solve the formula for the indicated variable h= k/j, for k

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:

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

[tex]

f(x)=a^x \\

f(1)^2\Longrightarrow f(1)=(a^x)^2 \\

f(1)=\boxed{a^{2x}}

[/tex]

Answer:

6 in.

Step-by-step explanation:

So first you do 4 divided by 2 to find how much is 1 in the ratio.

4/2 = 2

Then you times 3 by 2

3 x 2 = 6 in.

Answer:

6

Step-by-step explanation:

I did it on plato :))

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

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.

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:

The circle's center points are (0,3) and the radius is 11

Step-by-step explanation:

k should be 1, Check by calculating the x values for f(x) and confronting them with g(x)

The graph of g(x) is a vertical shift of the graph of f(x) by 1 unit up. Thus, the value of k is 1.

The graph of g(x) = f(x) + k is a vertical shift of the graph of f(x) by k units. We can see from the graph that the graph of g(x) is shifted up by 1 unit relative to the graph of f(x).

Therefore, the value of k is 1.

To confirm this, we can plug in a point on the graph of g(x) into the equation for g(x) and solve for k.

For example, we can see that the point (-1, 2) is on the graph of g(x). Plugging this point into the equation for g(x), we get:

2 = -2(-1) - 2 + k

2 = 0 - 2 + k

k = 2 + 2

k = 4

However, we know that this cannot be the correct answer, because the graph of g(x) is shifted up by 1 unit relative to the graph of f(x). Therefore, the only possible value of k is 1.

For similar question on vertical shift.

https://brainly.com/question/27925380

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Answer:

[tex]\large\boxed{A)\ x=-4}[/tex]

Step-by-step explanation:

[tex]\dfrac{x}{4}=\dfrac{x+1}{3}\qquad\text{cross multiply}\\\\3x=4(x+1)\qquad\text{use the distributive property}\\\\3x=4x+4\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\-x=4\qquad\text{change the signs}\\\\x=-4[/tex]

Answer:

[tex]b = 537[/tex]

Step-by-step explanation:

For this triangle we have to

[tex]a=640\\A=70\°\\B=52\°[/tex]

Now we use the sine theorem to find the length of b:

[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]

Then:

[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}\\\\b=\frac{sin(B)}{\frac{sin(A)}{a}}\\\\b=a*\frac{sin(B)}{sin(A)}\\\\b=(640)\frac{sin(52)}{sin(70)}\\\\b=537[/tex]

Make a proportion using the ratio (A:B) given and number of As and Bs really gotten in the class ([tex]\frac{A's}{B's}[/tex])

[tex]\frac{2}{5} = \frac{A}{40}[/tex]

Cross multiply

2 * 40 = 5 * A

80 = 5A

Isolate A by dividing 5 to both sides

80/5 = 5A/5

16 = A

If 40 people in the class got B's then 16 people got A's

Hope this helped!

~Just a girl in love with Shawn Mendes

16 people got A's if there were 40 people who got B's

The ratio of the number of A's in the class to B's in the class is given as:

Ratio = 2 : 5

This can be rewritten as:

A :  B = 2 : 5

When there are 40 B's, we have:

A :  40 = 2 : 5

Multiply the second ratio by 8

A :  40 = 16 : 40

By comparison, we have:

A = 16

Hence, 16 people got A's if there were 40 people who got B's

Read more about ratios at:

https://brainly.com/question/1781657

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

[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{3})~\hspace{10em} slope = m\implies \cfrac{1}{3} \\\\\\ \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-3=\cfrac{1}{3}[x-(-3)] \implies y-3=\cfrac{1}{3}(x+3) \\\\\\ y-3=\cfrac{1}{3}x+1\implies y=\cfrac{1}{3}x+4[/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]

Answer:

P(not red) = 0.6

Step-by-step explanation:

red = 20, blue = 10, green = 9, yellow = 11

total number of times, spinning a four colored spinner = 50

P(not red) = [tex]\frac{10 + 9 +11}{50}[/tex]

                = [tex]\frac{30}{50}[/tex]

                = 0.6

Answer:

Step-by-step explanation:

√(x)

Shifted 3 units down:

√(x) - 3

Shifted 2 units to the right:

√(x-2) - 3

It's the last one.

ANSWER

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

EXPLANATION

The given equation is

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

This is the parent square root function.

If we apply the transformation;

[tex]y = \sqrt{x - k} - c[/tex]

Then the parent function will shift c units down and k units to the right.

When we the given function 3 units down and 2 units right the equation becomes:

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

4 = GCF

Step-by-step explanation:

52/12 = 4.333

52/11 = 4.7272727

52/10 = 5.2

52/9 = 5.77777778

52/8 = 6.5

52/7 = 7.42

52/6 = 8.6666667

52/5 = 10.4

52/4 = 13 --> 4 works but does it work with 12

**check it.

12/4 = 3

**YES** So 4 is the GCF

Hello There!

The Greatest Common Factor Between "12" And "52" Is 4

Answer: it should be 25.

Step-by-step explanation: this is because the slope of the line is 25. you can see that because, when finding the slope, you see that it goes up 50 and over 2. 50/2 (rise/run) is 25.

Answer:

25

Step-by-step explanation:

On the graph, you can see the train has traveled from 0 to 150 miles (the Y-axis), and it did that in 6 hours (X-axis).

That means that it traveled 150 miles in 6 hours.

A speed is a distance divided by a time (like miles/hour). So, to get the speed, we need to divide the distance traveled by the time it took to do it:

S = 150 miles / 6 hours = 25 miles per hour

Answer:

A measures 72 and B measures 108

Step-by-step explanation:

If the angles are supplementary, that means that they add up to equal 180.  3x + 12 + 4x + 28 = 180.  Doing some algebra there gives you that 7x = 140 and x = 20.  Sub in 20 to angle A to get 3(20) + 12 = 72, and sub in 20 to angle B to get 4(20) + 28 = 108.  And of course, 108 + 72 = 180.

It’s 25 because (24x24)+(7x7) squared is 25

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.

Final answer:

The area of the parallelogram is calculated as the product of its base and height, resulting in 20 square inches.

Explanation:

The area of a parallelogram is calculated using the formula: Base x Height. In this case, the base (b) is 10 inches and the height (h) is 2 inches. Therefore, the area of the parallelogram can be found by multiplying the base by the height:

Area = Base x Height

Area = 10 in x 2 in

Area = 20 square inches

This calculation gives us the total area of the parallelogram in square inches.

The area of a parallelogram given its base and height dimensions as 10 in and 2 in is 20 square inches.

The area of a parallelogram can be calculated using the formula:

Area = Base x Height

Given that the base, b, is 10 inches and the height, h, is 2 inches, the area would be:

Area = 10 inches x 2 inches = 20 square inches

Answer:

The number is 25

Step-by-step explanation:

We let the number be x. The product of x and -2 is;

x(-2) = -2x

a hundred plus the above product is;

100 + (-2x) = 100 - 2x

The above result is said to be equal to 50;

100 - 2x = 50

2x = 100 - 50

2x = 50

x = 25

the number we are looking for is 25.

The student is asking for help with a basic algebra problem. To solve this problem, we need to set up an equation based on the description provided: 'hundred plus the product of a number and -2 equals 50.' This translates to the algebraic equation 100 + (-2)  n = 50. Our goal is to find the value of 'n'.

We first simplify the equation by subtracting 100 from both sides, which gives us -2n = 50 - 100. This simplifies to -2n = -50. Next, we divide both sides of the equation by -2 to isolate 'n'. The simplification gives us n = -50 / -2, which results in n = 25. Therefore, the number we are looking for is 25.

Answer:

[tex] - 3 | - 9 \\ - 2 | - 4 \\ - 1 | - 1 \\ \: \: 0 \: | \: 0 \\ \: \: \: 1 | - 1[/tex]

Step-by-step explanation:

[tex] - ( - 3) ^{2} = - 9 \\ - ( - 2) {}^{2} = - 4 \\ - ( - 1) {}^{2} = 1 \\ - (0) {}^{2} = 0 \\ - (1) {}^{2} = - 1[/tex]

then our rule is

[tex]f(x) = - (x) ^{2} [/tex]

[tex]where \: x \: is \: the \: input \: \\ and \: f(x) \: is \: the \: output .[/tex]

This is my idea. I hope it can help you.

Step-by-step explanation:

They are not equivalent because :

2/8=1/4 decimal: 0.25

3/4 decimal:0.75

3/4 is greater than 2/8 when they are decimals.

Answer: They are not equivalent.

The other person spelled the word equivalent wrong.

Answer: THEY ARE NOT EQUIVILENT

2/8= .25

3/4=.75

.75≠.25

MAKE ME BRAINLIEST

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.

learn more about the unitary method here :

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-Hello There-

B Correct

The area of the original shape will be

multiplied by 9 to get the area of the

image under a dilation with scale

factor 3.

15 × 9 = 135 cm2

The perimeter of the original shape

will be multiplied by 3 to get the

perimeter of the image.

20 × 3 = 60 cm

Answer:

[tex]\large\boxed{C=5.2\pi\ in\approx16.328\ in}[/tex]

Step-by-step explanation:

The formula of a circumference of a circle:

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

r - radius

We have r = 2.6 in. Substitute:

[tex]C=2\pi(2.6)=5.2\pi\ in[/tex]

[tex]\pi\approx3.14\to C\approx(5.2)(3.14)=16.328\ in[/tex]