y=x^2+5x-8 to factored form

Answer:

3 teaspoons

Step-by-step explanation:

Three teaspoons are equivalent to one tablespoon

[tex]5x+2y = 4~~~~~~~~~~...(i)\\\\7x +3y = 5~~~~~~~~~~...(ii)\\\\\text{Write in AX = B form.}\\\\~~~~~~\begin{bmatrix}5&2\\7&3 \end{bmatrix} \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\\\\\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\begin{bmatrix}5&2\\7&3 \end{bmatrix}^{-1}\\\\\\[/tex]

[tex]\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\cdot\dfrac{\begin{bmatrix} 3&-7\\-2&5\end{bmatrix}^{T}}{\begin{vmatrix}5&2\\ 7&3 \end{vmatrix}}\\\\\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\cdot\dfrac{\begin{bmatrix} 3&-2\\-7&5\end{bmatrix}}{5(3) -2(7)}\\\\\\[/tex]

[tex]\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\cdot\begin{bmatrix} 3&-2\\-7&5\end{bmatrix}\\\\\\ \implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix}12-10\\-28+25 \end{bmatrix}\\\\\\ \implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix}2\\-3\end{bmatrix}\\\\\\\text{Hence,}~ (x,y) = (2,-3)[/tex]

The solution to the system of equation is x = -7+√17/2 and -7-√17/2

Equations are expressions separated by an equal sign

Given the equation

x^2 = –7x – 8

Equate to zero

x^2+7x+8 = 0

Factorize

x = -7±√49-4(8)/2

x =  -7±√17/2

x = -7+√17/2 and -7-√17/2

Hence the solution to the system of equation is x = -7+√17/2 and -7-√17/2

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Answer:

Option 4

Step-by-step explanation:

The answer above is correct.

The system of inequalities with no solution is x > 3 x < 1

The systems of inequalities are given as:

x < 3 x < 1

x > 3 x > 1

x < 3 x > 1

x > 3 x < 1

As a general rule, it is impossible for a variable to be greater than a higher number and less than a smaller number.

This means that if x is greater than 3, then it must be greater than 1

Hence, the system of inequalities with no solution is x > 3 x < 1

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Answer:

Length C, B= 90 mi

Step-by-step explanation:

The small square in the corner in any shape always represent 90°

Hope it helps!!

Answer:

144 days

Step-by-step explanation:

Let's put the efficiency in terms of   b

m = 3b      w = 2b       b=b

starting with    6 m  = 18 b

                        8w =   16 b

                        16b = 16 b           total 50 b

then increase   12m = 36b

                         18w = 36b

                         28b = 28 b    total = 100 b

You doubled 'b'  workers  so work time will be halved     to  144 days

Answer:

This linear system has one solution.

Step-by-step explanation:

First equation: y = x + 2

Second equation: 6x - 4y = -10

Let's change the second equation in slope-intercept form y = mx + b.

Slope-intercept form

y = mx + b

m ... slope

b ... y-intercept

[tex]6x - 4y = -10[/tex]

[tex]6x + 10 = 4y[/tex]

[tex]\frac{6}{4}x + \frac{10}{4} = y[/tex]

[tex]\frac{3}{2}x + \frac{5}{2} = y[/tex]

If two lines have the same slope but different y-intercept, they are parallel - system has no solutions.

If two lines have the same slope and the same y-intercept, they are the same line and are intersecting in infinite many points - system has infinite many solutions.

If two lines have different slopes then they intersect in one point - system has one solution.

We see that lines have different slopes. First line has slope 1 and the other line has slope [tex]\frac{3}{2}[/tex]. So the system has one solution.

You can also check this by solving the system.

Substitute y in second equation with y from first.

6x - 4y = -10

6x - 4(x + 2) = -10

Solve for x.

6x - 4x - 8 = -10

2x = -2

x = -1

y = x + 2

y = -1 + 2

y = 1

The lines intersect in point (-1, 1). <-- one solution

Answer:  25

Reason:

The exponent 25 is not a multiple of 3. If it was something like 24, then we would have a perfect cube as shown below

[tex]w = 125x^{18}y^3z^{24}\\\\w = 5^{1*3}x^{6*3}y^{1*3}z^{8*3}\\\\w=(5^1x^6y^1z^8)^3\\\\w = (5x^{6}yz^{8})^3\\\\[/tex]

When going from step 2 to step 3, I used the rule that [tex](abcd)^e = a^eb^ec^ed^e[/tex]. Basically the exponent e gets applied to each factor inside.

Answer:

25

Step-by-step explanation:

The volume-to-surface-area ratio would be better for an ice cube is the highest possible one.

When you put ice into your drink, the goal is to have the ice chill your drink. This takes time. Therefore, you would want the ice to slowly melt and cool the drink for as long as you can.

You would want to have the highest possible volume to surface area ratio in an ice cube. If your ice cube is mostly surface area with less volume, it will melt quickly and water down your drink. If your ice cube has a higher ratio of volume to the surface area, it will stay solid longer and chill your drink longer.

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The data point that has the strongest association of its two factors is Ratio of those who like Hamburgers but not burritos

A) The percentage of respondents who do not like both hamburgers and burritos is; 33/250 * 100% = 16.09%

B) Marginal relative frequency of all customers that like hamburgers will be the ratio of the sum of the customers that like hamburgers to the total number of respondents. Thus;

MRF = 134/205 = 0.65

C) Let us first find the ratio of all the four data with the total;

Ratio of those who like Hamburgers and burritos = 39/134 = 0.29

Ratio of those who like Hamburgers but not burritos = 95/134 = 0.71

Ratio of those who like burritos but not Hamburgers = 38/71 = 0.53

Ratio of those who do not like burritos or Hamburgers = 33/71 = 0.47

Thus, The data point that has the strongest association of its two factors is Ratio of those who like Hamburgers but not burritos

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The correct statement is AngleL = 25° AngleL' = 25°.

We have given that,

Triangle JKL is transformed to create triangle J'K'L'.

We have to choose the correct option.

The following information should be considered:

In a rigid transformation, the image & pre-image are congruent.

Reflection, translation, and rotation are rigid transformations.

In a non-rigid transformation, the image and pre-image are similar.

Dilation is a non rigid transformation.

In a rigid or nonrigid transformation, the corresponding angles are the same.

If the corresponding sides are the same, then it is a rigid transformation.

If the corresponding sides are proportional, then it is a nonrigid transformation.

It can be a rigid or a nonrigid transformation based on whether the corresponding side lengths have the same measures.

Therefore option 3 is correct.

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[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^k~~ = ~~\cfrac{1}{x^{-1}}\implies x^k~~ = ~~x^1\implies k=1[/tex]

The factors of the expression x^2 - 9x + 14 are (x - 7) and (x - 2)

The expression is given as:

x^2 - 9x + 14

Expand

x^2 - 2x - 7x + 14

Factorize the expression

x(x - 2) - 7(x - 2)

Factor out x - 2 from the expression

(x - 7)(x - 2)'

Hence, the factorized expression of x^2 - 9x + 14 is (x - 7)(x - 2)'

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Answer:

3/8

Step-by-step explanation:

2 + 3=5, (8/8)-( 5/8) =3/8

Answer:

3/8

Step-by-step explanation:

The first step that we need to take before solving is to understand what the question is asking us to do and what is given to us to do that.  Looking at this problem, we are given the goal of this problem which is to solve for h and we are given an expression to do so.

The next step that we need to take is to distribute the -2 to the contents inside of the parenthesis.

Distribute

After we have distributed the -2 to the contents inside of the parenthesis we can move onto the next step to isolate h which is to subtract 12 from both sides which would just leave us with -2h.

Subtract 12 from both sides

The next step that we will take to finish the problem is to divide both sides by -2 which will isolate h.  Then we will simplify the expression and that will give us our final answer.

Divide both sides by -2

Simplify the expression

We have now completed solving for h for the expression that was provided in the problem statement and we were able to determine that h is equal to 10.

Answer:

1: sin B, cos B, and tan B = 36.87°

2: x = 11.7

Step-by-step explanation:

Question 1: As toy can see they all have the same angle answer just different methods of finding it

Question 2:

adjacent is the closest side to the angle

opposite is the side across from the angle

hypotenuse is always the longest side

x = 11.7025

Hope it helps :)

If you have any questions or anymore help lmk, happy to help with any school work!!

Have a nice day, you’ll make it thru <3

DONT BE AFRAID TO ASK IF YOU CANT READ MY HANDWRITTING

There are 6 terms in the sequence greater than 1.

A geometric series is  sum of infinite numbers which has a common ratio between its successive terms.

The missing common ratio value is -1/2

It is given in the question that

the number of terms in the sequence = 300

Sum = a₁ (1-rⁿ)/(1-r)

nth term is given by

aₙ = a₁r⁽ⁿ⁻ ¹⁾

1337(1/2)^(n - 1) = 1

(1/2)^(n - 1)  = 1/1337

Applying log on both sides

log (1/2)^(n - 1) = log (1/1337)

(n - 1) log(1/2)  = log(1/1337)

n  = log (1/1337)/ log (1/2) + 1 ≈ 11.384

the 11th term  is 1337(-1/2)^(10)  ≈ 1.305

and

And the 12th term is 1337(-1/2)^11  =  -.653

As the even terms are negative , they are less than 1 and , therefore the odd terms from 1 - 11 term will be positive and greater than 1.

Therefore there are 6 terms in the sequence greater than 1.

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Answer: See the attached images below.

The steps and explanations are on those screenshots, so there's not much for me to mention right here on this main page. The decimal results are approximate to 6 decimal places. Make sure your calculator is in degree mode.

Step-by-step explanation:

-2g(1+g)

-2g - 2g²

(-2)g - (2)g²

Answer: 130 degrees

Step-by-step explanation:

If we are assuming this is an isosceles trapezoid, then this means angles B and C are congruent.

Answer:

[tex]x = 2\\y = 2\sqrt{3}[/tex]

Step-by-step explanation:

**Look at the picture

Answer:

9

Step-by-step explanation:

[tex]f(x) = x^4 +5x^3 -18x +1\\\\f(-4) = (-4)^4 +5(-4)^3 -18(-4) +1\\\\~~~~~~~~~=256+5(-64)+72+1\\\\~~~~~~~~~=329-320\\\\~~~~~~~~~=9[/tex]

The solutions to the given system of equations is (3, 0) and (-4, 7). The correct option is the third option (3, 0) and (−4, 7)

From the question, we are to determine the solutions to the given system of equations

The given system of equations are

x + y = 3 ----------- (1)

y = x² - 9 ----------- (2)

From equation (1)

x + y = 3

We can write that

y = 3 - x -------- (3)

Substitute this into equation (2)

y = x² - 9

3 - x = x² - 9

x² +x -3 - 9 = 0

x² +x -12 = 0

Solve quadratically

x² +x -12 = 0

x² +4x -3x -12 = 0

x(x +4) -3(x +4) = 0

(x -3)(x +4) = 0

∴ x -3 = 0 OR x +4 = 0

x = 3 OR x = -4

Now, using equation (3)

When x = 3

y = 3 - x

y = 3 - 3

y = 0

When x = -4

y = 3 - -4

y = 3+4

y = 7

∴ When x = 3, y = 0; and when x = -4, y = 7

Hence, the solutions to the given system of equations is (3, 0) and (-4, 7). The correct option is the third option (3, 0) and (−4, 7)

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Let's see

[tex]\\ \rm\Rrightarrow \dfrac{s+1}{s^2+1}\div \dfrac{s^2}{6s^2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{s+1}{s(s+1)}\div\dfrac{1}{5s^2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1}{s}\times{5s^2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{5s^2}{s}[/tex]

[tex]\\ \rm\Rrightarrow 5s[/tex]

Answer:

  80

Step-by-step explanation:

The wording "130% more" suggests that we have the result of adding 130% of the original number to the original number.* This can be expressed as an equation to be solved for the original number.

__

Let x represent the original number. The given relation is ...

  184 = x + 130% × x

  184 = 2.30x . . . . . . . . . collect terms (130% = 1.3)

  80 = x . . . . . . . divide by 2.3

184 is 130% more than 80.

_____

* One needs to be a little careful here. You will often see the wording ...

"<some number> times more".

Usually the intention there is that the result is <some number> times the original amount. That is, percentages are often treated differently from other number expressions in problems like this.

Answer:

10+12x

Step-by-step explanation:

1. simplify both sides using PEMDAS.

(2 x 2) − ((2 x 2x) 2) −2x

4-8x-2x

4-10x

− (3 x 2) + 4x + 10 −(3x 2) +4x+10

-6+4x-6x+4x+20

2x+14

2. (2x+14)-(4-10x)= 10+12x

sorry if its rong it was kinda confusing finfing if it was an x or multiplecation.

After 7 years fund balance will be $2152336.05 if the philanthropist pledges to donate 10% of a fund each year.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent. [tex]\rm y = a^x[/tex]

where a is a constant and a>1

We have:

A philanthropist pledges to donate 10% of a fund each year.

We can find the amount left after 7 years as follows:

A = 450000(1 - 0.1)⁷

10% of a fund each year.

Rate r = 10% = 0.1

A = 450000(0.9)⁷

A = $2152336.05

Thus, after 7 years fund balance will be $2152336.05 if the philanthropist pledges to donate 10% of a fund each year.

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Randy sells, in average, 460 vacuum cleaners per month.

First, we know that Janice sells 690 units per year.

There are 12 months in a year, so the amount that she sells, in average, per month is:

J = 690/12 = 57.5

This means that Janice sells, in average, 57.5 units per month. And Randy sells 8 times as many, then we can solve the product:

R = 8*57.5 = 460

This means that Randy sells 460 units per month.

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Answer: 30

Step-by-step explanation:

     A LCD, or least common denominator, is the lowest common multiple of both denominators.

     Multiples of 5: 0, 5, 10, 15, 20, 25, 30, 35, 40, ...

     Multiples of 6: 0, 6, 12, 18, 24, 30, 36, 42, 48, ...

    We can see the LCD of 3/5 and 5/6 is:

           30

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The first step that we should take before attempting to solve any problem is to understand what the problem statement is asking for us to do and what is given to us to help us achieve that goal.  In this case, the problem is asking us to determine the LCD or least common denominator of two numbers.  We are provided with two fractions that we will use to help determine our solution.  However, before solving for the LCD let us first define what LCD means.

Looking at our problem we can see that the denominators that are given to us is 5 and 6 so let us determine the multiples of them until we have a duplicate.

Now that we have determine the multiples of 5 and 6 we were able to see that the lowest duplicate that we have is at 30 which means that 30 is our LCD.