On a map, the endpoints of a straight fence are located at A(4,12) and B(8,22). Lisa plans to install a gate in the fence and wants the gate’s hinges to be the same distance from both ends of the fence. At what point on the map will the gate hinges be placed?

The correct recursive function is: [tex]\[ f(n) = f(n-1) \times (1 - 0.30) + 25 \][/tex]

Let's break down the problem:

At the start, there are 100 t-shirts in the store (f(0) = 100).

Each month, 30% of the current stock is sold, and 25 new t-shirts arrive.

So, if we denote the number of t-shirts in the store at the beginning of the nth month as f(n), we can represent the recursive relationship as follows:

f(n) = f(n-1) * (1 - 0.30) + 25

This equation means that the number of t-shirts in the store at the beginning of the nth month is equal to 70% of the number of t-shirts at the beginning of the previous month (because 30% were sold), plus 25 (because 25 new t-shirts arrive).

In this function:

- [tex]\( f(n) \)[/tex] represents the number of t-shirts in the store at the beginning of the nth month.

- [tex]\( f(n-1) \)[/tex] represents the number of t-shirts in the store at the beginning of the (n-1)th month.

- [tex]\( (1 - 0.30) \)[/tex] represents 70% of the t-shirts from the previous month remaining after 30% are sold.

- [tex]\( + 25 \)[/tex] represents the 25 new t-shirts that arrive each month.

Complete question: A store had 100 t-shirts. Each month, 30% of the t-shirts were sold and 25 new t-shirts arrived in shipments. Which recursive function best represents the number of t- shirts in the store, given that f(0)=100?

a-f(n)=f(n-1) 0.3+25,n>0

b-f(n)=100-f(n-1) = ( 3.3+25 n>0

c-f(n)=f(n-1) -( 0.7+25 n>0

d-f(n)=100-f(n-1) - C 7+25 n>0

Answer:

The answer is 2.

2  since 6/4=3/2

Step-by-step explanation:

Since your relation is a direct variation then the points on your line are of the form y=kx where k is the constant of variation (also called constant of proportionality)

If y=kx then y/x=k.

So all the points in this relation since it is a direct variation will be equal to y-coordinate/x-coordinate.

So we are going to solve this proportion:

[tex]\frac{6}{4}=\farc{3}{x}[/tex]

Again I put y/x from each point. They should have same ratio because this is a direct variation.

Cross multiply:

[tex]6(x)=4(3)[/tex]

[tex]6x=12[/tex]

Divide boht sides by 6:

[tex]x=\frac{12}{6}[/tex]

[tex]x=2[/tex]

Answer:

Step-by-step explanation:

You are solving for the direct variation. This means that the amount of change for is consistent for both x & y:

Note: (x , y) & (x₁ , y₁)

(x , y) = (4 , 6)

(x₁ , y₁) = (x , 3)

Set the two equal to each other:

(4 , 6) = (x , 3)

Find common denominators (y). Remember that what you multiply to one you multiply to the other:

(4 , 6) = (x * 2, 3 * 2) = (2x , 6)

Simplify. Isolate the variable x. Divide:

(4) = (2x)

(4)/2 = (2x)/2

x = 4/2

x = 2

x = 2 is your answer.

Answer:

Explanation:

1) Vertex form of the function that represents a parabola.

The general form of a quadratic equation is Ax² + Bx + C = 0, where A ≠ 0, and B and C may be any real number. And the graph of such equation is a parabola with a minimum or maximum value at its vertex.

The vertex form of the graph of such function is: A(x - h)² + k

Where, A a a stretching factor (in the case |A| > 1) or compression  factor (in the case |A| < 1) factor.

2) Find the vertex of the first function, f(x) = x²

This is the parent function, for which, by simple inspection, you can tell h = 0 and k = 0, i.e. the vertex of f(x) = x² is (0,0).

3) Find teh vertex of the second function, g(x) = x² -10x + 2

The method is transforming the form of the function by completing squares:

That is the searched vertex form: g(x) = (x - 5)² - 23.

From that, using the rules of translation you can conclude immediately that the function f(x) was translated 5 units horizontally to the right and 23 units vertically downward.

Also, by comparison with the verex form A(x - h)² + k, you can conclude that the vertex of g(x) is (5, -23), and that means that the vertex (0,0)  was translated 5 units to the right and 23 units downward.

Answer:

Its A

Step-by-step explanation:

edge 2021 :))

Answer:

C. X= -1.25

Step-by-step explanation:

x + 5 = -3^x + 4

We change x for  -1.25

-1.25 + 5 = -3^(-1.25) + 4

3.75=-0.25+4

3.75=3.75

Same number on both sides, therefore is correct!

I hope you find this information useful and interesting! Good luck!

Answer:

C.

Step-by-step explanation:

So there are 20 kids with brown hair and this represents 80% of the class total.

So this means 20=.8n since we don't know the total number of kids.

20=.8n

Divide both sides by .8

25=n

So 25 is the total number of kids.

C. is the answer

You could also setup this equation given that 80% is 80/100:

[tex]\frac{20}{\text{ total }}=\frac{80}{100}

To figure out what that total is there you can divide top and bottom of the fraction on right hand side by 4 which gives you the 20 on top and the 25 on bottom.

Answer:

Y=3

Step-by-step explanation:

Sin30=y/6

y=6sin30

Y=3

Answer:

[tex]\large\boxed{n=\dfrac{-23}{11}=-2\dfrac{1}{11}}[/tex]

Step-by-step explanation:

[tex]\dfrac{6}{11}=\dfrac{n+7}{9}\qquad\text{cross multiply}\\\\11(n+7)=(6)(9)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(11)(n)+(11)(7)=54\\\\11n+77=54\qquad\text{subtract 77 from both sides}\\\\11n=-23\qquad\text{divide both sides by 11}\\\\n=\dfrac{-23}{11}[/tex]

Answer:

1080

Step-by-step explanation:

looking at the ratio of 1 : 3 : 6, we can say that the pupils are divided into 1 + 3 + 6 = 10 "parts".

Indian are 1 part, Malay are 3 parts, and Chinese are 6 parts.

So 3x (3 parts of malay) is 360 more than 1x (1 part of Indian). Thus:

3x - 360 = x

2x = 360

x = 180

We know chinese is 6 parts, or 6x, so Chinese would be 6 (180) = 1080

Hence, there are 1080 chinese pupils

Answer:

[tex]y=\frac{5}{4}x+\frac{15}{4}[/tex]

Step-by-step explanation:

x | y

-------

1     5

5   10

9    15

13   20

This one is linear because as x goes up by the same number so does y. So the ratio of difference of y to difference of x is the same per pair of points.

So a linear equation in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

To find the slope, I'm going to line up the points vertically and subtract, then put 2nd difference over 1st difference. Like so,

( 1    ,   5)

-( 5   ,  10)

----------------

-4          -5

So the slope is 5/4 which makes sense since the y's are going up by 5 each time and the x's are going up by 4 each time.

So we have m=5/4. Let's plug that into our y=mx+b.

y=5/4 x+b

To find b, we need to use y=5/4 x+b along with one of the given points.

Choose; it doesn't matter.  I like (1,5) I guess.

y=5/4 x +b with (1,5)

5=5/4 (1)+b

5=5/4    +b

Subtract 5/4 on both sides:

5-5/4=b

20/4-5/4=b  (Found a common denominator)

15/4=b

The y-intercept is 15/4 so b=15/4.

So the equation for the line in slope-intercept form is y=5/4 x +15/4.

[tex]y=\frac{5}{4}x+\frac{15}{4}[/tex]

Answer:

It is linear.

The equation is 5x - 4y = -15.

Step-by-step explanation:

If it is linear then the slope between consecutive points will be the same.

Slope = (10-5)/(5-1) = 5/4.

slope = (15-10)/ (9-5) = 5/4

slope = (20-15)/ (13-9) = 5/4.

So the data relationship is linear.

y - y1 = m(x - x1)

Using the point (1, 5)

y - 5 = 5/4(x - 1)

y = 5/4x - 5/4 + 5

y = 5/4x + 15/4

4y = 5x + 15

5x - 4y = -15.

Answer:

False

Step-by-step explanation:

What the attached image says that if two solids with equal heights and base areas are cut by any parallel plane to their bases then sections of equal area (volume) would be produced in them

Answer:

did this problem came with a chart becuase i dont know what youre talkin about

Step-by-step explanation:

Answer:

1 triangle will satisfy the condition.

Step-by-step explanation:

Answer:

approximately 3 ....to be exact 3.1 weeks

Step-by-step explanation:

he earns 225 a week we know that right? and he has to take out 180 to pay for things... so right there you have 225-180=45 so that's 45 dollars a week he has. the MP4 player is 195 and he already has 55 dollars saved so 195-55= 140 so he still needs 140 dollars to buy it the question now is how many weeks will it take for him to save up to 140 dollars? you simply take 140÷45 (bc that's what he gets each week) and it should = 3.1

Answer: 3.1

Step-by-step explanation:

1. 225 a week in pay

2. 180 take out of pay

3. 225-180=45 a week from paycheck

4. Mp3 cost 195.00

5. 55.00 money saved

6. 195-55=140

7. 140÷45 after rounding 3.1

There is the answer

Answer:

[tex]\frac{g(7)-g(4)}{7-4}=\frac{5}{6}[/tex]

So it looks like C.

Step-by-step explanation:

Average rate of a function g(x) on the interval from x=a to x=b is given by the formula:

[tex]\frac{g(b)-g(a)}{b-a}[/tex].

You can even say:

[tex]\frac{g(a)-g(b)}{a-b}[/tex].

So we have from x=4 to x=7, so the formula becomes:

[tex]\frac{g(7)-g(4)}{7-4}[/tex]

We are given this is equal to 5/6.

Answer:

Its C

Step-by-step explanation:

let's firstly convert the mixed fractions to improper fractions and then add.

[tex]\bf \stackrel{mixed}{2\frac{7}{10}}\implies \cfrac{2\cdot 10+7}{10}\implies \stackrel{improper}{\cfrac{27}{10}}~\hfill \stackrel{mixed}{8\frac{1}{2}}\implies \cfrac{8\cdot 2+1}{2}\stackrel{improper}{\cfrac{17}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{27}{10}+\cfrac{17}{2}\implies \stackrel{\textit{using an LCD of 10}}{\cfrac{(1)27+(5)17}{10}}\implies \cfrac{27+85}{10}\implies \cfrac{112}{10}\implies \cfrac{56}{5}\implies 11\frac{1}{5}[/tex]

Answer:

Explanation:

1) Find the expression that represents the situation.

The expression that represents the situation is an inequality:

Hence, the total weight must be less than or equal to (≤) 6 lbs, which is:

2) Graph of the inequality 2x + 3y ≤ 6

Line:

Shaded region:

Conclusion: the graph is the line passing through the points (3, 0) and (0,2), and the shaded region is below the line, so that is the first graph of the picture.

Note: strictly speaking, you should include the restrictions that the variables x and y cannot be negative, with which the graph would be only on the first quadrant but those constrains are not handled in the problem.

The graph is also attached.

Answer:

Answer is A

Step-by-step explanation:

Answer:

The correct option is D) Two pizzas are shared equally among zero people, and you want to know how much each person gets.

Step-by-step explanation:

Consider the provided information,

We need to identify the option which has no solution,

Consider the option A)

Six pizzas are shared equally among three people, and you want to know how much each person gets.

We can find how much each person gets by dividing the number or pizza with number of people:

Each person gets = 6/3 = 2

That means each person gets 2 pizza.

The problem has a solution.

Consider the option B)

Three pizzas are shared equally among two people, and you want to know how much each person gets.

We can find how much each person gets by dividing the number or pizza with number of people:

Each person gets = 3/2 = 1.5

That means each person gets 1.2 pizza.

The problem has a solution.

Consider the option C)

Zero pizzas are shared equally among three people, and you want to know how much each person gets.

We can find how much each person gets by dividing the number or pizza with number of people:

Each person gets = 0/3 = 0

That means each person gets 0 pizza.

The problem has a solution.

Consider the option D)

Two pizzas are shared equally among zero people, and you want to know how much each person gets.

We can find how much each person gets by dividing the number or pizza with number of people:

Each person gets = 2/0 = No solution

As we know any number divided by 0 has no solution.

Thus, the problem has no solution.

Hence, the correct option is D) Two pizzas are shared equally among zero people, and you want to know how much each person gets.

Answer: I think it’s t II k

Step-by-step explanation:

If m is parallel to k and m is also parallel to ℓ, then by the transitive property of parallel lines, k must be parallel to ℓ.

If m ∥ k and m ∥ ℓ, then k is parallel to ℓ. In terms of geometry, when a line m is parallel to lines k and ℓ, and all the lines are coplanar, then lines k and ℓ must be parallel to each other as well. This is due to the transitive property of parallel lines which states that if two lines are parallel to the same line, they are parallel to each other. An example of this could be railway tracks: if the sleepers (the wooden blocks) are considered to be line m, which is parallel to both rails (k and ℓ), the rails (k and ℓ) have to be parallel to each other in order for the train to travel smoothly.

https://brainly.com/question/2437149

#SPJ2

Answer:

15

Step-by-step explanation:

37.5÷2.5 goes in 15 times

Answer:

37.5 ÷ 2.5 = 15

Step-by-step explanation:

whuch topic does it belong to

Answer:  The required transformation from ABCDE to MNOPQ is the reflection across the y axis.

And, the co-ordinates of the vertices of polygon VWXYZ are V(1, 3), W(-1, 7), X(-7, 7), Y(-5, 3) and Z(3, 1).

Step-by-step explanation:  Given that a polygon ABCDE has the vertices A(2, 8), B(4, 12), C(10, 12), D(8, 8), and E(6, 6). Polygon MNOPQ has the vertices M(-2, 8), N(-4, 12), O(-10, 12), P(-8, 8), and Q(-6, 6).

A transformation or sequence of transformations that can be performed on polygon ABCDE to show that it is congruent to polygon MNOPQ.

We are to find the transformation.

We note that if (x, y) denotes the co-ordinates of a vertex of polygon ABCDE, then the corresponding vertex of polygon MNOPQ has co-ordinates (-x, y).

So, the sign before the x co-ordinate is changing, which gives the reflection across the y axis.

Therefore, the required transformation is the reflection across the y axis.

Also, the polygon is translated 3 units right and 5 units down so that it will coincide with a congruent polygon VWXYZ.

We are to find the co-ordinates of the vertices of polygon VWXYZ.

According to the given transformation rule, the co-ordinates of polygon MNOPQ changes as follows :

(x, y)   ⇒   (x+3, y-5).

So, the vertices of polygon VWXYZ are

V(-2+3, 8-5) = V(1, 3),

W(-4+3, 12-5) = W(-1, 7),

X(-10+3, 12-5) = X(-7, 7),

Y(-8+3, 8-5) = Y(-5, 3),

Z(-6+3, 6-5) = Z(-3, 1).

Thus, the co-ordinates of the vertices of polygon VWXYZ are V(1, 3), W(-1, 7), X(-7, 7), Y(-5, 3) and Z(3, 1).

For this case we must find an expression equivalent to:

[tex]\sqrt [4] {f}[/tex]

By definition of properties of powers and roots we have:

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

So, rewriting the given expression we have:

[tex]f ^ {\frac {1} {4}}[/tex]

Answer:

Option 1

Answer:

f^(1/4)

Step-by-step explanation:

The fourth power of f, expressed with a rational exponent, is f^(1/4).

Answer:

C

Step-by-step explanation:

Note that if x = h is a root of a polynomial f(x) then f(h) = 0

Note the sum of the coefficients of the given polynomial

x³ + 4x² + x - 6 is

1 + 4 + 1 - 6 = 0

Hence x = 1 is a root( zero) and (x - 1) is a factor

Answer:

[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

Given

[tex]\frac{2}{3}[/tex] × [tex]\frac{3}{5}[/tex]

Cancel the 3 on the numerator/denominator of the fractions leaving

[tex]\frac{2}{1}[/tex] × [tex]\frac{1}{5}[/tex] = [tex]\frac{2}{5}[/tex]

Answer:

2 over 5

Step-by-step explanation:

Answer:

96°

Step-by-step explanation:

An angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc.

x = 168/2 = 84°

A straight angle is 180 degrees

y = 180 - x = 180 - 84 = 96°

The perfect square [tex](x-a)^2[/tex] can be expanded as follows:

[tex](x-a)^2=x^2-2ax+a^2[/tex]

So, we have to think of the term [tex]-8x[/tex] as [tex]-2ax[/tex], which implies [tex]a=4[/tex].

Thus, we have to add [tex]a^2[/tex], i.e. 16, to complete the perfect square:

[tex](x-4)^2 = x^2-8x+16[/tex]

Answer:

scale factor = 5

Step-by-step explanation:

To determine the scale factor calculate the ratio of corresponding sides of the enlargement to the original, that is

scale factor = [tex]\frac{55}{11}[/tex] = [tex]\frac{45}{9}[/tex] = 5

Answer:

The correct answer is the last one, at the bottom.

Step-by-step explanation:

You need to change in f(x) every 'x' for the expression given in g(x), since you have to build a compound function (fºg)(x).

So F(g(x))= F(x4)=-9*(x4)+3

Resulting (fºg)(x)=-9x4+3 (I only changed 'x' for 'x4', the term +3 is not changed since that is not a variable term, is just a constant number.

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x^{-2}y^{-4}x^3)^{-2}\implies (x^{-2}x^3y^{-4})^{-2}\implies (x^{-2+3}y^{-4})^{-2}\implies (x^{1}y^{-4})^{-2} \\\\\\ \stackrel{\textit{distributing the exponent}~\hfill }{(x^{-2\cdot 1}y^{-2\cdot -4})\implies x^{-2}y^8}\implies \cfrac{1}{x^2}\cdot y^8\implies \cfrac{y^8}{x^2}[/tex]

Answer:

cosine theta equals plus or minus two times square root of two over three, tangent theta equals plus or minus square root of two over four

Step-by-step explanation:

Given:

sinθ=1/3

θ=19.47 degrees

then

cosθ= cos(19.47)=0.942 = 2(√2/3)

tanθ=tan(19.47)=0.35= √2/4

Hence option two is correct:cosine theta equals plus or minus two times square root of two over three, tangent theta equals plus or minus square root of two over four!

Answer:

So second choice.

[tex]\cos(\theta)=\pm \frac{2\sqrt{2}}{3}[/tex]

[tex]\tan(\theta)=\pm \frac{\sqrt{2}}{4}[/tex]

Step-by-step explanation:

I'm going to use a Pythagorean Identity, name the one that says:

[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex].

We are given: [tex]\sin(\theta)=\frac{1}{3}[/tex].

Inserting this into our identity above gives us:

[tex](\frac{1}{3})^2+\cos^2(\theta)=1[/tex]

Time to solve this for the cosine value:

[tex]\frac{1}{9}+\cos^2(\theta)=1[/tex]

Subtract 1/9 on both sides:

[tex]\cos^2(\theta)=1-\frac{1}{9}[/tex]

[tex]\cos^2(\theta)=\frac{8}{9}[/tex]

Square root both sides:

[tex]\cos(\theta)=\pm \sqrt{\frac{8}{9}}[/tex]

9 is a perfect square but 8 is not.

8 does contain a factor that is a perfect square which is 4.

So time for a rewrite:

[tex]\cos(\theta)=\pm \frac{\sqrt{4}\sqrt{2}}{3}[/tex]

[tex]\cos(\theta)=\pm \frac{2\sqrt{2}}{3}[/tex]

So without any other give information we can't know if cosine is positive or negative.

Now time for the tangent value.

You can find tangent value by using a quotient identity:

[tex]\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}[/tex]

[tex]\tan(\theta)= \frac{\frac{1}{3}}{\pm \frac{2\sqrt{2}}{3}}[/tex]

Multiply top and bottom by 3 get's rid of the 3's on the bottom of each mini-fraction:

[tex]\tan(\theta)=\pm \frac{1}{2 \sqrt{2}}[/tex]

Multiply top and bottom by sqrt(2) to get rid of the square root on bottom:

[tex]\tan(\theta)=\pm \frac{1(\sqrt{2})}{2\sqrt{2}(\sqrt{2})}[/tex]

Simplifying:

[tex]\tan(\theta)=\pm \frac{\sqrt{2}}{2(2)}[/tex]

[tex]\tan(\theta)=\pm \frac{\sqrt{2}}{4}[/tex]