Find the sixth term of the
geometric sequence, given the
first term and common ratio.
a1=5 and r=3/2​

Answer:y=4x+11

Step-by-step explanation:

Substitute the coordinates in each of the above equations,

Then the left hand side of the equation should be equal to the right hand side of the equation.

By substituting the above coordinates in the second answer,

-1= 4(-3)+11

-1=-1

Answer:

b

Step-by-step explanation:

Answer:

y - 11 = - 3(x + 2)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) is a point on the line

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (- 2, 11)

m = [tex]\frac{11-5}{-2-0}[/tex] = [tex]\frac{6}{-2}[/tex] = - 3

Use either of the 2 given points for (a, b)

Using (a, b) = (- 2, 11), then

y - 11 = - 3(x - (- 2)), that is

y - 11 = - 3(x + 2)

Answer:

Options A and B.

Step-by-step explanation:

An ellipse is represented by the equation [tex]\frac{(x+5)^{2}}{625}+\frac{(y-7)^{2}}{49}=1[/tex]

We have to find the foci of the given ellipse.

Ellipse having equation [tex]\frac{(x-h)^{2}}{a^{2} }+ \frac{(y-k)^{2} }{b^{2} }=1[/tex]

Then center of this ellipse is represented by (h, k) and foci as (c, 0) and (-c, 0).

And c is represented by c² = a² - b²

So we co relate this equation with our equation given in the question.

a = √625 = 25

b = √49 = 7

and c² = (25)² - (7)²

c² = 625 - 49 = 576

c = ±√576

c = ±24

Now we know center of the ellipse is at (-5, 7) so foci can be obtained by adding and subtracting x = 24 from the coordinates of the center.

Center 1 will be [(-5+24=19), 7] ≈ (19, 7)

Center 2 will be [(-5-24=-29), 7] ≈ (-29, 7)

Therefore, options A and B are correct.

Answer:

A and B

Step-by-step explanation:

Using the law of Tangents:

Tan(angle) = Opposite leg / Adjacent leg.

Using the provided information:

Tangent (61) = BC / 5.7

Solve for BC:

BC = 5.7 x tangent(61)

BC = 10.3 miles ( rounded to the nearest tenth).

The distance from point B to point C is 10.3 mi (to the nearest tenth).

If we have a right angle triangle,

Then, tanθ = Opposite side/ Adjacent side

Here in the right angle triangle ABC,

Adjacent side = AB = 5.7 mi

θ = 61°

We have to find the BC.

∴  tanθ = Opposite side/ Adjacent side

⇒ tanθ = BC/AB

⇒ tan61°= BC/5.7

⇒ BC = 5.7×tan61°

⇒ BC = 10.283 = 10.3 (to the nearest tenth)

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Answer:

x = 2.9.

Step-by-step explanation:

14.3 - 0.4x = 2.6x + 5.6​

14.3 - 5.6 = 2.6x + 0.4x

8.7 = 3x

x = 8.7 / 3 = 2.9 (answer).

Answer:

x=2.9

Step-by-step explanation:

14.3 -0.4x = 2.6x + 5.6​

Add .4x to each side

14.3 -0.4x+.4x = 2.6x+.4x + 5.6​

14.3 = 3x+5.6

Subtract 5.6 from each side

14.3 - 5.6 = 3x - 5.6

8.7 =3x

Divide each side by 3

8.7/3 = 3x/3

2.9=x

Answer:

True.

Step-by-step explanation:

It is because it is in the form [tex]a^2x^2+2abx+b^2[/tex] and this equals [tex](ax+b)^2[/tex].

Why it is in that form:  well comparing  [tex]a^2x^2+2abx+b^2[/tex], we have [tex]a=1, b=1[/tex]. Testing, plug in those values:

[tex](1)^2x^2+2(1)(1)x+(1)^2[/tex]

[tex]1x^2+2x+1[/tex]

[tex]x^2+2x+1[/tex].

This has the squared form of [tex](x+1)^2[/tex].

Test if you like:

[tex](x+1)^2[/tex]

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

Use foil to expand:

First: x(x)=x^2

Outer: x(1)=x

Inner: 1(x)=x

Last: 1(1)=1

---------------Add together

[tex]x^2+2x+1[/tex]

It does indeed equal.

Answer:

(-12,3)

Step-by-step explanation:

Since (6,3) is on the graph of f(x), then f(6)=3.

We want to see if we can use f(6)=3 to find a point on the graph of f(-1/2x).

If you compare -1/2x to 6, what must x be so they have the same value? x=-12.

If that wasn't obvious to you, just solve:

-1/2x=6

Multiply both sides by -2:

x=-12

So if we replace x with -12 in f(-1/2x) we get

f(-1/2*-12)

f(6)=3

And we were given this f(6)=3 so f(-1/2*-12)=3.

Answer:

21

Step-by-step explanation:

To find the greatest common factor between a set of numbers, you can list the factors of those numbers and find the largest one they each have in common.

A factor of a number is a number which can be multiplied against another number to get your original number.

Factors of 21: 1, 3, 7, 21

Factors of 63: 1, 3, 7, 9, 21, 63

Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105

21 is the greatest factor which all three have in common.

Answer:

21

Step-by-step explanation:

GCF of 21, 63 and 105

Break these numbers into prime factors

21 = 3*7

63 = 9*7 = 3*3*7

105 = 15*7 = 3*5*7

There is a 3, 7 in  all the terms

The largest number of 3's in the terms is 1

The largest number of 7's is 1

Multiply the largest number of terms together

3*7 =21

Answer:

D

Step-by-step explanation:

First, find the slope using the slope formula.  The slope is 3.

Now plug in any of the x and y values and the value of the slope into the slope-intercept form equation to solve for b.

9=3(3)+b, solve for b

b=0, Now convert the equation y=3x into slope-intercept form.

y-9=3(x-3) This is the equation of the line, the plant will be about 36 cm tall after 12 months.

Answer:

Step-by-step explanation:

2x3 out of 10x5+4x4+8x3.2x3(5x2+2x+4)

Answer:

2*5*5 +2*2*2*2 + 2*2*2*3

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

The line with equation x = - 5

Is a vertical line parallel to the y- axis and passing through all points with an x- coordinate of - 5

Answer:

Part 1) The measure of arc AB is 50°

Part 2) The measure of angle AOB is 50°

Part 3) The measure of angle BDA is 25°

Step-by-step explanation:

step 1

Find the measure of arc AB

we know that

arc AD+arc BD+arc AB=360° -----> by complete circle

substitute the given values

212°+98°+arc AB=360°

310°+arc AB=360°

arc AB=360°-310°=50°

step 2

Find the measure of angle AOB

we know that

The measure of angle AOB is the same that the measure of arc AB by central angle

so

m∠AOB=arc AB=50°

step 3

Find the measure of angle BDA

we know that

The inscribed angle measures half that of the arc comprising

so

m∠BDA=(1/2)[arc AB]

we have

arc AB=50°

substitute

m∠BDA=(1/2)[50°]=25°

The arc of a circle is defined as the part or segment of the circumference of a circle.

The measure of arc AB is 50 degrees.

An angle of a circle is an angle that is formed between the radii, chords, or tangents of a circle.

The measure of angle AOB is 50 degrees.

The measure of angle BDA is 25 degrees.

The measure of arc AB is

The measure of angle AOB is

The measure of angle BDA is

The arc of a circle is defined as the part or segment of the circumference of a circle.

An angle of a circle is an angle that is formed between the radii, chords, or tangents of a circle.

1. The measure of arc AB is,

[tex]\rm Arc \ AD+Arc \ BD+Arc \ AB=360\\\\212+98+Arc\ AB=360\\\\310+Arc \ AB=360\\\\ Arc \ AB=360-310\\\\ Arc\ AB = 50[/tex]

The measure of arc AB is 50 degrees.

2. The measure of angle AOB is,

[tex]\rm m\angle \ AOB=Arc \ AB=50 degrees[/tex]

The measure of angle AOB is 50 degrees.

3. The measure of angle BDA is,

[tex]\rm m \angle BDA=\dfrac{1}{2}\times Arc AB\\\\ m \angle BDA=\dfrac{1}{2}\times 50\\\\ m \angle BDA = 25[/tex]

The measure of angle BDA is 25 degrees.

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Answer:

Step-by-step explanation:

Later on in the course, I hope you are told that answers should not rely on diagrams.

Since you have to answer the question somehow, the answer (directly) is BCA. Since this is an appearance question (that's what the answer looks like), you can only state the answer, There really (in this case) is no what to offer a proof).

Answer:

The average rate of speed = 53.8 mph

Step-by-step explanation:

Sharon drove 188.3 miles.

She was driving for 3 1/2 hours = 7/2 = 3.5hours

To find the average speed simply divide the miles she drove by driving hours:

188.3/3.5

53.8 mph.

Therefore the average rate of speed = 53.8 mph....

Answer:

Hi there!

The answer to this question is: C. -3/2

Step-by-step explanation:

You first find the slope of the equation using the change of y over the change of x formula. You should get 2/3. Then it asks its perpendicular that is simply the negative reciprocal of the original slope. All you do is flip the fraction and make it negative, your final answer should be -3/2

Answer:

C

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, - 1 ) and (x₂, y₂ ) = (3, 3)

m = [tex]\frac{3+1}{3+3}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{2}{3} }[/tex] = - [tex]\frac{3}{2}[/tex] → C

Answer:

[tex]\sqrt{7^{2}+5^{2}  }[/tex]

Step-by-step explanation:

Since the whole base of the triangle is 14, we can half it to find the base of one triangle which is 7.

Pythagoras Theorem states a² + b² = c²

In this case a² = 7 and b² = 5 so,

a² + b² = c²

a² = 7 and b² = 5

7² + 5² = c²

49 + 25 = c²

74 = c²

√74 = c

Answer:

[tex] \sqrt{2}[/tex]

Step-by-step explanation:

You can multiply by sqrt 6/sqrt 6 to get rid of the sqrt in the denominator. This leaves you with 2(sqrt 3)(sqrt 6)/sqrt 36. The sqrt's in the numerator can be multiplied to get 2(sqrt 18). The sqrt 36 can be simplified to just 6. Sqrt 18 can be split into sqrt 9 and sqrt 2. The sqrt 9 can be taken out and simplified as 3. 3x2=6. This leaves you with 6(sqrt 2)/6. The 6 in the numerator cancels the 6 in the denominator and just leaves sqrt 2.

Answer:

aaaaaaaaaaa

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\text{For}\ f(x)=a^{(x+h)}+k\\\\\text{always}\ a>0\\\\\text{If}\ a>1,\ \text{then the function is  increasing}\\\\\text{If}\ 0<a<1,\ \text{then the function is decreasing}\\\\<-h,\ k>-\text{translation vector}\\\\============================[/tex]

[tex]\text{From the graph:}\\\\\text{the function is decreased}\to 0<a<1\\\\h<0\\\\k>0[/tex]

The correct answer is: Option: C

              C.  0<a<1

We are given a graph of a exponential function as:

             [tex]f(x)=a^{x+h}+k[/tex]

We know that the function is a exponential decay function if: 0<a<1

and it represents a exponential growth function if: a>1

Hence, by looking at the graph we observe that the graph is continuously decreasing with increasing values of x.

This means that the graph is a graph of exponential decay function.

Hence, we get:   0<a<1

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=years\dotfill &3 \end{cases} \\\\\\ I=(500)(0.02)(3)\implies I=30~\hfill \stackrel{\textit{total amount in the account}}{500+30\implies 530}[/tex]

Answer:

[tex]5x^2 y^2[/tex]

Step-by-step explanation:

We need to use the properties shown below to solve this:

1. [tex]\sqrt[n]{x^a} =x^{\frac{a}{n}}[/tex]

2. [tex]\sqrt{x}\sqrt{x}  =x[/tex]

3.  [tex]\sqrt{x} \sqrt{y}=\sqrt{x*y}[/tex]

Area of a triangle is given by  1/2 * base * height, so we do that and simplify:

[tex]A=\frac{1}{2}(\sqrt{5x^3} )(2\sqrt{5xy^4} )\\A=\frac{1}{2}(5x^3)^{\frac{1}{2}}*2*(5xy^4)^{\frac{1}{2}}\\A=\sqrt{5}x^{\frac{3}{2}}*\sqrt{5}\sqrt{x} }  y^2\\A=\sqrt{5} \sqrt{5}x^{\frac{3}{2}} x^{\frac{1}{2}}y^2\\A=5*x^2y^2\\A=5x^2 y^2[/tex]

Answer:

No this is not a solution

Step-by-step explanation:

Substitute the points in and see if the equation is true

-16 = 3(99) - -51

-16  = 297+51

-16 =348

False, so this is not a solution

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{8}{ h},\stackrel{4}{ k})\qquad \qquad radius=\stackrel{4}{ r} \\\\[-0.35em] ~\dotfill\\\\ (x-8)^2+(y-4)^2=4^2\implies (x-8)^2+(y-4)^2=16[/tex]

Answer:

wht are da choices

Step-by-step explanation:

Answer:

graph 2

Step-by-step explanation:

It is partially written in Slope-Intercept Form [y = mx + b]. That 2 tells you to move up two units.

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The graph of f(x) +2 graph 3.

 since  y-intercepts is 2

The answer is option C

            slope(m)=tan∅=y axis/x axis.

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Answer:

[tex]x1=-5+\sqrt{2} \\x2=-5-\sqrt{2}[/tex]

Step-by-step explanation:

First we need to simplify your equation by grouping coefficients:

[tex]x^{2} +10x+23=0[/tex]

Now, there are two valid values for your variable, wich are determined by the following expressions:

[tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a} \\\\x=\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]

We will call those expression as (eq1) and (eq2) in their respective order

In both scenarios the following is derived from your grouped equation.

[tex]a=1\\b=10\\c=23[/tex]

[tex]x1=\frac{-10+\sqrt{10^{2}-4*1*23 } }{2*1}\\x2=\frac{-10-\sqrt{10^{2}-4*1*23 } }{2*1}[/tex]

[tex]x1=\frac{-10+\sqrt{8 } }{2}\\\\x2=\frac{-10-\sqrt{8} }{2}[/tex]

We can simplify these expressions a little more by doing the following

[tex]x1=\frac{-10+2 \sqrt{2 } }{2}\\\\x2=\frac{-10-2\sqrt{2} }{2}[/tex]

The result is

[tex]x1=-5+\sqrt{2} \\x2=-5-\sqrt{2}[/tex]

We can not simplify these expresions anymore

Answer:

68%

Step-by-step explanation:

According to the empirical rule:

So first we have to find how many standard deviations away from the mean are the given two values. This can be done by converting them into z scores.

The formula to calculate the z-score is:

[tex]z=\frac{\text{Data Value}-\text{Mean}}{\text{Standard Deviation}}[/tex]

Using the given values in above formula, we get:

For x = 2.3

[tex]z = \frac{2.3-2.9}{0.6}=-1[/tex]

For x = 3.5

[tex]z = \frac{3.5-2.9}{0.6}=1[/tex]

This means we have to tell how many data values are within one standard deviation of the mean. According to the empirical rule 68% of the values are between z= -1 and z = 1. So the answer is 68%

68% of students at the college have a GPA between 2.3 and 3.5.

The empirical rule states that for a normal distribution, 68% of the values falls within one standard deviation, 95% of the values falls within two standard deviation, and 99.7% of the values falls within three standard deviation.

Hence:

For a mean of 2.9 and a standard deviation of 0.6.

68% falls within 2.9 ± 0.6 = (2.3, 3.5)

68% of students at the college have a GPA between 2.3 and 3.5.

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Answer:

Step-by-step explanation:

What he did at the end of the given equations is solve for x in x + 8y= 21

x = 21 - 8y                Substitute that result in the top equation.

7(21 - 8y) + 5y = 14  is the correct step To continue Remove the brackets

147 - 56y + 5y = 14   Combine

147 - 51y = 14             Add 51y to both sides.

147 = 51y + 14            Subtract 14 from both sides.

133 = 51y                   divide by 51

y = 2.61 rounded.

The incorrect step is underlined and italicized.

Answer:

1/4

Step-by-step explanation:

Slope of a line can be found if given two points by using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1) \text{ and } (x_2,y_2)[/tex] are points on the line.

However, I like to line up the points vertically and subtract then put 2nd difference over 1st difference.

Like this:

(   3   ,   3   )

-(  -1   ,    2  )

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

   4          1

So the slope is 1/4.

Answer:

The slope is 1/4.

Step-by-step explanation:

To find the slope, you'd need to use formula of slope. The slope is y2-y1/x2-x1=rise/run.

y2=3

y1=2

x2=3

x1=(-1)

3-2/3-(-1)

3-2/3+1

3-2=1

3+1=4

Therefore, the slope is 1/4, which is our answer.

I hope this helps!

Answer:

[tex]4(2+\sqrt{2})\text{ square unit}[/tex]

Step-by-step explanation:

Given function that shows the area of the opening,

[tex]A(\theta)=16 \sin\theta (\sin \theta + 1)[/tex]

If [tex]\theta = 45^{\circ}[/tex]

Hence, the area of the opening would be,

[tex]A(45^{\circ})=16 \sin 45^{\circ} (\cos 45^{\circ} + 1)[/tex]

[tex]=16\times \frac{1}{\sqrt{2}}\times (\frac{1}{\sqrt{2}}+1)[/tex]

[tex]=16(\frac{1}{2}+\frac{1}{\sqrt{2}})[/tex]

[tex]=8+\frac{16}{\sqrt{2}}[/tex]

[tex]=8+4\sqrt{2}[/tex]

[tex]=4(2+\sqrt{2})\text{ square unit}[/tex]

Answer:

[tex]\sin( 115 \degree) = 0.906[/tex]

Step-by-step explanation:

The general point on a unit circle is given by

[tex]x = \cos( \theta) [/tex]

[tex]y = \sin( \theta) [/tex]

where

[tex] \theta = 115 \degree[/tex]

is the terminal side of the angle in standard position.

Therefore

[tex]x = \cos( 115 \degree) [/tex]

[tex]y = \sin(115 \degree) [/tex]

lies on this circle

This angle intersects the unit circle at

[tex]( - 0.423,0.906)[/tex]

Hence we must have

[tex] \cos( 115 \degree) = - 0.463[/tex]

[tex]\sin( 115 \degree) = 0.906[/tex]

let's recall that, on the number line, for the positive side, the farther from zero, the larger the number, thus 100 is a much larger number than 10.

now, on the negative side of the number line, the farther from zero, the smaller the number, thus -1 is much much larger number than -1,000,000,000.

is -3 ≥ -15, is -3 larger or equals to -15, well, certainly is not equal but is certainly larger, yes.