algebra 7.5 factor the polynomial

x^2+5x+4

The rule that can be used to find the next term of the sequence 27, 40, 53, 66, 79,... is given by: Option C: a_n = a_(n-1) + 13

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

[tex]a, a + d, a + 2d, ... , a + (n+1)d, ...[/tex]

Its nth term is

[tex]T_n = a + (n-1)d[/tex]

(for all positive integer values of n)

And thus, the common difference is

[tex]T_{n+1} - T_n[/tex]

for all positive integer values of n

Here, the considered sequence is 27, 40, 53, 66, 79,...

We see that:

40-27=13

53-40=13

and so on, the difference between each consequtive pair of terms of this sequence is 13.

Thus, due to having common difference in consequtive terms, this is an arithmetic sequence.

For this series, we've got:

Thus, its nth term is given by:

[tex]T_n = a+(n-1)d= 27 +(n-1)13 = 13n + 14[/tex]

Since the options are using the notation [tex]a_n[/tex] instead of [tex]T_n[/tex], so we will use that too. Thus, nth term and (n-1)th terms are:

[tex]a_n = 13n + 14\\a_{n-1} = 13(n-1) + 14 = 13n + 1\\[/tex]

Thus, we can write nth term in the form of (n-1)th term as:

[tex]a_n = 13n + 14 = 13n + 1 + 13 = a_{n-1} + 13\\\\a_n = a_{n-1} + 13[/tex]

Thus, the rule that can be used to find the next term of the sequence 27, 40, 53, 66, 79,... is given by: Option C: a_n = a_(n-1) + 13

Learn more about arithmetic sequence here:

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Answer:

c

Step-by-step explanation:

[tex]\log_x (1)+\log_y (y)\\\\=\log_x x^0 + 1\\\\=0\cdot \log_x x +1\\\\=0+1\\\\=1[/tex]

Answer:

y=mx+b

Step-by-step explanation:

use that formula

Answer:

                                                                            = length x width x height

Answer:

Tables 3,4 and 5

Step-by-step explanation:

Answer on quizlet.

Answer:

h

Step-by-step explanation:

Part I: Converting the terms into fraction form

Given equation:

First, let's convert the terms (that are in decimals) into fractions.

Replace the fraction forms in the equation:

Part II: Simplifying the division being performed

Since the expression in the parenthesis can't be simplified, we can open the parenthesis. Before we do that, we need to divide the expression by 9/10 (as division is third in BODMAS). This can be done by converting the divisor into it's reciprocal and changing the sign to a multiplication sign.

Since there is no other division being performed, we can simplify the distributive property (as multiplication is fourth in BODMAS).

Part III: Isolating "k" to determine it's value

Combine like terms as needed:

Subtract 7/10 both sides of the equation to isolate "x" and it's coefficient.

Cancel the denominators (as a/b = c/b ⇔ a = c)

Divide both sides by 25 to isolate "k"

Step-by-step explanation:

The answer is -2.2y-1.8

The equivalent expression is -2.2y-1.8

Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Given expression:

1.2y+4.5-3.4y-6.3

To find the equivalent expression:

Simplifying,

= 1.2y - 3.4y + 4.5 - 6.3

= -2.2y-1.8

The above expression is an equivalent expression.

Therefore, -2.2y-1.8 is the equivalent expression.

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Answer:

x = 8

Step-by-step explanation:

Theorem

When a secant segment and a tangent segment meet at an exterior point, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

Secant:  a straight line that intersects a circle at two points

Tangent: a straight line that touches a circle at only one point

Given:

⇒ x² = 16 · 4

⇒ x² = 64

⇒ x² = √(64)

⇒ x = ±8

As distance is positive, x = 8

Answer:

Are you asking for the selling price? If yes the answer should be $50 x (1+25%) = $62.5

The total points earned depends on the number of correct answers.

Hope this helps!

Answer:94.5

Step-by-step explanation:First you have to multiply 3.5x4.5 and the multiply that by 2 which gives you 31.5. Then you multiply 9x3.5 and then you also multiply that by 2 which gives you 63 and then you add 31.5 and 63 which would give you 94.5.

Answer:

Step-by-step explanation:

Given, line equation is

We have to find the line equation which is perpendicular to the given line in slope intercept form.

Now, let us find the slope of the given line.ven line is in slope intercept form,  

y = mx + c where m is slope and c is intercept.

So, by comparison, slope of given line is

Now, we know that product of slopes of perpendicular lines = -1

SLope of that perpendicular line And we are also given that, perpendicular line passes x aixs at 36. Which means that intercept of x – axis is 36.

Answer:

Step-by-step explanation:

Vertically opposite angles are congruent.

∠A = ∠C

∠A + ∠C = 254

∠A + ∠A = 254

      2∠A = 254

        ∠A = 254/2

∠A = 127

Linear Pair: In two adjacent angles, if the non common arms are opposite  rays, then they are called linear and they add up to 180

∠A + ∠B = 180  {linear pair}

127 + ∠B = 180

        ∠B = 180- 127

        ∠B = 53°

Answer:

13

Step-by-step explanation:

(24+2)/2 would be the expression.

PEMDAS so first complete the numbers in the Parantheseis:

(24+2)/2 = 26/2

Since there are no exponents or mulitplication, divide:

26/2 = 13

Hope this helps!

Answer:

30

Step-by-step explanation:

red : blue = 5:3

since difference between 5&3 is automatically 2....then just add 0 to 3

96

In this type of box plot, the two end lines are the absolute maximum and minimum values, each edge of the box is the lower and upper 25%, respectively from left to right, and the line in the box is 50%

So the answer here is the right edge of the box, or 96

Answer:

14 hotdogs

Step-by-step explanation:

Each hotdog is $2.50. Subtract $140 from $175 giving you $25 left to earn. You then take 25 and divide by the unit rate(cost of one hotdog) and you should get 14 more hotdogs need sold to reach $175.

Answer:

40%

Step-by-step explanation:

147 - 105 = 42

42/105 = .4

.4 × 100 = 40%

Answer:

x ≈ 37.13°

Step-by-step explanation:

using the sine ratio in the right triangle

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{13.4}{22.2}[/tex] , then

x = [tex]sin^{-1}[/tex] ( [tex]\frac{13.4}{22.2}[/tex] ) ≈ 37.13° ( to the nearest hundredth )

Answer:

Step-by-step explanation:

Volume of cylinder = base area * height

height of the cylinder = Volume of the cylinder ÷ base area

                                   = 1205.76 ÷ 200.96

                                   = 6 in

Answer:

1/2 anwser is B

Step-by-step explanation:

rolled 2 fair number 500 times right? okay so the sum is a number of anytotal added up correct?

it was shown on the cubes each time ,so you can assume wit 42+10=52?2=x well then just divide that by 500! wich is 1/2

Answer:

B

Step-by-step explanation:

31.112 is actually greater than 30.678 because 31 is a greater number than 30. so the statement stated is false.

24.510 is greater than 24.5 because if you add 2 zeros to 24.5, it would be 24.500(adding zeros after decimal point doesnt change the value). 24.500 is less than 24.510. the numbers are not equal.

72.49 is greater than 72.469 because if you add a zero to 72.49, it will be 72.490. 72.490 is greater than 72.469.

Basically only B is true because 81 is greater than 80.

Answer:

6 feet

Step-by-step explanation:

took the test and got it right

Answer:

6 feet

Step-by-step explanation:

(c) 6 feet

Answer:

B) − 2/9

Explanation:

[tex]\hookrightarrow \sf \dfrac{11}{18} * -\dfrac{4}{11}[/tex]

join both fractions

[tex]\hookrightarrow \sf \dfrac{11*-4}{18*11}[/tex]

simplify by multiplying

[tex]\hookrightarrow \sf \dfrac{-44}{198}[/tex]

simplify the following

[tex]\hookrightarrow \sf -\dfrac{2}{9}[/tex]

[tex]\bold{Heya!}[/tex]

[tex]\sf{\frac{11}{18}(-\frac{4}{11})[/tex]

Apply rule :  [tex]\sf{a(-b) = -ab}[/tex]

[tex]\sf{\frac{11}{18}(-\frac{4}{11}) = -\frac{11}{18}[/tex] × [tex]\sf{\frac{4}{11}[/tex]

[tex]\sf{= -\frac{11}{18}[/tex] × [tex]\sf{\frac{4}{11}[/tex]

Cross - cancel common factor: [tex]\sf{11}[/tex]

[tex]\sf{= -\frac{4}{18}[/tex]

Factor the number: [tex]\sf{4 = 2}[/tex] × [tex]\sf{2}[/tex]

[tex]\sf{= -\frac{2 \: x \: 2}{18}[/tex]

Factor the number: [tex]\sf{ 18 = 2 \: x \: 9}[/tex]

[tex]\sf{= - \frac{2 \: x \: 2}{2 \: x \: 9}[/tex]

Cancel common factor: [tex]\sf{2}[/tex]

[tex]\sf{-\frac{2}{9}[/tex]

Hopefully This Helps ! ~

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[tex]\underline{Answer :}[/tex]

Jaceysan ~

Answer:

I think area will me 24 sq unit

AC=6

BD=8

1/2 × 8 × 6 = 24

[tex]\large{\underline{\underline{\pmb{\frak {\color {blue}{Answer:}}}}}}[/tex]

Arrhenius theory of an acid: This theory was discovered by Sir Svante Arrhenius in 1887. According to this theory acids are hydrogen containing compounds, when dissolves in water it gives (H+) ions.

[tex]\large{\underline{\underline{\pmb{\sf{\color {red}{Question:}}}}}}[/tex]

[tex] \sf \red{What \: is \: Arrhenius's \: definition \: of \: an \: acid?}[/tex]

[tex] \implies[/tex] (B) substance that dissociates.in water to produce hydrogen ions (H+).So, option (B) is correct.

[tex] \boxed{ \frak \red{happy \: learning}}[/tex]

Answer:

∠ MLK = 51°

Step-by-step explanation:

the secant- secant angle MLK is half the difference of the measures of the intercepted arcs , that is

∠ MLK = [tex]\frac{1}{2}[/tex] ( NJ - MK ) ← substitute values

4x + 3 = [tex]\frac{1}{2}[/tex] (170 - (5x + 8) ) ← multiply both sides by 2 to clear the fraction

8x + 6 = 170 - 5x - 8

8x + 6 = 162 - 5x ( add 5x to both sides )

13x + 6 = 162 ( subtract 6 from both sides )

13x = 156 ( divide both sides by 13 )

x = 12

Then

∠ MLK = 4x + 3 = 4(12) + 3 = 48 + 3 = 51°

Answer:

6

Step-by-step explanation:

10 runners

explanation:

1/4 x 10 = 2 1/2

Answer:

2 hours

Step-by-step explanation:

You can express each person's total earning as the formula for a line. (y=mx+b) Use the amount per hour that can be earned as the slope (m) and the amount already earned as the y intercept (b)

Sophie: y=4x+7

Marcos: y=6x+3

Since y is the total amount of money saved and you know that both people need to earn the same amount of money, we know that y is the same in both equations so we can use substitution to substitute one of the equations in for y in the other equation like this:

4x+7=6x+3

From here, solve algebraically

Subtract 3

4x+4=6x

Subtract 5x

4=2x

Divide by 2

x=2

So they will have the same amount of money after 2 hours.