Factorise x squared - 5x - 6

Answer:

31

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

[tex]\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}[/tex] or [tex]\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}[/tex]

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

[tex]\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}[/tex]

Therefore, the solution is 31.

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Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as [tex]\displaystyle \large{a_{n-1} \cdot r = a_n}[/tex] meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as:

[tex]\displaystyle \large{r=\frac{a_{n+1}}{a_n}}[/tex]

Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:

[tex]\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}\\\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}[/tex]

Above should be applied for series that have common ratio not equal to 1.

[tex]\displaystyle \large{S_n=a_1 \cdot n}[/tex]

Above should be applied for series that have common ratio exactly equal to 1.

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Topics

Sequence & Series — Geometric Series

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Others

Let me know if you have any doubts about my answer, explanation or this question through comment!

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The Area of the shaded portion = area of 5 shaded squares = 80 in.².

Area of a square = s², where the edge length is s.

Edge length of each small square = 12/3 = 4 in.

Area of the shaded portion = area of 5 shaded squares = 5(s²)

s = 4 in.

Area of the shaded portion = 5(4²)

Area of the shaded portion = 80 in.²

Therefore, the Area of the shaded portion = area of 5 shaded squares = 80 in.².

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The quadratic function f(x) = 2x² – 44x + 185 is written in vertex form is f(x) = 2(x –  11)² – 57.

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

The quadrattic equation is f(x) = 2x² – 44x + 185.

Take common 2 from the equation, we have

[tex]f(x) = 2(x^2 - 22x )+ 185[/tex]

Add and subtract 121, we have

[tex]f(x) = 2(x^2 - 22x +121 - 121 )+ 185\\\\f(x) = 2[(x^2 - 11)^2-121]+ 185\\\\f(x) = 2(x-11)^2 - 242 + 185\\\\f (x ) = 2(x-11)^2 -57[/tex]

And we know that the standard equation

f(x) = a(x - h)² + k

On comparing, we have

The vertex (h, k) is (11, -57).

More about the quadratic equation link is given below.

https://brainly.com/question/2263981

Answer:

1. 2

2. 2

3. 11

4. -57

Step-by-step explanation: actual answers

Answer:

slope = 7

Step-by-step explanation:

Slope-intercept form of a linear equation:  y = mx + b

(where m is the slope, and b is the y-intercept)

Therefore, for the equation: y = 7x + 9/16

Answer:

Mixed Fraction: [tex]5\frac{1}{5}[/tex]

Improper Fraction: [tex]\frac{26}{5}[/tex]

Step-by-step explanation:

[tex]\mathrm{Rewrite\:as}[/tex]

[tex]=5+0.2[/tex]

[tex]\mathrm{Convert\;0.2\;to\;a\;fraction}:\frac{1}{5}[/tex]

[tex]=5+\frac{1}{5}[/tex]

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

[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fraction:}\:a\frac{b}{c}=\frac{a\cdot \:c+b}{c}[/tex]

[tex]5\frac{1}{5}=\frac{5\cdot 5+1}{5}=\frac{26}{5}[/tex]

[tex]=\frac{26}{5}[/tex]

~lenvy~

Hello!

First, let's convert 5.2 into a fraction:

[tex]\bf{5\displaystyle\frac{2}{10} }[/tex]

Simplify:

[tex]\bold{5\displaystyle\frac{1}{5}}[/tex]

We turned this number into a mixed number.

That's why it's mixed - we have a whole number and a fraction.

Now, convert the mixed number into an improper fraction.

Step 1: Multiply the whole number times the denominator.

5×5=25

Step 2: Add the numerator.

25+1=26

The denominator stays the same.

Therefore, the answer is

[tex]\bold{\displaystyle\frac{26}{5}}[/tex]

Hope everything is clear.

Let me know if you have any questions!

#KeepLearning :-)

Answer:

Step-by-step explanation:

The volume of cone formula:

Substitute te given values into the formula and solve for r:

Answer:

10 cm

Step-by-step explanation:

Volume of a cone

  [tex]\sf V= \dfrac{1}{3} \pi r^2 h[/tex]

where:

Given information:

To find the length of the radius, substitute the given values into the formula and solve for r:

[tex]\begin{aligned}\sf V& = \sf \dfrac{1}{3} \pi r^2 h\\\\\implies \sf 400 \pi & = \sf \dfrac{1}{3} \pi r^2(12)\\\\ \sf 400 \pi & = \sf \dfrac{12}{3} \pi r^2\\\\ \sf 400 \pi & = \sf 4\pi r^2\\\\ \sf \dfrac{400 \pi}{4 \pi} & = \sf r^2\\\\ \sf r^2 & = \sf 100 \\\\ \sf \sqrt{r^2} & = \sf \sqrt{100}\\\\ \sf r & = \sf 10\end{aligned}[/tex]

Therefore, the length of the radius of the cone is 10 cm.

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Step-by-step explanation:

i) linear

ii)2

iii) 1

iv) 1

v) -1/5

First one can u type the options in the comment

Answer:

1225p

Step-by-step explanation:

1 minute = 35p

07:40 to 08:15 : 35 minute

=> 35 minute *35p=1225p

    To answer these questions, we need to graph the equation as well as turn this into slope-intercept form, this is y = mx + b. The m is our slope and the b is the y-intercept.

-> See attached for graph

   1.5x + 4.5y = 18

   4.5y = -1.5x + 18

   y = -[tex]\frac{1}{3}[/tex]x + 4

      The slope is -[tex]\frac{1}{3}[/tex]

                y = -1/3x + 4

       The y-intercept is (0, 4)

                The x-intercept is (12, 0)

Circles are perfectly round figures that have only one central angle

The measure of JML is 233 degrees

The question is incomplete, so I will give a general explanation using the following parameter:

JL = 127 degrees.

Angles at a point add up to 360 degrees

So, we have:

JML + 127 = 360

Make JML the subject

JML = 360 - 127

JML = 233

Hence, the measure of JML is 233 degrees

Read more about circles and arcs at:

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Answer:

11mi² = 28489869m²

Step-by-step explanation:

m² = mi² / 0.00000038610

The solutions to the system of the equations graphed below are where the graphs intersect:

In this case, the two graphs intersect at (0,6) and (-3, -3)

So the solutions are (0,6) and (-3,-3)

Hope that helps!

The solution to the system of the equations below is: (0,6) and (-3,-3)

The solutions are where the two graphs of the equations intersect

Answer:

the value of n is -1.5

Step-by-step explanation:

I hope the question was to find the unknown.

Answer:

n= -3/2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

n=−32

Decimal Form:

n=-1.5

Mixed Number Form:

n=−112

The computation of the significance level shows that the p-value is less than 0.01 and the conclusion is that Americans use the internet more than 7 hours weekly.

It should be noted that the significance level simply means the probability that an event occured by chance.

From the complete question, it can be noted that at 0.01 significance level, the t statistic is 17.873 and the degree of freedom is 539.

The p-value for the right tailed test is 0. Therefore, since the p value is less than 0.01, we will reject the null hypothesis. The conclusion is that Americans use the internet more than 7 hours weekly.

Learn more about significance level on:

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Answer:

10x^3+8x^2-4x+1 is answer

First, you know that Jackson (let call her J) scored 42 more points than L (Leslie).  What we don't know is how many points L scored so we can use a variable that will be 'x'.

So the equation will be J=42+x.

We also know that the total points is 1,144.

To find out what x is we first subtract 1,144-42.  We then get 1,102.

We are now left with 2x and 1,102 so we divide 1,102 by 2 and get 551.

551=x so now we can plug that in.

J = 551 + 42

Jackson scored 593 points and Leslie scored 551 points

(You can use bar modeling to do solve this problem.  An example of bar modeling is shown below.  

Answer:

Yes they are similar

Step-by-step explanation:

Divide the length VW by ST

24 ÷ 16 = 1.333

Divide the length VU by SR

16 ÷ 12 = 1.333

→ As they have the same scale factor, they are similar.

Answer:

Step-by-step explanation:

First when triangles are similar angles are congruent and the side ratio are the same .

18/24=12/16=m/32

3/4=3/4=m/32

3/4=m/32

4m=96

m=24

Answer:

A = 5

I hope you have an amazing day!

Answer: C. 125.66 in²

Step-by-step explanation:

      This is asking us to find the surface area of this cone. We can use the formula and solve.

A = πrl + πr²

A = π(4)(6) + π(4)²

A = π(4)(6) + π(4)²

A ≈ 125.66 in²

      It would take C. 125.66 in² of toilet paper to cover the surface of this cone.

Answer:

4 084 080 ways

Step-by-step explanation:

The number of ways is :

[tex]C^{3}_{18}\times C^{6}_{15}\times C^{9}_{9}[/tex]

___________

Since

  18C3=816

  15C6=5 005

  9C9=1

then

[tex]C^{3}_{18}\times C^{6}_{15}\times C^{9}_{9}=816\times5005\times1= 4\ 084\ 080[/tex]

Answer:

c

Step-by-step explanation:

because you can simplify 4/6 by 2.

2 goes into 4 twice and then 2 goes into 6 3 times

2/3

Answer:

3/10

Step-by-step explanation:

Hope this helped

Answer:

[tex]23n + 64[/tex]

Step-by-step explanation:

Hope this helps

Check the picture below.

Two other examples of linear relationships are changes of units and finding the total cost for buying a given item x times.

Two examples of linear relationships that are useful are:

Changes of units:

These ones are used to change between units that measure the same thing. For example, between kilometers and meters.

We know that:

1km = 1000m

So if we have a distance in kilometers x, the distance in meters y is given by:

y = 1000*x

This is a linear relationship.

Another example can be for costs, if we know that a single item costs a given quantity, let's say "a", then if we buy x of these items the total cost will be:

y = a*x

This is a linear relationship.

So linear relationships appear a lot in our life, and is really important to learn how to work with them.

If you want to learn more about linear relationships, you can read:

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Using the t-distribution, as we have the standard deviation for the samples, it is found that the data does not provide statistical evidence that there is a difference.

At the null hypotheses, it is tested if there is no difference in the means, that is, the subtraction is of 0, hence:

[tex]H_0: \mu_1 - \mu_2 = 0[/tex]

At the alternative hypotheses, it is tested if there is a difference, hence:

[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]

For each sample, they are given by:

[tex]\mu_1 = 1.82, s_1 = \frac{1.51}{\sqrt{100}} = 0.151[/tex]

[tex]\mu_2 = 1.65, s_2 = \frac{1.39}{\sqrt{100}} = 0.139[/tex]

Hence, for the distribution of differences, they are given by:

[tex]\overline{x} = \mu_1 - \mu_2 = 1.82 - 1.65 = 0.17[/tex]

[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.151^2 + 0.139^2} = 0.205[/tex]

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Then:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

[tex]t = \frac{0.17 - 0}{0.205}[/tex]

[tex]t = 0.83[/tex]

Considering that it is a two-tailed test, as we are testing if the mean is different of a value, with 100 + 100 - 2 = 198 df and a significance level of 0.02, the critical value is of [tex]|t^{\ast}| = 2.3453[/tex].

Since the absolute value of the test statistic is less than the critical value, we do not reject the null hypothesis, which means that the data does not provide statistical evidence that there is a difference.

More can be learned about the t-distribution at https://brainly.com/question/13873630

graphed below:

[tex]\sf f(x)=3x^2-6x+5[/tex]

Answer:

Given function:    [tex]f(x)=3x^2-6x+5[/tex]

Vertex form:  [tex]y=a(x-h)^2+k[/tex]  

(where [tex](h, k)[/tex] is the vertex)

Expand vertex form:

[tex]y=ax^2-2ahx+ah^2+k[/tex]

Compare coefficients of given function with expanded vertex form

Comparing coefficient of [tex]x^2[/tex]:

[tex]3=a[/tex]

Comparing coefficient of [tex]x[/tex]:

[tex]\ \ \ \ \ -6=-2ah\\\implies-6=-2 \cdot 3h\\\implies -6=-6h\\\implies h=1[/tex]

Comparing  constant:

[tex]\ \ \ \ \ \ 5=ah^2+k\\\implies5=3(1)^2+k \\\implies 5=3+k\\\implies k=2[/tex]

Therefore, the vertex is (1, 2)

As the leading coefficient is positive, the parabola will open upwards.

Additional plot points:

[tex]f(0)=3(0)^2-6(0)+5=5[/tex]

[tex]f(2)=3(2)^2-6(2)+5=5[/tex]

(0, 5) and (2, 5)

The perimeter of the isosceles right triangle comes to be 6+3√2.

Given that the length of one leg of an isosceles right triangle = 3 ft

A right-angle triangle having sides other than hypotenuse equal to each other is called an isosceles right triangle.

So, The length of the other leg of an isosceles right triangle = 3 ft

From Pythagoras theorem

Hypotenuse²=Perpendicular²+Base²

So, in the given isosceles right triangle

Hypotenuse²=Leg 1²+Leg2²

Leg 1=Leg2 = 3 feet

Hypotenuse² =  3²+3²

Hypotenuse = 3√2 ft.

So, the perimeter of the triangle = 3+3+ 3√2

The perimeter of the triangle =6+3√2

Therefore, The perimeter of the isosceles right triangle comes to be 6+3√2.

To get more about the right triangle visit:

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Answer:

6 + 3 StartRoot 2 EndRoot ft

Step-by-step explanation:

Edge2022

Answer:

146

Step-by-step explanation:

Given;

 ∠A and ∠B are supplementary. The measure of ∠A is 34°.

To Find;

What is the measure of ∠B?

Note:

Supplementary = 180 degree

Solve:

Since supplementary = 180 degree

34 + x = 180

Subtract 34 from both sides

x + 34 - 23 = 180 - 34

Simplify

x = 146

Hence, the measure of ∠B is 146

~Learn with Lenvy~