If (x+k) is a factor of f(x) which of the following must be true

Answer:

The equation of the tangent at x=-6 is [tex]y=-\frac{3}{4}x-\frac{15}{2}[/tex]

Step-by-step explanation:

The equation of a circle with center (h,k) with radius r units is given by:

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

The given circle has center (-3,1) and radius 5 units.

We substitute the center and the radius into the equation to get;

[tex](x--3)^2+(y-1)^2=5^2[/tex]

[tex](x+3)^2+(y-1)^2=25[/tex]

To find the slope, we differentiate implicitly to get:

[tex]2(x+3)+2(y-1)\fra{dy}{dx}=0[/tex]

[tex]2(y-1)\frac{dy}{dx}=-2(x+3)[/tex]

[tex]\frac{dy}{dx}=-\frac{x+3}{y-1}[/tex]

When x=-6;we have [tex](-6+3)^2+(y-1)^2=25[/tex]

[tex]\implies 9+(y-1)^2=25[/tex]

[tex]\implies (y-1)^2=25-9[/tex]

[tex]\implies (y-1)^2=16[/tex]

[tex]\implies y-1=\pm \sqrt{16}[/tex]

[tex]\implies y-1=\pm4[/tex]

[tex]\implies y=1\pm4[/tex]

[tex]y=-3[/tex] or  [tex]y=5[/tex]

From the graph the reuired point is (-6,-3).

We substitute this point to find the slope;

[tex]\frac{dy}{dx}=-\frac{-6+3}{-3-1}[/tex]

[tex]\frac{dy}{dx}=-\frac{3}{4}[/tex]

The equation is given by [tex]y-y_1=m(x-x_1)[/tex].

We plug in the slope and the point to get:

[tex]y--3=-\frac{3}{4}(x--6)[/tex]

[tex]y=-\frac{3}{4}(x+6)-3[/tex]

[tex]y=-\frac{3}{4}x-\frac{9}{2}-3[/tex]

[tex]y=-\frac{3}{4}x-\frac{15}{2}[/tex]

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=-3x+6\\y=9\end{array}\right\\\\\text{Put the value of y to the first equation:}\\\\9=-3x+6\qquad\text{subtract 6 from both sides}\\3=-3x\qquad\text{divide both sides by (-3)}\\-1=x\to x=-1[/tex]

Answer:

(-1,9) is correct in edg2020

Step-by-step explanation:

ANSWER

[tex]C=22\pi \: m[/tex]

EXPLANATION

The circumference of a circle is calculated using the formula:

[tex]C=2\pi \: r[/tex]

where r=11 meters is the radius of the circle.

Let us substitute the radius into the formula to obtain,

[tex]C=2\pi \: \times 11[/tex]

This simplifies to:

[tex]C=22\pi[/tex]

When we substitute

[tex]\pi = 3.14[/tex]

We get

[tex]C=22(3.14) = 69.08m[/tex]

to the nearest hundredth.

Answer:

y= -3x + 4

Step-by-step explanation:

Answer:

[tex]slope=-3\\b=4\\[/tex]

Equation of the line

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

Step-by-step explanation:

To find the slope we need two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] In this case we have the points [tex](0,4)[/tex] and [tex](2, -2)[/tex]

[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex] (1)

We replace the points in the equation (1)

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\frac{-2-4}{2-0} =\frac{-6}{2} =-3[/tex]

We know the equation of the line:

[tex]y=mx+b[/tex] (2)

To find b we replace the slope,  x and y with one of the points in the equation (2)

[tex]4=-3*0+b\\4=0+b\\b=4[/tex]

We substitute m and b in the general equation of the line

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

Answer:

D. 597

Step-by-step explanation:

This question is on  finding the inverse of a 3×3  matrix

The general formula of finding a 3×3 matrix is given by;

[tex]A=\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right] = a.D\left[\begin{array}{ccc}e&f&\\h&i&\\&&\end{array}\right] -b.D\left[\begin{array}{ccc}d&f&\\g&i&\\&&\end{array}\right] + c.D\left[\begin{array}{ccc}d&e&\\g&h&\\&&\end{array}\right][/tex]

where D is determinant

Given ;

[tex]k=\left[\begin{array}{ccc}14&-13&0\\3&8&-1\\-10&-2&5\end{array}\right] then ;\\\\\\\\ =14 D \left[\begin{array}{ccc}8&-1&\\-2&5&\\&&\end{array}\right]  -13D\left[\begin{array}{ccc}3&-1&\\-10&5&\\&&\end{array}\right] + 0.D\left[\begin{array}{ccc}3&8&\\-10&-2&\\&&\end{array}\right][/tex]

= 14 [ 40-2] - -13[ 15-10] + 0

=14 [38] - [-65]+0

=532+65

=597

Answer: Option B.

Step-by-step explanation:

You need to use the formula for calculate the volume of a cylinder:

[tex]V=\pi r^2h[/tex]

Where "r" is the radius and "h" is the height.

You know that the paint can has a radius of 9.5 centimeters and a height of 28 centimeters:

[tex]r=9.5cm\\h=28cm[/tex]

Then, you need to substitute these values into  [tex]V=\pi r^2h[/tex] to get the final result (In this case you can use [tex]\pi=3.14[/tex])

 [tex]V=(3.14) (9.5cm)^2(28cm)[/tex]

[tex]V=7934.78cm^3[/tex]

Answer:

Part a) The equation of the line is

[tex]y-32=1.8(x-0)[/tex] or [tex]y=1.8x+32[/tex]

Part b) The slope of the line is [tex]m=1.8\frac{\°F}{\°C}[/tex]

Part c) The y-intercept is 32 (For a degrees Celsius equal to zero, the degrees Fahrenheit is equal to 32)

Step-by-step explanation:

Let

x ----> degrees Celsius

y ----> degrees Fahrenheit

we have the points

[tex](0,32),(100,212)[/tex]

Part a) Find the equation of the line

Find the slope m

[tex]m=(212-32)/(100-0)[/tex]

[tex]m=180/100[/tex]

[tex]m=1.8\frac{\°F}{\°C}[/tex]

The equation of the line into slope point form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=1.8\frac{\°F}{\°C}[/tex]

Point [tex](0,32)[/tex]

substitute

[tex]y-32=1.8(x-0)[/tex] ----> equation of the line into slope point form

[tex]y=1.8x+32[/tex] ---> equation of the line into slope intercept form

Part b) What is the slope of the line?

The slope of the line is [tex]m=1.8\frac{\°F}{\°C}[/tex]

That means

The rate of change of the temperature is 1.8 degrees Fahrenheit by each degree Celsius

Part c) What is the y-intercept of the line?

we have

[tex]y=1.8x+32[/tex] ---> equation of the line into slope intercept form

The y-intercept is 32

The y-intercept is the value of y when the value of x is equal to zero

That means

For a degrees Celsius equal to zero, the degrees Fahrenheit is equal to 32

Answer:

Step-by-step explanation:

The value of (f+g)(x) is x^2 + 3x - 11

You can combine this by simply adding the like terms. Start by adding together all of the x^2 terms. Since only g(x) has one of those, we use that in its entirety.

x^2

Next we add together the x terms. f(x) has 7x and g(x) has -4x.

7x + -4x = 3x

Finally, we add together the constants. f(x) has -3 and g(x) has -8.

-3 + -8 = -11

With all of the like terms combined, we simply take the answers and put them together.

x^2 + 3x - 11

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For this case we have the following functions:

[tex]f (x) = 7x-3\\g (x) = x ^ 2-4x-8[/tex]

We must find [tex](f + g) (x):[/tex]

By definition we have to:

[tex](f + g) (x) = f (x) + g (x)\\(f + g) (x) = 7x-3 + x ^ 2-4x-8[/tex]

We add similar terms, taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed.

[tex](f + g) (x) = x ^ 2 + 3x-11[/tex]

Answer:

[tex](f + g) (x) = x ^ 2 + 3x-11[/tex]

Answer:

The equation to calculate what divided by 72 equals 12 is as follows:

X/72 = 12

Where X is the answer. When we solve the equation by multiplying each side by 72, you get get:

X = 864

Therefore, the answer to what divided by 72 equals 12 is 864.

I hope it helps!!

To find the value of x in the equation x/12 = 12/72, simplify 12/72 to get 1/6. Then, multiply both sides by 12 to solve for x, resulting in x = 2.

To solve the equation x divided by 12 = 12 divided by 72, we need to perform some algebraic manipulation to isolate x. First, rewrite the equation as a fraction:

Next, simplify the fraction on the right-hand side:

Now the equation looks like this:

To solve for x, multiply both sides of the equation by 12:

So, the value of x is 2.

Answer:

B. 225 - 45 = 10d

Step-by-step explanation:

The remainder Ezra needs to save can be earned by walking ten dogs.

Let remainder = r

Let dogs = d

This means:

r = 10d

Make 'r' numerical values.

r = Total cost of snowboard - Current savings

r = $225 - $45

Therefore:

225 - 45 = 10d

The equations that can be solved to find how much Ezra is paid for walking each dog is  B. 225 - 45 = 10d.

The subject in an equation is the/a variable(s) we're solving the equation for.

Usually, we want it to stay separated and clean without mixing with other constants or variables so that its value is clearly visible.

Ezra is saving money to buy a snowboard that costs $225.

He already has $45 and can earn the rest by walking ten dogs.

If d represents how much he earns for walking each dog,

Let r be the remainder that needs to save can be earned by walking ten dogs.

So,

r = 10d

Make 'r' numerical values.

r = Total cost of snowboard - Current savings

r = $225 - $45

Therefore,

225 - 45 = 10d

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To find the local and global extrema of the function f(x) = x(25 - x), we first find the derivative and set it equal to zero. Next, we evaluate the function at the critical point and the endpoints of the interval [0, 20]. The local maximum is 156.25 and the global maximum is also 156.25.

To find the local and global extrema of the function f(x) = x(25 - x), we can start by finding the critical points. Critical points occur where the derivative of the function is equal to zero or undefined. Let's find the derivative of f(x) first:

f'(x) = 25 - 2x

Setting f'(x) equal to zero, we get:

25 - 2x = 0

Solving for x:

x = 12.5

The critical point is x = 12.5. Now, let's evaluate f(x) at the endpoints of the interval [0, 20] and the critical point:

f(0) = 0

f(20) = 0

f(12.5) = 12.5(25 - 12.5) = 156.25

Therefore, the local maximum is f(12.5) = 156.25 and the global maximum value on the given interval is also f(12.5) = 156.25.

Answer:

C

Step-by-step explanation:

First use distribution

4(3x+y)= 12x+4y

and

-2(x-5y)= -2x+10y

combine the 2 answers

10x+14y

The algebraic expression 4(3x + y) – 2(x – 5y) simplifies to 10x + 14y after distributing the multipliers and combining like terms.

To simplify the algebraic expression 4(3x + y) – 2(x – 5y), we'll follow these steps:

The final simplified expression is 10x + 14y, which corresponds to option C.

For this case we must multiply the following expression:

[tex](3x-5) (- x + 4)[/tex]

We must apply distributive property, which by definition establishes that:[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]

[tex](3x-5) (- x + 4) = (3x) (- x) + (3x) (4) + (- 5) (- x) + (- 5) (4) = - 3x ^ 2 + 12x + 5x-20 = -3x ^ 2 + 17x-20[/tex]

Answer:

[tex]-3x ^ 2 + 17x-20[/tex]

Answer:

It goes up by 2.5

Step-by-step explanation:

Mean equation: (n₁ + n₂ + n₃ + ...)/n

Current mean: (2 + 4 + 7 + 6 + 3 + 6 + 7)/7 = 35/7 = 5

New mean: (2 + 4 + 7 + 6 + 3 + 6 + 7 + 25)/8 = 60/8 = 7.5

Difference: 7.5 - 5 = 2.5

Answer:

the answer is 60

Step-by-step explanation:

2+4= 6

6+7= 13

13+6= 19

19+3=22

22+6= 28

28+7= 35

35+25= 60

Answer:

B

Step-by-step explanation:

221-60=161 which means that you can be 161 max to ride with your friend in the same car.

i just saw this too and someone else said b so yeth

For this case we have to define trigonometric relations of rectangular triangles that:

Then, according to the figure we have:

[tex]Sin (G) = \frac {15} {17}\\Cos (G) = \frac {8} {17}[/tex]

Answer:

[tex]Sin (G) = \frac {15} {17}[/tex]

Option D

2x²+x-3. The quotient resulting of the division of the polynomial [tex](2x^{4} -3x^{3} -3x^{2} +7x-3)[/tex] ÷[tex](x^{2} -2x+1)[/tex] is 2x²+x-3.

In order to find the quotient we have to apply the division of the polynomial [tex](2x^{4} -3x^{3} -3x^{2} +7x-3)[/tex] ÷[tex](x^{2} -2x+1)[/tex] is 2x²+x-3.

We divide the first monomial of the dividend [tex](2x^{4})[/tex] between the first monomial of the divisor [tex](x^{2})[/tex].

(2x^{4})÷[tex](x^{2})[/tex]=[tex]2x^{2}[/tex]

This result [tex]2x^{2}[/tex] is put under the box and we multiply it by each term of the divisor polynomial and the result is subtracted in the polynomial dividend:

2x^4 -3x^3 -3x^2 +7x -3 ║ x^2 -2x +1

-2x^2+4x^3 -2x^2            ║ 2x^2+x-3 -----------> This is the quotient

            x^3 -5x^2 +7x  -3

           -x^3 +2x^2 -  x +0

                    -3x^2 +6x -3

                     3x^2 -6x +3

                                      0

Answer:

The correct answer is,

2x² + x - 3

Step-by-step explanation:

It is given that,

(2x4 – 3x3 – 3x2 + 7x – 3) ÷ (x2 – 2x + 1)

To find the quotient

                                       2x² + x - 3

x² - 2x + 1  | 2x4 – 3x3 – 3x2 + 7x – 3

                  2x⁴ - 4x³ + 2x²              

                           x³ - 5x² + 7x

                           x³ - 2x² + x            

                                -3x² + 8x - 3

                                -3x² + 6x - 3

                                           2x

Therefore the quotient is   2x² + x - 3

Answer:

C. 25%

Step-by-step explanation:

percent change = (new number - old number)/(old number) * 100%

The new number is the increased time, 75 minutes, and the old number is the original time, 60 minutes.

percent change = (75 min - 60 min)/(60 min) * 100%

percent change = (15 min)/(60 min) * 100%

percent change = 0.25 * 100%

percent change = 25%

Since the percent change is a positive number, it is a percent increase.

The percent increase was 25%.

Answer: C. 25%

Answer:

< FAD and <DAH  make 90 degrees  so they are complementary

<EAC and CAH make a straight line so they are supplementary

Step-by-step explanation:

Complementary angles add to 90 degrees

< FAD and <DAH  make 90 degrees  so they are complementary

Supplementary angles add to 180 degrees ( a straight line)

<EAC and CAH make a straight line so they are supplementary

Answer:

B(2,1,1)

Step-by-step explanation:

Given:

-3x-3y+2z=-7  

z=1  

-2x-3y+z=-6

Let -3x-3y+2z=-7   be equation i,  z=1  be equation ii and -2x-3y+z=-6  be equation iii

Solving the system of simultaneous equation by substituting value of z from equation ii to i , we get:

-3x-3y+2=-7

-3x-3y=-7-2

-3x-3y=-9                      -------iv

Solving the system of simultaneous equation by substituting value of z from equation ii to iii, we get:

-2x-3y+1=-6

-2x-3y=-6-1

-2x-3y=-7

re-arranging the above equation, we get

3y=-2x+7

substituting value of 3y from above in equation iv, we get

-3x-(-2x+7)=-9

-3x+2x-7=-9

-x=-9+7

-x=-2

x=2

Now putting x=1 from above in equation v, we get

3y=-2(2) +7

3y=-4+7

3y=3

y=3/3

y=1

Hence the solution of system of given equations is (2,1,1) !

The answer is:

The correct option is B.(2, 1, 1)

We can solve the system of equations by using the reduction method. The reduction method consists of reducing the variables in order to be able to calculate the other variables to finally calculate all the variables.

We are given the equations:

I.

[tex]-3x-3y+2z=-7[/tex]

II.

[tex]z=1[/tex]

II.

[tex]-2x-3y+z=-6[/tex]

Since the second equation is already solved, let's work with the first and third one, so, calculating we have:

[tex]\left \{ {{-3x-3y+2z=-7} \atop {-2x-3y+z=-6}} \right.[/tex]

Now, multiplying the first equation by -1 in order to reduce the variable "y", we have:

[tex]\left \{ {{3x+3y-2z=7} \atop {-2x-3y+z=-6}} \right\\\\x-z=1[/tex]

Then, substituting "z" into the obtained equation:

[tex]x-1=1\\x=1+1=2[/tex]

Now, substituting "x" and "z" into the first equation, we have:

[tex]-3x-3y+2z=-7[/tex]

[tex]-3*(2)-3y+2*(1)=-7[/tex]

[tex]-6-3y+2=-7[/tex]

[tex]-3y-4=-7[/tex]

[tex]-3y=-7+4[/tex]

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

[tex]y=\frac{-3}{-3}=1[/tex]

Hence, we have that the solutions are:

[tex]x=2\\y=1\\z=1[/tex]

So, the correct option is B.(2, 1, 1)

Have a nice day!

Answer:

5log(a) +2log(b)

Step-by-step explanation:

you were close, but you dont multiply the exponents together since a and b are two different variables

Answer:

[tex]5\log(a)+2\log(b)[/tex]

Step-by-step explanation:

The logarithm of a product is the sum of the logarithms:

[tex]\log(a^5b^2) = \log(a^5)+\log(b^2)[/tex]

By the same rule, we have [tex]\log(a^n)=n\log(a)[/tex]:

[tex]\log(a^5)+\log(b^2) = 5\log(a)+2\log(b)[/tex]

Answer:

The height of the pyramid is [tex]2.4\ ft[/tex]

Step-by-step explanation:

we know that

The volume of a square pyramid is equal to

[tex]V=\frac{1}{3}b^{2}h[/tex]

we have

[tex]V=20\ ft^{3}[/tex]

[tex]b=5\ ft[/tex]

substitute and solve for h

[tex]20=\frac{1}{3}(5)^{2}h[/tex]

[tex]60=(25)h[/tex]

[tex]h=60/(25)=2.4\ ft[/tex]

- I think if it was standard notation then it would be 3.05 * 10 = 30.5 - 3 = 27.5.

Answer:

80°

Step-by-step explanation:

Since they are vertical angles, they are congruent to each other.

∠r ≅ 80°

Answer : 80

Opposite angles have same size

Answer:

A. [tex]x=-6[/tex]

Step-by-step explanation:

The zero of a function refers to the x-intercept of the graph of the function.

It is also the solution or the root of the function.

From the graph, the curve intersects the x-axis at x=-6.

Therefore the zero of the given function is:

[tex]x=-6[/tex]

The correct answer is A.

Step-by-step explanation:

[tex]\dfrac{-14x^3}{x^3-5x^4}\qquad\text{where}\ x^3-5x^4\neq0\\\\x^3-5x^4\neq0\qquad\text{distributive}\\\\x^3(1-5x)\neq0\iff x^3\neq0\ \wedge\ 1-5x\neq0\\\\x\neq0\ \wedge\ x\neq\dfrac{1}{5}\\\\\dfrac{-14x^3}{x^3(1-5x)}\qquad\text{cancel}\ x^3\\\\=\dfrac{-14}{1-5x}\qquad\text{where}\ x\neq\dfrac{1}{5}[/tex]

The perimeter of the ΔJkL is 78 units .

Perimeter is the distance around the edge of a shape. Learn how to find the perimeter by adding up the side lengths of various shapes.

This question will be solved using circle tangent theorem. Recalling circle tangent theorem. This theorem states that if from one external point, two tangents are drawn to a circle then they have equal tangent segments. So by this theorem, we can have J, L and K as an external points.

So JA = JB = 13      

and LA = LC= 19    

KC = KB  =7

so perimeter of triangle JKL,

Perimeter = JA + AL + LC + CK + KB + BL

Perimeter = 13 + 13 +19 +19+ 7+ 7

Perimeter = 78 units

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Let's use the properties of tangents to a circle to find the perimeter of triangle JKL.
First, some basic properties of tangents to a circle that are relevant to this problem:
1. Tangent segments to a circle that are drawn from the same external point are equal in length.
2. If two tangent segments are drawn from the same external point to a circle, the lines joining the points of tangency to the external point form a triangle with the segment that joins the two points of tangency.
Using this information, let's analyze the given lengths:
- JA = 13: This means that JK, the tangent from point J to the point of tangency on the circle (which we will call point K), is also 13 units long because JK is also tangent to the circle from point J.
- AL = 19: This means that JL, the tangent from point J to the point of tangency on the circle (which we will call point L), is also 19 units long because JL is also tangent to the circle from point J.
- CK = 7: This means that CL, the tangent from point C to the point of tangency on the circle (which we will call point L), is also 7 units long because CL is also tangent to the circle from point C.
Now, let's find the length of KL.
Since AL and CL are both tangents from point L to the circle, and we've established that AL = 19 and CL = 7, the full length of KL, which is the segment from K to L, is the sum of AL and CL:
KL = AL + CL
KL = 19 + 7
KL = 26 units long
Now, we have the lengths of all three sides of triangle JKL:
- JK = 13 units (since it's the same length as JA)
- KL = 26 units
- LJ = 19 units (since it's the same length as AL)
The perimeter of a triangle is the sum of the lengths of its sides, so the perimeter of triangle JKL is:
Perimeter of JKL = JK + KL + LJ
Perimeter of JKL = 13 + 26 + 19
Perimeter of JKL = 58 units
Therefore, the perimeter of triangle JKL is 58 units.

The volume of a cylinder with a given diameter and height using the formula V = πr²h is equal to 8471π km³.

The volume of the cylinder can be calculated using the formula for the volume of a cylinder: V = πr²h.

Given a diameter of 22 km (which means a radius of 11 km) and a height of 7 km, substitute these values into the formula to find the volume.

Substitute the values into the formula:

V = π × (11 km)²×7 km

Calculate the volume:

V = 8471π km³

Therefore, the volume is 8471π km³.

Answer:

$3.95

Step-by-step explanation:

The cost of one Yummy flake cereal box which Sharon bought is $3.95.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Sharon pays $98.75 for twenty-five 14-ounce boxes of Yummy flakes cereal.

This means Sharon bought 25 boxes of cereal for $98.75.

Now to obtain the cost of one cereal box we have to divide the total amount by the total no.of boxes.

Therefore the cost of one cereal box is,

= (98.75/25).

= $3.95.

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Answer:

12.5

Step-by-step explanation:

Average = (numbers added together)/ number of numbers

               =(12+13)/ (2)

               =25/2

              =12.5

Answer:

12.5

Step-by-step explanation:

To find the average of two numbers: (n₁ + n₂)/2, where n₁ and n₂ are the numbers to find the average of.

Plug in: (12 + 13)/2

Add: 25/2

Divide: 12.5