\times3\times3\times3[/tex]

= 113.04 cubic cm

Case 2:

Lets say the radius is twice 3 cm that is 6 cm.

Volume = [tex]\frac{4}{3}\times3.14\times6\times6\times6[/tex]

= 904.32 cubic cm.

The volume of the larger ball is [tex]\frac{904.32}{113.04}[/tex] = 8 times the smaller one.

So, the answer is option D : 8 times.

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{6}{ h},\stackrel{-1}{ k})\qquad \qquad radius=\stackrel{4}{ r} \\\\[-0.35em] ~\dotfill\\[1em] [x-6]^2+[y-(-1)]^2=4^2\implies (x-6)^2+(y+1)^2=16 \\\\\\ \stackrel{\mathbb{F~O~I~L}}{(x^2-12x+36)}+\stackrel{\mathbb{F~O~I~L}}{(y^2+2y+1)}=16\implies x^2+y^2-12x+2y+37=16 \\\\\\ x^2+y^2-12x+2y+37-16=0\implies x^2+y^2-12x+2y+21=0[/tex]

ANSWER

Option A

EXPLANATION

When a circle has it's center at (h,k) and and radius r units, then its equation in standard form is

[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

The given circle has its center at (6,-1) and its radius is r=4 units.

We plug in these values to get

[tex]{(x - 6)}^{2} + {(y - - 1)}^{2} = {4}^{2} [/tex]

[tex]{(x - 6)}^{2} + {(y + 1)}^{2} =16[/tex]

We now expand to obtain

[tex] {x}^{2} - 12x + 36 + {y}^{2} + 2y + 1 = 16[/tex]

[tex] {x}^{2} + {y}^{2} - 12x +2 y + 36 + 1 - 16 = 0[/tex]

[tex]{x}^{2} + {y}^{2} - 12x +2 y + 21 = 0[/tex]

This is the equation in general form of the circle.

Answer:

I am sure it is D

Check the picture below.

make sure your calculator is in Degree mode.

Answer:

53.06°

Step-by-step explanation:

In triangle ABC, since ∠CAB is 90 degree, therefore consider AB to be the opposite and AC be the adjacent.

Now to find the angle, ∠ACB using trigonometry,

tan θ = opposite / adjacent

tan θ = AB / AC

given AC = 6 and AB = 8

tan θ = 8 / 6

tan θ = 1.33

therefore, θ = [tex]tan^{-1}[/tex] 1.33

                 θ = 53.06°

Therefore, the bearing from post C to post B is 53.06°

Answer:

Step-by-step explanation:

the curve is representing the projectile. at t=0, the projectile is on the ground.  at t=6, the projectile has finished its journey and is back on the ground.  In between t=0 and t=6 will be the projectile's peak altitude.  the point between t=0 and t=6 is t=3.  So plug in t=3 and solve for s(t), and you get 36ft.  gg

C. 112.5

The Angles of Intersecting Chords Theorem  states:

"If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle"

So, the arc intercepted by the angle ∠5 is:

360° - 50° - 115° - 85° = 110°

On the other hand, the arc intercepted by its vertical angle is:

115°

Therefore:

[tex]\angle 5 = \frac{1}{2}(110^{\circ}+115^{\circ}) \\ \\ \boxed{\angle 5 = 112.5^{\circ}}[/tex]

Answer:

D. 113°, Consecutive interior angles theorem.

Step-by-step explanation:

We use the interior angle theorem which states that when 2 lines are parallel and are intersected by a transversal, the interior angles on one side add up to 180°

67° and angle 2 are therefore supplementary angles.

67+ angle2=180°

angle2= 180-67 =113°

Answer:

3 gallons per mile, slope of 3

Step-by-step explanation:

To find out how many gallons the train uses per mile, look at the point (50,150). If you know that the train used 150 gallons to travel 50 miles, do 150/50 to get an answer of 3 gallons per mile.

For the second part, you know that as x increases by 1 (miles traveled) y (gallons) increases by 3, so therefore the slope is 3. You can also check this value by plugging in the points (150,450) and (50,150) into the [tex]m=\frac{x_{2}  - x_{1}}{y_{2}  - y_{1}}[/tex]

Answer:

The solution is the point (-4,-2)

Step-by-step explanation:

we have

-0.1x-0.8y=2 -----> equation A

0.6x-0.5y=-1.4 ----> equation B

Solve by graphing

Remember that the solution of the system of equations by graphing is the intersection point both lines

using a graphing tool

The intersection point is (-4,-2)

see the attached figure

therefore

The solution is the point (-4,-2)

Answer:

Step-by-step explanation:

14n+6p-8n=18p

6n=12p

n=2p

Answer:

Step-by-step explanation:

[tex]14n+6p-8n=18p\qquad\text{combine like terms}\\\\(14n-8n)+6p=18p\qquad\text{subtract}\ 6p\ \text{from both sides}\\\\6n=12p\qquad\text{divide both sides by 6}\\\\n=2p[/tex]

Answer:

Step-by-step explanation:

Let f(x) = x^7 - 4e^x .

Then f '(x) = 7x^6 - 4e^x, and

f "(x) = 42x^5 - 4e^x, and so:

f '(-1) = 7(-1)^6 - 4e^(-1)  =  7 + 4/e

and

f "(x) = 42(-1)^5 - 4e^(-1)  =  -42 + 4/e

Answer:

The number is 80

Step-by-step explanation:

The question in English is

The excess of one number over 20 equals three quarters of the same number. What is the number?

Let

x ------> the number

we know that

The linear equation that represent this situation is

[tex]x-20=\frac{3}{4}x[/tex]

Solve for x

[tex]x-\frac{3}{4}x=20[/tex]

[tex]\frac{1}{4}x=20[/tex]

[tex]x=80[/tex]

therefore

The number is 80

Answer:

The answer should become clearer once we convert everything to a common denominator:

14/15,12/15,10/15,8/15

We can now see we have an arithmetic sequence with common difference 2/5. The next term is thus

6/15=2/5

2/5 is the answer

Answer:

2/5

Step-by-step explanation:

because I someone didn't let me solve it the way I normally do;

you need to convert all of them to a common denominator;

making them [tex]\frac{14}{15}[/tex], [tex]\frac{12}{15}[/tex], [tex]\frac{10}{15}[/tex], [tex]\frac{8}{15}[/tex]

making the next one [tex]\frac{6}{15}[/tex] or [tex]\frac{2}{5}[/tex]