geometric sequence
-48, 96, -192, 384, …

Answer:

5(x + 1)(x - 1)

Step-by-step explanation:

Given

5x² - 5 ← factor out 5 from each term

= 5(x² - 1) ← x² - 1 is a difference of squares

= 5(x + 1)(x - 1)

The factors are 5, (x + 1) and (x - 1)

Final answer:

When the expression 5x² − 5 is completely factored, one of its factors is 5, and after applying the difference of squares, the fully factored form is 5(x + 1)(x − 1).

Explanation:

When the expression 5x2 − 5 is completely factored, what we're looking for is a common factor that can be taken out of both terms. In this case, both terms have a factor of 5, so we can factor out 5 from the expression, yielding:

5(x² − 1).

This expression can be further factored as the difference of squares, which is a special factoring rule that applies to expressions in the form of a² − b²:

5(x + 1)(x − 1).

So, one of the factors is 5, another factor is (x + 1), and the last factor is (x − 1).

ANSWER

The area of the triangle is 48.6 square feet to the nearest tenth.

EXPLANATION

The area of the triangle is calculated using the formula

[tex]Area= \frac{1}{2} bc \sin(A) [/tex]

where A=94° is the included angle, b=7.5 inches and c=13 inches.

We substitute the values into the formula to obtain:

[tex]Area= \frac{1}{2} \times 7.5 \times 13 \sin(94 \degree) [/tex]

Area=48.6 ft² to the nearest tenth.

Answer:

2625080

Step-by-step explanation:

just multiply by 365

Answer: 2,625,080

Explanation: 1 day = 7192, 365 days x 7192 = 2,625,080

Answer:

We could say 10

Step-by-step explanation:

1) Remove unneeded info

2) Divide the length by the distance between posts

68/7

3) Will give you a decimal but ro7nd up to 10

Answer:

Total = Principal * (1 + 6%/2)^2*years

Total = 11,000 * (1.03)^2*10

Total = 11,000 * (1.03)^20

Total = 11,000 * 1.8061112347

Total = 19,867.22

Step-by-step explanation:

Answer: C. [tex]25.6\ cm^2 [/tex]

Step-by-step explanation:

Given: Circle M has a radius = 7.0 cm.

The shortest distance between P and Q on the  circle (arc length)= 7.3 cm.

Now, the central angle 'x' is given by :-

[tex]x=\dfrac{l}{r}\\\\\Rightarrow\ x=\dfrac{7.3}{7}=1.04285714286\ radian[/tex]

Now, the area of sector is given by :-

[tex]A=\dfrac{1}{2}r^2x\\\\\rightarrow\ A=\dfrac{1}{2}(7)^2(1.04285714286)\\\\\Rightarrow\ =25.55\approx25.6\ cm^2 [/tex]

Answer:

C.

Step-by-step explanation:

I did the test.

ANSWER

(2,2)

EXPLANATION

Since f(x) and its inverse function are symmetric about the line y=x, if (a,b) lies on the graph of f, then (b,a) must lie on f inverse.

The point (2,2) lies on f and the same time on f inverse.

The solution is a point that satisfies both equations.

Hence the correct choice is:

(2,2)

Answer:

Did the test. Answer is (2,2).

Answer:

diameter

Step-by-step explanation:

A chord is a line segment connecting any 2 points on the circumference of the circle.

The diameter connects 2 points and also passes through the centre of the circle, making it the longest chord.

Answer:

Linear   Quadratic   Exponential

Step-by-step explanation:

Answer:

First table models Linear, second quadratic and third one exponential functions.

Step-by-step explanation:

To find whether the given table models a linear function there should be a constant change in y values with the constant change in x values of the table.

We take the example of first table written as linear.

Here change in x values is

6 - 5 = 1

7 - 6 = 1

8 - 7 = 1

Similarly change in y values is

1 - 4 = -3

-2 - 1 = -3

-5 -(-2) = -3

There is a common difference in y values = -3

So the given table models linear function.

We take the second table.

For quadratic function with the constant change in x values, difference of difference in y values is constant.

Change in x - values

6 - 5 = 1

7 - 6 = 1

8 - 7 = 1

Difference in y values

1 - 0 = 1

4 - 1 = 3

9 - 4 = 5

Now difference in difference of y values

3 - 1  = 2

5 - 3 = 2

Here, difference in difference of y values is 2

So the given table models a quadratic equation.

Now we take the third table.

For exponential function in the form of [tex]f(x) = a(r)^{n}[/tex] there should be a common ratio in the terms of y values.

[tex]\frac{\text{Second term of y}}{\text{First term of y }}= \frac{2}{1}=2[/tex]

[tex]\frac{\text{Third term of y}}{\text{Second term of y }}= \frac{4}{2}=2[/tex]

So there is a common ratio of 2 in each term.

Therefore, the given table models exponential equation.

First table models Linear, second quadratic and third one exponential functions.

____________________________________________________

Answer:

Your answer would be 0.343.

____________________________________________________

Step-by-step explanation:

In the probability questions like this one, in order to get the answer,we would use the multiplication rule.

In your questions, we are trying to find the probability of ALL of your friends going to the mall with you.

Lets make it easier for you.

Whenever in probability you can say and, you multiply.

This means that you would try to find if friend 1 and friend 2 and friend 3 will say yes.

That's the same as saying friend 1's probability × friend 2's  probability × friend 3's  probability

We know that each friend has a 0.70 chance of saying yes.

Using the multiplication rule, we would just multiply 0.7 three times.

[tex]0.7 *0.7*0.7=0.343[/tex]

When you multiply, you should get 0.343.

There is a 0.343 chance of ALL your friends saying yes to go to the mall with you.

0.343 would be your FINAL answer.

____________________________________________________

To solve this problem, you need to consider the probability of each friend agreeing to go to the mall individually, then multiply these probabilities together to find the probability that all three will say yes.
Since each friend has a 0.70 chance of saying yes, we can calculate the combined probability as follows:
For the first friend, the probability is 0.70.
For the second friend, the probability is also 0.70.
For the third friend, the probability remains 0.70.
To find the combined probability that all three friends will say yes, we multiply the individual probabilities together:
\( Probability (All Say Yes) = Probability (Friend1 says Yes) \times Probability (Friend2 says Yes) \times Probability (Friend3 says Yes) \)
\( Probability (All Say Yes) = 0.70 \times 0.70 \times 0.70 \)
When you calculate this, you get:
\( Probability (All Say Yes) = 0.343 \)
So the answer is c. 0.343.

Answer:

the answer will be the letter Y

Step-by-step explanation:

because the darker shaded side are at the bottom and one is at the top and don't forget about the two triangles

Answer:

2. B

3. C

4. B

5. D

Step-by-step explanation:

2) The sequence is multiplying by -2 each time. This means that it is geometric.

The next two terms would be:

[tex]32*-2=-64\\-64*-2=128\\128*-2=-256[/tex]

This means that the answer is B

3) The sequence is being multiplied by [tex]\frac{1}{3}[/tex] each time. This means that it is geometric.

The next 3 terms would be:

[tex]3*\frac{1}{3} =1 \\\\1*\frac{1}{3} =\frac{1}{3} \\\\\frac{1}{3} *\frac{1}{3} =\frac{1}{9}[/tex]

I am assuming that the answer is C and that you were unable to type the fractions.

4) We know that the common difference is 1.5, so that is the coefficient of our variable and the starting value is 15. This means that we can write an equation as follows

[tex]f(x)=1.5(x-1)+15[/tex]

Now we can find the first 4 terms

[tex]f(1)=15.0\\f(2)=16.5\\f(3)=18.0\\f(4)=19.5[/tex]

This would mean that the answer is B

5) We know that this is a geometric series, we know the common ratio, and we know the first term. This means we can write the equation as follows

[tex]f(x)=4.5(10)^{x-1}[/tex]

Now we can find the first 4 terms

[tex]f(1)=4.5\\f(2)=45\\f(3)=450\\f(4)=4500[/tex]

Unless you meant that the ratio was [tex]\frac{1}{10}[/tex], the answer is D, none of the above

Answer:

Hence final answer is x=46

Step-by-step explanation:

We need to find the value of x using given triangle.

Given that ED is angle bisector of angle E.

Then we can apply this formula

[tex]\frac{EG}{EH}=\frac{DG}{DH}[/tex]

[tex]\frac{63.8}{55}=\frac{58}{x+4}[/tex]

[tex]\frac{63.8}{55}=\frac{58}{x+4}[/tex]

Cross multiply

63.8(x+4)=55(58)

63.8(x+4)=3190[tex]x+4=\frac{3190}{63.8}[/tex]

x+4=50

x=50-4

x=46

Hence final answer is x=46

Answer:

Option D. 5

Step-by-step explanation:

we know that

The initial value of the function is the y-intercept, so is the value of the function when the value of x is equal to zero

In this problem observing the table

For x=0

The value of y is equal to y=5

therefore

The initial value is 5

Answer:

It is 5!

Step-by-step explanation:

I just did the test and got it correct.

Answer:

48

Step-by-step explanation:

Assuming that the numbers went in a pattern instead of a random order it would be 48 because 48 divided by 3 would be 24. 24 would be the first number though, so it would be 48 because 24 plus 24 is 48.

Hope this helps, have a great day!

Thhe answer is 48 :]

Answer:

V = (1/3)(π)(6 in)²(10 in) = 120π in³

Step-by-step explanation:

The volume of a cone of radius r and height h is V = (1/3)πr²h.

Here, that volume is V = (1/3)(π)(6 in)²(10 in) = 120π in³

Answer:

120pi

Step-by-step explanation:

Answer:

26.9

Step-by-step explanation:

Right now we have '8' in the tenths place.  That '6' following the '8' requires us to round up.  Thus, 26.86 to the nearest tenth is 26.9.

Less than 95%

Why because if you change .9 into a percentage, it turns into 90%

I hope that was correct

[tex]\text{Hey there!}[/tex]

[tex]\text{Is .9 greater or less than 95\%?}[/tex]

[tex]\bf{.9\rightarrow0.9\rightarrow\frac{18}{20}}[/tex]

[tex]\bf{95\%\rightarrow0.95\rightarrow\frac{19}{20}}[/tex]

[tex]\bf{You\ could\ reask\ yourself\ is\frac{18}{20}\ greater\ or\ less\ than\frac{19}{20}}?[/tex]

[tex]\text{Note: Solve the fractions/ decimals/ percentages to where you can}[/tex] [tex]\text{understand it better}[/tex]

[tex]\text{After that you'd find your result to your question}[/tex]

[tex]\boxed{\boxed{\text{Thus your answer will be: .9 is LESS THAN 95\%}}}[/tex] [tex]\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer: The constant of proportinality is 150.

Step-by-step explanation:

The equation of inverse proportion has the following form:

[tex]y=\frac{k}{x}[/tex]

Where "k" is the constant of proportionality.

In this case, you can observe that R is inversely proportional to d², because it has the form of inverse proportion:

[tex]R=\frac{150}{d^2}[/tex]

Therefore, you can identify that the constant of proportionality "k" is:

[tex]k=150[/tex]

Answer: A. 150

Step-by-step explanation:

However, point slope equations can be awkward to use in some algebraic operations. In such cases, it may be helpful to convert the equation into a different form, the standard form. The standard form of an equation is Ax + By = C. In this kind of equation, x and y are variables and A, B, and C are integers.

Answer:

m = - 1/6

Step-by-step explanation:

Since 2/3 is larger than 1/2, m is going to be less than 0 because you have to subtract 2/3 to get to the right. That makes a and b incorrect. I can tell you that the answer doesn't appear to be there.

m + 2/3 = 1/2    Subtract 2/3

m = 1/2 - 2/3     The common denominator is 6

m = 3/6 - 4/6     Do the subtraction

m = - 1/6  

You might want to check out the - 1/8.  

The Answer: m = - 1/6

12√18-6√20-3√50-8√45

*Break each radical up into the product of a radical of a perfect square and a second radical*

12(√9*√2)-6(√4*√5)-3(√25*√2)-8(√9*√5)

*Simplify the radicals*

12(3√2)-6(2√5)-3(5√2)-8(3√5)

*Distribute*

36√2-12√5-15√2-24√5

*Combine like terms*

21√2-36√5

Hope this helps!!

The simplified form of the expression is 21√2-36√5.

Given,

12√18-6√20-3√50-8√45

Here,

12√18-6√20-3√50-8√45

⇒ Break each radical up into the product of a radical of a perfect square and a second radical.

Rewriting the expression,

12(√9*√2)-6(√4*√5)-3(√25*√2)-8(√9*√5)

⇒ Simplify the radicals

12(3√2)-6(2√5)-3(5√2)-8(3√5)

⇒ Distributive property

36√2-12√5-15√2-24√5

⇒ Combine like terms

21√2-36√5

Thus the simplified expression is 21√2-36√5.

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Answer:

A. 12 in^2

Step-by-step explanation:

Polygon ABCD is a kite. The area of a kite is equal to the product of the diagonals divided by 2.

One diagonal is segment AC.

AC = AE + CE = 2 + 2 = 4

The other diagonal is segment BD.

BD = BE + ED

BD = BE + 2BE

BD = 3BE

BD = 3(2) = 6

The diagonals measure 4 inches and 6 inches.

area = diagonal1 * diagonal2/2

area = 4 * 6 /2

area = 24/2

area = 12

Answer: A. 12 in^2

Answer: D. 2.8 - 0.6t

Step-by-step explanation:

The t represents how much time it takes. So, it goes down by 0.6 per second until it gets to 0.

A garage door's bottom is 2.8 meters above the ground. The door descends at a pace of 0.6 meters per second when a button is pressed. The equation for the above situation is 2.8 + 0.6t = 0. Option C is correct.

Equations are statements that affirm the equivalence of two expressions that are joined by the equals symbol "=". An equal sign ("=") links two expressions together to form an equation.

It is given that, the bottom of a garage door is 2.8 meters above the ground. When a button is pushed, the door moves down at a rate of 0.6 meters per second.

The two expressions on each side of the equals sign are referred to as the "left-hand side" and "right-hand side" of the equation. The right side of an equation is typically assumed to be zero.

Suppose t represents the number of seconds, The equation for the given condition is,

2.8 + 0.6t = 0.

Thus, a garage door's bottom is 2.8 meters above the ground. The door descends at a pace of 0.6 meters per second when a button is pressed. The equation for the above situation is 2.8 + 0.6t = 0. Option C is correct.

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Answer:

[tex]\large\boxed{Domain:\ x\in\left(0;\ \dfrac{1}{4}\right>\to0<x\leq\dfrac{1}{4}}[/tex]

Step-by-step explanation:

[tex]f(x)=\sqrt{x-1},\ g(x)=\dfrac{1}{4x}\\\\f\bigg(g(x)\bigg)-\text{instead of x in the function equation f(x) put}\ \dfrac{1}{4x}:\\\\f\bigg(g(x)\bigg)=\sqrt{\dfrac{1}{4x}-1}=\sqrt{\dfrac{1}{4x}-\dfrac{4x}{4x}}=\sqrt{\dfrac{1-4x}{4x}}\\\\\text{The domain}\ D:\\\\\dfrac{1-4x}{4x}\geq0\ \wedge\ 4x\neq0\\\\\dfrac{1-4x}{4x}\geq0\iff(1-4x)(4x)\geq0\\\\1-4x=0\to4x=1\to x=\dfrac{1}{4}\\\\4x=0\to x=0\\(look\ at\ the\ picture)\\\\(1)\qquadx\in\left<0,\ \dfrac{1}{4}\right>\\\\\\4x\neq0\qquad\text{divide both sides by 4}\\\\(2)\qquad x\neq0[/tex]

[tex]\text{From}\ (1)\ \text{and}\ (2)\ \text{We have}\ x\in\left(0,\ \dfrac{1}{4}\right>[/tex]

Answer:

[tex]\sin (\frac{\pi}{12})=\frac{\sqrt{6}-\sqrt{2}}{4}[/tex]

Step-by-step explanation:

We want to find the exact value of

[tex]\sin \frac{\pi}{12}[/tex]

We rewrite the given expression to obtain:

[tex]\sin \frac{\pi}{12}=\sin (\frac{\pi}{3}-\frac{\pi}{4})[/tex]

We use the identity:

[tex]\sin (A-B)=\sin A \cos B-\sin B \cos A[/tex]

[tex]\sin ( \frac{\pi}{3}- \frac{\pi}{4})=\sin \frac{\pi}{3} \cos \frac{\pi}{4}-\sin \frac{\pi}{4} \cos \frac{\pi}{3}[/tex]

[tex]\sin ( \frac{\pi}{3}- \frac{\pi}{4})=\frac{\sqrt{3}}{2} \times \frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2} \times \frac{1}{2}[/tex]

[tex]\sin ( \frac{\pi}{3}- \frac{\pi}{4})=\frac{\sqrt{6}-\sqrt{2}}{4}[/tex]

The exact value of sin(π/12) is ±√(2 - √3)/2 by using half-angle formula

To find the exact value of sin(π/12), we can use the half-angle formula for sine:

sin(x/2) = ±√[(1 - cos(x))/2]

In this case, x = π/6.

Therefore, we can use the half-angle formula with x = pi/6 to find the exact value of sin(π/12).

sin(pi/12) = ±√[(1 - cos(π/6))/2]

Let's calculate the value step by step:

cos(π/6) = √3/2

sin(π/12) = ±√[(1 - √3/2)/2]

To simplify further, let's rationalize the denominator:

sin(π/12) = ±√[(2 - √3)/4]

sin(π/12) = ±√(2 - √3)/2

Therefore, the exact value of sin(π/12) is ±√(2 - √3)/2.

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It is -10

Because when you take two points from the table and put it into the equation y=my+b...

So for example, take (-4,-16) from the table and substitute into x and y...

-16=m(-4) + b

And then substitute all the options given in the question, so I tried -10 first and put it in the place of m( in the equation) because m is the slope.

Then the equation would look like this:

-16= -10(-4) +b

Now solve for b

B= 24

And then check your answer by the RHS and LHS Method..

-16=-40 +24

Which is equal to:

-16=-16

There fore the the slope of this equation is 10

Answer: 5

Step-by-step explanation:

The formula to find slope is given by :-

[tex]\text{Slope}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the given table in picture,

Take [tex]x_1=0\ ;\ y_1=4\\\\x_2=2\ ;\ y_2=14[/tex]

Then, slope of the given function will be given by :-

[tex]\text{Slope}=\dfrac{14-4}{2-0}\\\\\Rightarrow\text{Slope}=\dfrac{10}{2}=5[/tex]

Hence, the slope of the given function  = 5

x -5 > -2

Add 5 to both sides:

x > 3

The answer is the 3rd choice.

Answer:

x>3

Step-by-step explanation:

just add 5 to both sides :p

Equation 1: -x-y = 1y, -x = 2y

Equation 2: 1y = x+3 , y = x+3

Substitute equation 2 into equation 1

-x = 2y

-x = 2(x+3)

-x = 2x + 6

-3x = 6

x = -2

Substitute x=-2 into equation 2

y = x+3

y = -2+3

y = 1

So, (x,y) = (-2,1)

0.13 times 15 is 1.95. Which means the coral reef grows 1.95 m in 15 weeks.

For this case we have reef coral grows 0.13 meters per week, if we want to indicate how much will have grown in 15 weeks we have the following rule three:

0.13 metrs ---------------> 1 week

x -------------------------------> 15 weeks

Where "x" is the number of meters reef coral grows in 15 weeks.

[tex]x = \frac {15 * 0.13} {1}\\x = 1.95 \ m[/tex]

Thus, in 15 weeks it grows 1.95 meters.

Answer:

[tex]1.95 \ m[/tex]