What is the value of ax² + bx + c at x = a ?​

Answer:

1093

Explanation:

Given expression:

Summation:

Formula:

Compute:

[tex]\rightarrow \sf 3^0 + 3^1 + 3^2 + 3^3 + 3^4 + 3^5 + 3^6[/tex]

[tex]\rightarrow \sf 1 + 3 + 9 + 27 + 81 + 243 + 729[/tex]

[tex]\rightarrow \sf 1093[/tex]

Answer:

[tex] \boxed{\rm \: SUM = 1093 }[/tex]

Step-by-step explanation:

Given:

[tex] \huge\rm {{ \sum}^6_{n=0\:} (3)^n}[/tex]

To Find:

Sum of the given finite series

Solution:

We'll use this formula:

[tex] \boxed{\rm SUM = a \cdot\bigg( \cfrac{1 - r {}^{n} }{1 - r} \bigg)}[/tex]

where,

Let's find out the ratio R by using this formulae:

[tex] \rm \: r = \cfrac{a_{n + 1} }{a_n}[/tex]

According to the question,

Substitute:

[tex] \rm \: r = \cfrac{3 {}^{n + 1} }{3 {}^{n} } [/tex]

Apply law of exponents:[a^m/a^n] = a^m-n

[tex] \rm \: r = {3}^{n + 1 - n} [/tex]

Rearrange it as:

[tex] \rm \: r = 3 {}^{n - n + 1} [/tex]

[tex] \rm \: r = 3 {}^{1} = 3[/tex]

So,the ratio R is 3.

Now let's find out the First term A.

To find, substitute the value of n in 3^n:

[tex] \rm \: a = 3 {}^{0} [/tex]

[tex] \rm \: a = 1[/tex]

Hence, first term A is 1.

NOW Substitute the value of the first term A and ratio R onto the formulae of sum:

[tex] \rm \: a \cdot\bigg( \cfrac{1 - r {}^{n} }{1 - r} \bigg)[/tex]

Simplify.

[tex] \rm SUM = \rm \: 1 \times \cfrac{1 - 3 {}^{7} }{ 1 - 1 \times 3} [/tex]

[tex] \rm \: SUM = \cfrac{ - 2186}{1 - 3} [/tex]

[tex] \rm \: SUM = \cfrac{ \cancel{ - 2186} \: \: {}^{1093} }{ \cancel{ - 2} \: \: ^{1} } [/tex]

[tex] \rm \: SUM = 1093[/tex]

We're done!

Hence, the sum of the given Finite series is 1093.

[tex] \rule{225pt}{2pt}[/tex]

Answer:

Hi,

Step-by-step explanation:

Answer B : 51

1+4+7+10+13+16=51

Answer:

84 R4

Step-by-step explanation:

Answer:

84 R4

Step-by-step explanation:

[tex]9\sqrt{760}[/tex]

multiply 9 by each answer choice then pick the one that makes sense

9×84= 756    9×83=747   9×85=765

756+4= 750 747+3= 750  

Answer:

y = -3x+4

Step-by-step explanation:

The slope intercept form of a line is given by

y = mx+b  where m is the slope and b is the y intercept

y = -3x+4

Step-by-step explanation:

We have,

We know that,

y = mx+c

y = -3x+4

Hence, option (D) is correct.

The equation of a line perpendicular to the line 2x − 5y = 7 is y = (-5/2)x + b

An equation is an expression that shows the relationship between two or more variables or numbers.

Two lines are said to be perpendicular if the product of their slopes is equal to -1.

The slope of the line:

2x - 5y = 7

5y = 2x - 7

y = (2/5)x - 7

The slope of the line 2x - 5y = 7 is 2/5. The slope of the line perpendicular is -5/2

Hence:

The equation of a line perpendicular to the line 2x − 5y = 7 is y = (-5/2)x + b

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Answer:

Because the part is missing, this is a subtraction problem. Example: There are 98 hats, 20 of them are pink and the rest are yellow.

Step-by-step explanation:

If the parent graph is transformed to x^2 + 6, this shows that the parent function translated 6 units up the graph to create the graph x^2+6

These are graph with function of leading degree of 2. The parent function for a quadratic graph is x^2

f(x)= x^2

If the parent graph is transformed to x^2 + 6, this shows that the parent function translated 6 units up the graph to create the graph x^2+6

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Answer:

Y = 9.5

(option C)

From the solution, Kevin made an error in step 3 by adding 2 and 3 instead of multiplying 6 and 2. The correct solution is 66

Given the expression solves by Kevin below;

75 - 6 (8 - 6) + 3

Step 2: Simplify the expression in parenthesis

75 - 6(2) + 3

Step 3: Solve the product (PEMDAS)

75 - 12 + 3

75 - 9

Step 4: 66

From the solution, Kevin made an error in step 3 by adding 2 and 3 instead of multiplying 6 and 2

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The expression equivalent to this sentence expression is (5/3) . (5/3) . (5/3). Letter A

.

We know that a power is a multiplication of equal factors - according to the exponent.

A power is represented by aⁿ, where: 'a' indicates base and 'n' indicates exponent.

To represent this expression in multiplication, let's just:

[tex] \large \sf ( \dfrac{5}{3} ) {}^{3} [/tex]

[tex] \blue { \boxed{ \large \sf \dfrac{5}{3} \times \dfrac{5}{3} \times \dfrac{5}{3} }} \\ [/tex]

So, the answer correct is (5/3) . (5/3) . (5/3).

Answer:

10√7

Step-by-step explanation:

[tex]4 \sqrt{7} + 3 \times 2 \sqrt{7} \\ 4 \sqrt{7} + 6 \sqrt{7} \\ 10 \sqrt{7} [/tex]

Answer:

10√7    

Step-by-step explanation:

To combine the radicals, you must have the same number under both radicands. Luckily, you can simplify one of the radicands. This is done by separating the radicand (√28) into its common factors (√4 x √7) and taking the square root of one of the factors (√4 = 2).

4√7 + 3√28                                 <---- Original expression

4√7 + 3(√4 x √7)                         <---- Expand √28

4√7 + (3 x 2)√7                           <----- Take √4

4√7 + 6√7                                   <---- Multiply coefficients

10√7                                            <---- Add both terms

Answer:

$11.12

Step-by-step explanation:

Since the sale is 25% and the shoe was originally priced at $45; you can find the price of the sandal on sale by knowing that 25% means 1/4, so you can just find 1/4 of 45 which is 11.12. 45 * 1/4

Answer:

C. $33.75

Step-by-step explanation:

I took the test

The volume of the three-dimensional object (cone) formed is equal to 32π cubic units.

In this scenario, the effect of rotating the right triangle around line segment AB would form a three-dimensional object known as a cone, with the following dimensions:

Mathematically, the volume of a cone can be calculated by using this formula:

V = 1/3 × πr²h

Substituting the given parameters into the formula, we have;

V = 1/3 × π × 4² × 6

V = π × 16 × 2

V = 32π cubic units.

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Complete Question:

In the diagram below, right triangle ABC has legs whose lengths are 4 and 6. What is the volume of the three-dimensional object formed by continuously rotating the right triangle around line segment AB?

(1) 32π

(2) 48π

(3) 96π

(4) 144π

Answer:

a) $2000

b) 15000(3.20)/(24+x) = new gasoline cost (replace with variable of your choice)

c) 2000-(15000(3.20)/(24+x)) = money saved (replace with variable)

d) ~34.29 miles (34.28571 miles)

Step-by-step explanation:

a) [15000(3.20)]/24 = 2000

b) use the formula above, but the denominator is 24+x (or variable of your choice) because the amount of mpg is increased

c) take the formula from a, then subtract formula in b from it

d) take formula c, replace the variable (variable = money saved) with 600

Answer:

range

Step-by-step explanation:

,domain describes the input values and range describes the output

Answer:

b = 9

Step-by-step explanation:

All the steps are correct. This final step in finding the value of "b" is to take the square root of both sides. This gets rid of the power that "b" is raised to. Once you do this, you are just left with the variable and the answer of 9.

b² = 81

√b² =√81

b = 9

Answer:

Step-by-step explanation:

AB = DC

AD = BC

we use AB and DC

6x - 26 = 8x - 38

-26 + 38 = 8x - 6x

12 = 2x

x = 12 : 2

x = 6

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

check

6 * 6 - 26 = 8 * 6 - 38

36 - 26 = 48 - 38

10 = 10

the answer is good

now we use AD and BC

6y + 12 = 3x + 24

-3x + 6y - 12 = 0

3y - 12 = 0

3y = 12

y = 12 : 3

y = 4

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

check

6 * 4 + 12 = 3 * 6 + 24

24 + 12 = 12 + 24

36 = 36

the answer is good

a, a² + 1 and a + 6 are all in arithmetic progression, in which there is a fixed difference d between consecutive terms. This mean we have

a² + 1 = a + d

a + 6 = a² + 1 + d

Eliminate d and solve for a :

(a² + 1) - (a + 6) = (a + d) - (a² + 1 + d)

a² - a - 5 = -a² + a - 1

2a² - 2a - 4 = 0

a² - a - 2 = 0

(a - 2) (a + 1) = 0

a - 2 = 0   or   a + 1 = 0

a = 2   or   a = -1

The probability of spinning vanilla ice cream with chocolate a rainbow sprinkles is 1/12

Flavor of ice cream: Vanilla, Strawberry, Chocolate

Topping: Rainbow sprinkles, Caramel sauce, Nuts, Cherries

Using the dataset above, we have:

Ice cream = 3

Topping = 4

The number of different combinations is calculated as:

Combination = ice cream * Topping

Evaluate

Combination = 3 * 4

Combination = 12

Hence, the number of different combinations is 12

The vanilla ice cream with chocolate a rainbow sprinkles is just one of the 12 combinations.

So, the probability is:

P = 1/12

Hence, the probability of spinning vanilla ice cream with chocolate a rainbow sprinkles is 1/12

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[tex]12^{-2} \times 4^3\\\\=(4 \times 3)^{-2} \times 4^3\\\\=4^{-2} \times 4^3 \times 3^{-2}\\\\=4^{-2+3} \times 3^{-2}\\\\=4^1 \times \dfrac1{3^2}\\\\=\dfrac 49[/tex]

Answer:

4:12pm

Step-by-step explanation:

85 minutes = 1 hour and 25 minutes

2:47pm  + 1 hour 25 minutes = 3:72 pm

72 minutes = 1 hour 12 minutes so add another 1 hour to 3 and the balance is 12 minutes so walk ends at 4:12pm

Another way to look at it is as follows:
After 13 minutes, the time is 2:47 + 0:13 = 3pm

Remaining time left is 85-13 = 72 minutes = 1 hour: 12 minutes. Add that to 3pm and you get 4:12pm

Answer: hmmm, all i could say it is 2,2 function, you have to calculete the other parts yourself.

Step-by-step explanation:

Answer:

10:4

Step-by-step explanation:

it can be simplified

We can actually deduce here that the honey to oats ratio that doesn't follow the pattern in the table is: 10:4.

Ratio actually refers to the way that two or more numbers are compared in relation to their size to each other. It shows how much of one number is found in another.

From the honey to oats ratio, we can see that the pattern goes thus:

This is because 10 - 3 = 7

Then 15 - 7 = 8

Therefore, the ratio that doesn't follow the pattern is 10:4.

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Answer:

41.87 cm²

Step-by-step explanation:

Area of shaded region :

Answer:

No, I don't think so....

Step-by-step explanation:

Volume = 1/2 * Base * Height * Length

     Height =  Base * tan 10  

The underlined items you have,but there is still 2 unknowns and only one equation to solve them <=====  so I think you need one more piece of the puzzle to solve....    either the base or the length of the prism.

Answer:

8 ≤ x

Step-by-step explanation:

6(2 − 6x) ≤ 4 − 35x

Expand bracket;

12 - 36x ≤ 4 − 35x

Add 36x to both sides to get;

12 ≤ 4 + x

Subtract 4 from both sides to get;

8 ≤ x

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to solve the inequality 6(2-6x)≤4-35x.

[tex]\triangle~\fbox{\bf{KEY:}}\star[/tex]

First, we can use the distributive property and distribute 6:

[tex]\star\large\pmb{12-36x\leq4-35x}[/tex]

Now, add 35x to both sides:

[tex]\star\large\pmb{12-x\leq 4}[/tex]

And now, subtract 12 from both sides:

[tex]\star\large\pmb{-x\leq-8}[/tex]

Divide both sides by -1 and watch what happens:

[tex]\star\large\pmb{x\geq 8}[/tex]

Have you noticed that the inequality sign changed from "less than" to "greater than"?

Well, that happened because we divided both sides by a negative number, -1.

Thus, [tex]\star~\large\pmb{x\geq 8}[/tex]

Hope this helps you out! :D

Ask in comments if any queries arise.

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[tex]\pmb{M^ar_ib^el\:P^eri}[/tex]

[tex]P=(\stackrel{\stackrel{x}{adjacent}}{2\sqrt{2}}~~,~~\stackrel{\stackrel{y}{opposite}}{2\sqrt{2}}) \\\\\\ tan(\theta )=\cfrac{\stackrel{opposite}{2\sqrt{2}}}{\underset{adjacent}{2\sqrt{2}}}\implies \theta =tan^{-1}\left( \cfrac{2\sqrt{2}}{2\sqrt{2}} \right)\implies \theta =tan^{-1}(1)\implies \theta =45^o[/tex]

Make sure your calculator is in Degree mode.

Answer:

6 cups

Step-by-step explanation:

hope this helps!

Answer:

B

Step-by-step explanation: