What is the value of -7(x^2-6)+2y when x=2 and y=-6? A. –1 B. 0 C. 1 D. 2

Answer: c

Step-by-step explanation:

Answer:

[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right) = \log(\frac{1}{100})[/tex]

Step-by-step explanation:

Given

[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right)[/tex]

Required

The sum

Using the laws of logarithm, we have:

[tex]\log(a) + \log(b) = \log(ab)[/tex]

Take the first two terms of the series

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3}) = \log(\frac{1}{2} * \frac{2}{3})[/tex]

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3}) = \log(\frac{1}{3})[/tex]

Include the third term

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) = \log(\frac{1}{3} * \frac{3}{4})[/tex]

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) = \log(\frac{1}{4})[/tex]

Include the fourth term

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) + \log(\frac{4}{5}) = \log(\frac{1}{4} *\frac{4}{5})[/tex]

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) + \log(\frac{4}{5}) = \log(\frac{1}{5})[/tex]

Notice the following pattern

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3}) = \log(\frac{1}{3})[/tex] ---------------- n =2

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) = \log(\frac{1}{4})[/tex] -------------- n = 3

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) + \log(\frac{4}{5}) = \log(\frac{1}{5})[/tex] ----------- n = 4

So the sum of n series is:

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ ............ + \log(\frac{n}{n+1}) = \log(\frac{1}{n+1})[/tex]

So, the sum of the series is:

[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right)[/tex]

[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right) = \log(\frac{1}{99+1})[/tex]

[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right) = \log(\frac{1}{100})[/tex]

Answer: [tex]100\ cm^3[/tex]

Step-by-step explanation:

Given

The ratio of mixture of sand and cement is 5:3

If the total volume of mixture is [tex]160\ cm^3[/tex]

Suppose there is 5x and 3x cubic centimeter of sand and cement respectively i.e.

[tex]\Rightarrow 5x+3x=160\\\Rightarrow 8x=160\\\Rightarrow x=20\ cm^3[/tex]

Sand [tex]5x=5\times 20=100\ cm^3[/tex]

So, there is [tex]100\ cm^3[/tex] of sand in the mixture

Answer:

x=37

Step-by-step explanation:

50+24=74

74/2=37

Answer: 79 more

Step-by-step explanation:

Answer:

GIRL NO WAY IM LITTERALY TAKING THAT TEST RN AND IM TRYING TO FIGURE OUT THAT SAME QUESTION LOL

Step-by-step explanation:

BUT I THINK ITS -0.5 DONT TAKE MY WORD FOR IT IM JUST ASSUMING ITS THE ANSWER BC ITS THE ONLY ONE THAT MAKES SENSE

Step-by-step explanation:

To find the equation of a parabola we need to have 3 points. The intercept of the X axis is the X intercept. The definition of an intercept is when the other value is equal to zero. (3,0) and (9,0)

There appears to not be enough points to answer your question. we also need a vertex

Answer:

662.44 total paid

Step-by-step explanation:

907.07X.33(33% off)=299.33 discount

907.07-299.33=607.74 sales price

607.74+.09=54.70 sales tax

607.74+54.70=662.44 sales price including sales tax

Answer:19

Step-by-step explanation: draw the tanks put 6 fish in each tank until you get all 115 in each tank

Answer:

(a) -1

(b) -2

Step-by-step explanation:

(a) Replace the a's with 1 and the b's with 3 to get 1*3 = 1-3+1 = -1

(b) We already figured out that (1*3) equals -1 so we just need to find -1*2. Using same strategy as part a, replace a and b with -1 and two, respectively. -1*2 = -1-2+1= -2. Hope this helps and sorry if I made a mistake. :)

Answer:

4/27

Step-by-step explanation:

F(x) = 4(1/3)^x

Let x =3

F(3) = 4(1/3)^3

Exponents first

F(3) = 4 * 1/27

Then multiply

f(3) = 4/27

Answer:

4/27

Step-by-step explanation:

f(x) = 4(1/3)^x

f(3) = 4(1/3)^3

f(3) = 4(1/27)

f(3) = 4/27

hope that helps

Answer:

Step-by-step explanation:

123 X 8000 = 984000

984000/48 = 20500(PUT EURO SIGN)

Answer:

[tex]P(Win) = 0.30[/tex]

Step-by-step explanation:

Given

[tex]P(Win) = 0.30[/tex]

[tex]P(Lose) = 0.55[/tex]

Required

[tex]P(Win)[/tex]

This is already stated in the question as:

[tex]P(Win) = 0.30[/tex]

Answer:

Step-by-step explanation:

3rd one

Answer:

[tex]\frac{-7}{12} , \frac{-6}{12} , \frac{-5}{12},\frac{-4}{12} ,\frac{-3}{12} ,\frac{-2}{12} ,\frac{-1}{12},\frac{1}{12} ,\frac{2}{12}[/tex]

Step-by-step explanation:

Given :

To find rational number between -2/3 and 1/2

Firstly need to equate their denominator

[tex]\frac{-2(4)}{3(4)} =\frac{-8}{12} \\\frac{1(3)}{4(3)} =\frac{3}{12}[/tex]

Now,

Rational number between these two numbers will be :

[tex]\frac{-7}{12} , \frac{-6}{12} , \frac{-5}{12},\frac{-4}{12} ,\frac{-3}{12} ,\frac{-2}{12} ,\frac{-1}{12},\frac{1}{12} ,\frac{2}{12}[/tex]

Answer:

20 km

Step-by-step explanation:

Circumference is given by

C = pi*d

20 pi = pi *d

Divide  each side by pi

20 =d

I dkabouthtisoneiuisrhihurg

Step-by-step explanation:

answer is in photo above

Answer:

0.25

Step-by-step explanation:

f(1)=(1/4)^1

0.25

Answer:

[tex] \displaystyle b = - 14[/tex]

[tex] \displaystyle c = - 54[/tex]

Step-by-step explanation:

to figure out b we can consider the following formula:

[tex] \displaystyle \frac{ - b}{2a} = h[/tex]

the form of vertex coordinate given by

[tex] \displaystyle (h,k)[/tex]

so according to the question

[tex] \displaystyle (h,k) = ( - 7, - 5)[/tex]

by order pair we obtain:

[tex] \displaystyle h = - 7, k = - 5[/tex]

now substitute the value of h and a to the formula:

[tex] \displaystyle \frac{ - b}{2(- 1)} = - 7[/tex]

simplify multiplication:

[tex] \displaystyle \frac{ - b}{ - 2} = - 7[/tex]

cross multiplication:

[tex] \displaystyle - b = 14[/tex]

divide both sides by -1:

[tex] \displaystyle b = - 14[/tex]

now we need to figure out C to do so substitute -7 for x and -5 for y which yields:

[tex] \displaystyle - {7}^{2} - 14( - 7) + c = - 5[/tex]

simplify square:

[tex] \displaystyle -49 - 14( - 7) + c = - 5[/tex]

simplify multiplication:

[tex] \displaystyle -49 + 98+ c = - 5[/tex]

simplify addition:

[tex] \displaystyle 49+ c = - 5[/tex]

cancel 49 from both sides:

[tex] \displaystyle c = - 54[/tex]

hence,

___________________________________

[tex]\quad\quad\quad\quad\tt{ a{x}^{2} + bx + c}[/tex]

[tex]\quad\quad\quad\quad\tt{ a \: = - 1}[/tex]

[tex]\quad\quad\quad\quad\tt{ h = - 7}[/tex]

[tex]\quad\quad\quad\quad\tt{ k \: = - 5}[/tex]

[tex]\quad\quad\quad\quad\tt{y = a(x - h {)}^{2} } + k[/tex]

[tex]\quad\quad\quad\quad\tt{y = - 1(x - ( - 7) {)}^{2} } + ( - 5)[/tex]

[tex]\quad\quad\quad\quad\tt{y = - 1(x + 7 {)}^{2} } - 5[/tex]

[tex]\quad\quad\quad\quad\tt{ \boxed{y = - {x}^{2} - 14x - 54}}[/tex]

[tex]\quad\quad\quad\quad\tt{ \boxed{ \boxed{ \color{magenta}{b = - 14}}}}[/tex]

[tex]\quad\quad\quad\quad\tt{ \boxed{ \boxed{ \color{magenta}{c = - 54}}}}[/tex]

[tex]\quad\quad\quad\quad\tt{ - 7 = \frac{b}{2(a)} }[/tex]

[tex]\quad\quad\quad\quad\tt{ - 7 = \frac{b}{2(-1)} }[/tex]

[tex]\quad\quad\quad\quad\tt{ - 7 = \frac{b}{-2} }[/tex]

[tex]\quad\quad\quad\quad\tt{ (- 2)( - 7) = - b }[/tex]

[tex]\quad\quad\quad\quad\tt{ \frac{ (- 2)( - 7)}{ - 1} = b }[/tex]

[tex]\quad\quad\quad\quad\tt{ \frac{ 14}{ - 1} = b }[/tex]

[tex]\quad\quad\quad\quad\tt{ \boxed{ - 14 = b }}[/tex]

[tex]\quad\quad\quad\quad\tt{y = - {(-7)}^{2} - 14(-7) - 54}[/tex]

[tex]\quad\quad\quad\quad\tt{y = - 49 +98 - 54}[/tex]

[tex]\quad\quad\quad\quad\tt{y = - 49 +98 - 54}[/tex]

[tex]\quad\quad\quad\quad\tt{y = 49 - 54}[/tex]

[tex]\quad\quad\quad\quad\tt{ \boxed{y = - 5}}[/tex]

[tex]\quad\quad\quad\quad\tt\huge{ \boxed{ \boxed{ \color{magenta}{b = - 14}}}}[/tex]

[tex]\quad\quad\quad\quad\tt\huge{ \boxed{ \boxed{ \color{magenta}{c = - 54}}}}[/tex]

___________________________________

#CarryOnLearning

✍︎ C.Rose❀

Answer:

i think its 110

Step-by-step explanation:

hope it helps

Answer:

There are no graphs

Step-by-step explanation:

"what graph below best represents the range for a tip "

Brian

120 * .2 = 24

24 < d

Hayden

120 * .25 = 30

d ≤ 30

24 < d ≤ 30

Answer:

B. [tex]\frac{x + 6}{10x}[/tex]

Answer:

question one:

x = 6.018150231520483

adjacent angle = 7.986355100472928

Step-by-step explanation:

i have no links, but try to search triginometry calculator and pick carbide calculator for fast trigonometry calculations

it automaticly does sin, cos, and tan for you.

Answer:

The length of AC is 12.08 cm.

Step-by-step explanation:

Given:

In triangle ABC, AB = 8.2 cm, C = 13.5 cm and angle A = 81 degrees.

Solution:

https://brainly.com/question/21977218

This is erinna's answer, no need to thank me, thank her instead

Using Law of Sines, we get

Using angle sum property, we get

Now,

Therefore, the length of AC is 12.08 cm.

The length of the side AC of the triangle ABC whose side AB is of 8.2 cm and side BC is of 13.5 cm length with angle A of 81° is 12.1 cm approx.

Let there is triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

[tex]a^2 + b^2 -2ab\cos(\theta) = c^2[/tex]

(c is opposite side to angle A)

When one angle and two sides of a triangle are known, and we want to know the length of the remaining third side, then we can use the law of cosines.

We're specified that:

Let the third side's length = |AC| = b cm (don't mix this notation with the notation of the formula said above. We just used notation such that its the smaller case version of the vertex opposite to that side, for example, opposite to AC lies b).

For using formula, we just need to take care that the angle θ is the angle opposite to the side which is going to be on one side (the notation c^2 in the formula given and here since we know the angle A, so the side opposite to A which is BC will be used in one side of the cosine rule, as shown below).

The side opposite to the angle A is BC, thus, we get:

[tex]|BC|^2 = |AB|^2 + |AC|^2 -2|AB||AC| \cos(m\angle A)\\\\13.5^2 = 8.2^2 + b^2 -2(8.2)b \cos(81^\circ)\\\\b^2 - 2.566 b - 115.01 \approx 0\\\\b \approx \dfrac{2.566 \pm \sqrt{2.566^2 - 4(-115.01)}}{2}\\\\b= 12.0835, -9.5175[/tex]

b represents side length, therefore positive. Thus, we obtained the length of the side |AC| approximately 12.1 cm

Thus, the length of the side AC of the triangle ABC whose side AB is of 8.2 cm and side BC is of 13.5 cm length with angle A of 81° is 12.1 cm approx.

Learn more about law of cosines here:

https://brainly.com/question/17289163

Answer:

Step-by-step explanation:

constant of proportionality : 60/4 = 15

Number : 2

Cost : 15 * 2 = $30

Number 6

Cost = 15 * 6 = $90

Number 8

Cost = 15 * 8 = $120

Given:

Consider the dimensions of the rectangle are [tex](x^2+7x-9)[/tex] and [tex](3x^2-2x)[/tex].

To find:

The perimeter in terms of x, of the rectangle.

Solution:

Let the length of the rectangle be [tex](x^2+7x-9)[/tex] and the width of the rectangle is [tex](3x^2-2x)[/tex] units.

The perimeter of a rectangle is:

[tex]P=2(l+w)[/tex]

Where, l is the length and w is the width of the rectangle.

Substituting [tex]l=(x^2+7x-9)[/tex] and [tex]w=(3x^2-2x)[/tex] in the above formula, we get

[tex]P=2((x^2+7x-9)+(3x^2-2x))[/tex]

[tex]P=2(4x^2+5x-9)[/tex]

[tex]P=2(4x^2)+2(5x)+2(-9)[/tex]

[tex]P=8x^2+10x-18[/tex]

Therefore, the perimeter of the rectangle is [tex]8x^2+10x-18[/tex] units.

Answer:

∠ RST = 68°

Step-by-step explanation:

Since RT = ST then the triangle is isosceles with 2 base angles congruent

∠ RST = [tex]\frac{180-44}{2}[/tex] = [tex]\frac{136}{2}[/tex] = 68°