A sequence is defined by the recursive function f(n + 1) = –10f(n).

If f(1) = 1, what is f(3)?

3
–30
100
–1,000

Answer:

There are  8 boys in the chorus and 16 girls in the chorus

The graph in the attached figure

Step-by-step explanation:

Let

x----> the number of boys

y----> the number of girls

we know that

[tex]y=2x[/tex] -----> equation A

[tex]x=y-8[/tex] ----> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (8,16)

see the attached figure

therefore

There are  8 boys in the chorus

There are  16 girls in the chorus

Answer:

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

Step-by-step explanation:

[tex]-4x+3=19\qquad\text{subtract 3 from both sides}\\\\-4x+3-3=19-3\\\\-4x=16\qquad\text{divide both sides by (-4)}\\\\\dfrac{-4x}{-4}=\dfrac{16}{-4}\\\\x=-4[/tex]

Step 1: Combine like terms ( 3 and 19) by subtracting 3 to both sides

-4x + (3-3) = 19 -3

-4x = 16

Step 2: Isolate x by dividing -4 to both sides

[tex]\frac{-4x}{-4} =\frac{16}{-4}[/tex]

x = -4

Hope this helped!

Answer:

a building

Step-by-step explanation:

Your exams? Probably at home, unless it’s AZmerit or CAmerit.

Answer:

option B

(−1, 0) and (0, 6)

Step-by-step explanation:

Given in the question two equations,

Equation 1

y =−x² + 5x + 6

Equation 2

−6x + y = 6

plug value of y in second equation

−6x −x² + 5x + 6 = 6

-x² -6x + 5x +6 - 6 = 0

-x² - x + 0 = 0

-x² -x = 0

-x(x+1) = 0

x = 0

and

x = -1

plug value of x in second equation to find y

x = 0

−6(0) + y = 6

 0 + y = 6

 y = 6

 and

x = -1

−6(-1) + y = 6

6 + y = 6

y = 0

Answer:

(−1, 0) and (0, 6)

Step-by-step explanation:

The given system of equations is

[tex]y=-x^2+5x+6[/tex]

and

[tex]-6x+y=6[/tex]

Solve for y in this second equation

[tex]y=6x+6[/tex]

We equate the two equations to get;

[tex]-x^2+5x+6=6x+6[/tex]

[tex]x^2+x=0[/tex]

[tex]x(x+1)=0[/tex]

x=0,x=-1

When x=0,

y=6(0)+6

y=6

When x=-1

y=6(-1)+6

y=0

Answer:

5(pi) (exactly) or 15.7 (approximately)

Step-by-step explanation:

The length of arc of an entire circle is the circumference of the circle.

The length of arc of a semicircle circle is half of the circumference of the circle.

C = pi * d

For a semicircle:

arc length = 0.5 * pi * d

arc length = 0.5 * pi * 10

arc length = 5(pi)

arc length = 15.7

I mean... I think it's a reasonable guess because not gonna lie- chips can get expensive. BUT- It doesn't really make sense because like, she bought so many lollipops. My brain isn't really functioning to do the math- but my best guess would beeeee... UNreasonble. I'm super super sorry if it's wrong. Math isn't my strong point, sorry. Have a nice day!

Answer:

no

Step-by-step explanation:

because 20×.25 = 5 so the lollipop cost $5.00 and then you only have 3.20 left over

Answer:

(7x-1)(x-3)

Step-by-step explanation:

7x^2 - 22x + 3

The factors have to add to -22, but multiply to equal 3. But since the "a" value has a number on it, you have to use it too.

(7x +/- [n1]) ( x +/- [n2]) = 7x^2 - 22x + 3

Since the two numbers multiply to a positive value, they have to have the same sign. (7x-1) (x-3) works to produce the expression when it's foiled.

Answer:

(7x-1)(x-3)

Look in the photos. I hope this helps!

Let me know if you're unsure about anything! Thanks! :)

Let's say the first truck weighs x tons

Then, the weight of 2nd truck = x+2 tons

The weight of 3rd truck = (x + 2) + 2 = x+4 tons

The weight of 4th truck = (x + 4) + 2 = x+6 tons

Total weight of 4 trucks:

x + (x+2) + (x+4) + (x+6) = 32

which can be solved easily to give x = 5

Answer:

92°

Step-by-step explanation:

The supplementary relationship between angles 2 and 3 means lines a and b are parallel. Since those lines are parallel, corresponding angles 1 and 4 are congruent.

m∠1 = m∠4 = 92°

From this triangle we know:

THE AREA:

[tex]A=80cm^2[/tex]

THE HEIGHT:

[tex]H=B+12[/tex]

We know that the area, height, and base of a triangle are related according to the following formula:

[tex]A=\frac{BH}{2} \\ \\ Substituting \ H: \\ \\ A=\frac{B(B+12)}{2} \\ \\ Substituting \ A: \\ \\  80=\frac{B(B+12)}{2} \\ \\ 2(80)=B(B+12) \\ \\ 160=B^2+12B \\ \\ B^2+12B-160=0[/tex]

Solving B by quadratic formula:

[tex]B_{12}=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ B_{12}=\frac{-12 \pm \sqrt{12^2-4(1)(-160)}}{2(1)} \\ \\ B_{12}=\frac{-12 \pm \sqrt{12^2-4(1)(-160)}}{2(1)} \\ \\ B_{1}=8 \ and \ B_{2}=-20[/tex]

Since we can’t have a negative value of the base, the correct option is:

[tex]B=8cm[/tex]

We must use the formula:

[tex]h(t)=-5.2t^2+v_{0}t+h_{0}[/tex]

Since James drops the balloon from a height of 45m, then this is the initial height, so [tex]h_{0}=45m[/tex]. Moreover, at the very instant he drops the balloon the initial velocity is zero, so [tex]v_{0}=0[/tex]. When the ballon hit the ground [tex]h(t)=0[/tex]. Therefore:

[tex]0=-5.2t^2+45[/tex]

Solving this equation:

[tex]5.2t^2=45 \\ \\ t^2=\frac{45}{5.2} \\ \\ t^2=8.653 \\ \\ t=\sqrt{8.653} \\ \\ t=2.941s[/tex]

Rounding to the nearest tenth:

[tex]\boxed{t=2.9s}[/tex]

Finally, the water balloon will hit the ground after 2.9 seconds.

We have the equation:

[tex]h(t)=-16t^2+32t+12[/tex]

But we know that this equation follows the form:

[tex]h(t)=-16t^2+v_{0}t+h_{0}[/tex]

According to this:

The height of the platform is [tex]h_{0}=12ft[/tex]

The initial velocity of the ball is [tex]v_{0}=32ft/s[/tex]

Answer:

Part 1) The inscribed angle is the angle ∠TRS and the intercept arc is the arc LST

Part 2) The inscribed angle is the angle ∠YWX and the intercept arc is the minor arc XY

Part 3) The inscribed angle is the angle ∠YXZ and the intercept arc is the arc YBZ

Part 4) The figure does not show an inscribed angle

Step-by-step explanation:

Part 1) The figure shown a inscribed angle

The inscribed angle is the angle ∠TRS

The intercept arc is the arc LST

Remember that

The inscribed angle measures half that of the arc comprising

so

∠TRS=(1/2)[arc LST]

Part 2) The figure shown a inscribed angle

The inscribed angle is the angle ∠YWX

The intercept arc is the minor arc XY

Remember that

The inscribed angle measures half that of the arc comprising

so

∠YWX=(1/2)[minor arc XY]

Part 3) The figure shown a inscribed angle

The inscribed angle is the angle ∠YXZ

The intercept arc is the arc YBZ

Remember that

The inscribed angle measures half that of the arc comprising

so

∠YXZ=(1/2)[arc YBZ]

Part 4) The figure does not show an inscribed angle

The figure shown a interior angle ∠BAC

Answer:

8cm

Step-by-step explanation

In between AE and DE

Answer:

See below.

Step-by-step explanation:

x^2 + 2x = 19

(x + 1)^2 - 1 = 19

(x + 1)^2 = 20.

Answer:

(x+1)2+2x=19

Step-by-step explanation:

i just did it on a p e x

Answer:

B, A and C.

Step-by-step explanation:

(7x^2-5x+3)+(2x^2+3x-1) is equivalent to expression B .

(3x^2-4x-4)+(-12x^2+2x+11) is equivalent to expression A .

(4x^2-3x-9)+(5x^2+5x+2) is equivalent to expression C .

You combine like terms to arrive with the answer.

The answer is:

- The first operation match with the polynomial:

B.  [tex]9x^{2} -2x+2[/tex]

- The second operation match with the polynomial:

A. [tex]-9x^{2}-2x+7[/tex]

- The third operation match with the polynomial:

C. [tex]9x^{2} +2x-7[/tex]

In order to solve the given operations, we need to group the like terms.

Remember, like terms are terms that share the same variable and the same exponent.

For example:

[tex]x^{2} +2x^{2} +3x^{3} +2=3x^{2} +3x^{3} +2[/tex]

We only operate with the variables that shares the same exponent.

Also, we need to remember the distributive property:

[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]

So, we are given the following polynomials:

[tex]A.9x^{2} -2x+7\\\\B. 9x^{2} -2x+2\\\\C. 9x^{2} +2x-7[/tex]

And we need to perform the following operations:

First operation,

[tex](7x^{2}-5x+3)+(2x^{2} +3x-1)=7x^{2} +2x^{2} -5x+3x+3-1\\\\7x^{2} +2x^{2} -5x+3x+3-1=9x^{2} -2x+2[/tex]

So, the first operation match with the polynomial:

B.  [tex]9x^{2} -2x+2[/tex]

Second operation,

[tex](3x^{2}-4x-4)+(-12x^{2}+2x+11)=3x^{2} -12x^{2} -4x+2x-4+11\\\\3x^{2} -12x^{2} -4x+2x-4+11=-9x^{2}-2x+7[/tex]

So, the second operation match with the polynomial:

A. [tex]-9x^{2}-2x+7[/tex]

Third operation,

[tex](4x^{2} -3x-9)+(5x^{2} +5x+2)=4x^{2}+5x^{2} -3x+5x-9+2\\\\4x^{2}+5x^{2} -3x+5x-9+2=9x^{2} +2x-7[/tex]

So, the second operation match with the polynomial:

C. [tex]9x^{2} +2x-7[/tex]

Have a nice day!

Answer:

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The rate of change of a linear function is the slope m

h(x) = 2x is a linear function with slope m = 2

Hence rate of change is 2

Answer:

B

Step-by-step explanation:

A(rectangle) = 14 * 21 = 294

A(triangle) = ((21 - 12) * 16) / 2 = 72

A(figure) = 294 + 72 = 366

Answer:

B 366 cm²

Step-by-step explanation:

Multiply 21 by 14 to find area of the rectangle

21 × 14 = 294

Subtract 12 from 21

21 - 12 = 9

Multiply 9 by 16

144

Divide 144 by 2 to get area of triangle

144 ÷ 2 = 72

Add 72 with 294 to get final answer

72 + 294 = 366

Answer: B 366 cm²

Substitute:

f(3) = (1/8)(8^(3))

Evaluating the function gives us the answer of 64.

f(3) = 64

let's keep in mind that perpendicular lines have negative reciprocal slopes, hmmm what is the slope of line S anyway?

[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-7}{6-2}\implies \cfrac{-6}{4}\implies -\cfrac{3}{2} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{3}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{2}{3}}\qquad \stackrel{negative~reciprocal}{\cfrac{2}{3}}}[/tex]

so, we're really looking for the equation of a line whose slope is 2/3 and runs through (5,2)

[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{2})~\hspace{10em} slope = m\implies \cfrac{2}{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-2=\cfrac{2}{3}(x-5)\implies y-2=\cfrac{2}{3}x-\cfrac{10}{3} \\\\\\ y=\cfrac{2}{3}x-\cfrac{10}{3}+2\implies y=\cfrac{2}{3}x-\cfrac{4}{3}[/tex]

To find the volume of a rectangular prism, we use the formula

Volume = length × width × height.

Since the rectangular prism has a length of 4 m, a width of 2 m, and a height of 1 m we can plug this information into the formula.

(4 m) (2 m) (1 m)

4 m × 2 m = 8 m

8 m × 1 m = 8 m³

Therefore, the volume of the rectangular prism is 8 m³.

Answer:

8

Step-by-step explanation:

L=Length

W=Width

H=Height

L=4

W=2

H=1

4 x 2 x 1

4 x 2 = 8

8 x 1 = 8

Rearranging to check my work:

1 x 4 x 2

1 x 4 = 4

4 x 2 = 8

I was right.

Hope this answers your question.

Answer: Option D.

Step-by-step explanation:

You need to remember that the circumference of a circle can be calculated with this formula:

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

Where "r" is the radius of the circle and [tex]\pi =3.14[/tex]

In this case the distance 150 feet (From the edge of the track to the center of the circle) is the radius.

Since she walks her horse 4 times around the track, you need to multiply the circumference by 4 to calculate the approximate number of feet that she and her horse will travel:

 [tex]C=4[2(3.14)(150ft)]=3,768ft[/tex]

Answer:

$5

Step-by-step explanation:

Answer:

the answer is 5$

Step-by-step explanation:

A. Getting recommended by a teacher

A getting recommended by a teacher the reason the reason why this is correct is because the teacher is not randomly picking you she already knows who she wants to recommend

Answer:

m = 33*g.

Step-by-step explanation:

The consumption of gas = 396 / 12

= 33 miles / gallon.

m = 33*g (answer).

Answer:

∠E = ∠F = 41°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 given angles and equate to 180

x + x + 98 = 180 ( subtract 98 from both sides )

2x = 82 ( divide both sides by 2 )

x = 41

Hence

∠E = ∠F = 41°

Answer:

y=3.11x

Step-by-step explanation:

Not sure if it's correct. But my reasoning behind it is that 23.81-20.70=3.11 which means every year the cost goes up by $3.11

Answer: The answer is 100.

Step-by-step explanation: 40 divided by 2 = 20

x=20

20x5=100

Answer: answer is 140 on gradpoint.com

Answer:

A. 7 units

Step-by-step explanation:

Answer:

The correct option is A. The length of chord ST in P is 7 units.

Step-by-step explanation:

Given information: QR=7, distance between center and QR is 3.2 units and the distance between center and ST is 3.2 units.

If two chords are equidistant from the center of the circle, then the length of both chords are same.

From the given figure it is clear that the two chords QR and ST are equidistant from the center of the circle,so the length of both chords are same.

[tex]QR=ST[/tex]

[tex]7=ST[/tex]

The length of chord ST in P is 7 units. Therefore the correct option is A.

Answer:a squared-b squared

Step-by-step explanation:

Answer:

[tex](a+b)(a-b)=a^{2} -b^{2}[/tex]

Step-by-step explanation:

This is a example of remarkable identities.

We know that the result of multiplication is called product and the values ​​that multiply are called factors.

We call remarkable identities to certain algebraic expressions with binomial products very frequent in the calculation.

For this example, we got a Product of the sum for the difference of two binomials.

[tex](a+b)(a-b)[/tex]

The product of the sum for the difference of two binomials is equal to the square of the first quantity, minus the square of the second.

[tex](a+b)(a-b)=a^{2} -b^{2}[/tex]

Demostration:

[tex](a+b)(a-b)= a^{2} -ab+ab-b^{2}=a^{2} -b^{2}[/tex]

.

Answer:

1  3/4 miles in 1/4 hour.

Step-by-step explanation:

Write and solve an equation of ratios:

 x           (1/4) hr

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

14 mi       2 hr

Cross multiplying, we get 2x = (1/4)(14), or

                                              x = (1/4)(7), or x = 7/4

Steve can jog 7/4 miles in 1/4 hour.  That's 1  3/4 miles in 1/4 hour.

Answer:

Step-by-step explanation: