Solve the system algebraically. -6x+3y=27 -5x-3y=-16

Answer:

a. [tex]8x^{2} -14x-15[/tex]

b. [tex](x+3)(x+2)[/tex]

Step-by-step explanation:

A. There are 3 methods (that I know of). The easiest method is the lattice multiplication, while the most commonly used is the FOIL method (First+Outer+Middle+Last)

For F, take the first terms of the 2 and multiply

[tex]4x*2x=8x^{2}[/tex]

For O, take the outer terms and multiply

[tex]4x*-5=-20x[/tex]

For I, take the inner terms and multiply

[tex]3*2x=6x[/tex]

For L, take the last terms and multiply

[tex]3*-5=-15[/tex]

After that, add all of them up

[tex]8x^{2} +(-20x)+6x+(-15)=8x^{2}-14x-15[/tex]

B. Since the equation is in the form x^2+bx+c,

[tex](x+?)(x+?)[/tex]

Now we need to find 2 numbers that will add up to 5 and multiply to 6.

Here are some of the combinations of numbers that multiply to 6

3*2

1*6

-3*-2

-1*-6

3 and 2 add up to 5 so:

[tex](x+3)(x+2)[/tex]

Answer:

The expression b/(a +b) does not exist when a = -b or b = -a

Step-by-step explanation:

The expression b/(a + b) does not exist if the denominator a + b = 0.

So, a = - b or b = -a.

So, the expression b/(a + b) does not exist when a = -b or b = -a.

When a = -b values, the denominator a + b = -b + b = 0. This will make the expression b/(a + b) = b/0 = ∞ which undefined or does not exist.

When b = -a values, the denominator a + b = a + (-a) = a - a = 0. This will make the expression b/(a + b) = -a/0 = -∞ which undefined or does not exist.

So the expression b/(a +b) does not exist when a = -b or b = -a

Answer:

Step-by-step explanation:

Hello,

This question requires us to convert numbers from standard form to scientific form. This can easily be done using a calculator or just writing the number down then put a decimal point after the first digit and count the rest which would be raised to the power of that number.

Budget = 69.1 billion

Converting this to scientific form = 6.91×10¹⁰

Population = 11.67 million

Converting this to scientific form = 1.167×10⁷

Budget per capita refers to budget allocated to each individual in the population.

Budget per capita is used to compare economic indices or indicators of various countries with different population sizes.

Budget per capita = budget / total population

Budget per capita = 6.91×10¹⁰ / 1.169×⁷

Budget per capita = 5911.03

What this implies is that for each individual living in the state of Ohio, the amount budgeted for that particular period (mostly in a given year) is 5911.03

Answer:

a. 63 ft²

Step-by-step explanation:

A= 1/2(b1+b2)h

Answer:

[tex]63 {ft}^{2} [/tex]

Answer A is correct

Step-by-step explanation:

[tex]area = \frac{1}{2} (a + b)h \\ = \frac{1}{2} \times (7 + 14) \times 6 \\ = \frac{1}{2} \times 21 \times 6 \\ = \frac{126}{2} \\ = 63 {ft}^{2} [/tex]

hope this helps

Perpendicular slopes multiply to -1, so are negative reciprocals.

-1 / -3 = 1/3

Answer: B.  1/3

Answer:

Blue

Step-by-step explanation:

I just got this question correct

Answer:

Blue

Step-by-step explanation:

[tex]answer \\ b = 15 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]

The measure of angle b is 15 degrees and this can be determined by using the properties of the isosceles triangle.

Given :

The following steps can be used in order to determine the measure of angle b:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

[tex]\angle Q + \angle P + \angle R = 180[/tex]

[tex]\angle Q + 2\angle R = 180[/tex]

[tex]2\angle R = 180-60[/tex]

[tex]\angle R = 60^\circ[/tex]

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

[tex]\angle P + \angle S + \angle R = 180[/tex]

[tex]\angle S + 2\angle R = 180[/tex]

[tex]2\angle R = 180-90[/tex]

[tex]\angle R = 45^\circ[/tex]

Step 4 - Now, the measure of angle b is calculated as:

[tex]\angle b = 60-45[/tex]

[tex]\angle b = 15^\circ[/tex]

The measure of angle b is 15 degrees.

For more information, refer to the link given below:

https://brainly.com/question/7915845

Answer:

Step-by-step explanation:

18

Answer:

see below

Step-by-step explanation:

There are 36 possible outcomes when rolling 2 die

P( number) = number of times the sum appears / total outcomes

p(1) =0/36

P(2) = 1/36

p(3) = 2/36

p(4) = 3/36

p(5) = 4/36

p(6) = 5/36

p(7) = 6/36

p(8) = 5/36

p(9) = 4/36

p(10) = 3/36

p(11) = 2/36

p(12) = 1/36

Since he picked first he has the greatest odds so he is most likely to win

Answer:

The answer would be £198

principal (p) = 2200

Rate (R) = 0.5%

Time (T) = 18

Interest(I) = ?

Now,

or, Interest. = P×T×R/100

or, Interest = 2200×18×0.5/100

or, Interest = 19800/100

Hence, Interest = 198

d. is a rational number.

Because it shows halfs and and halfs is a ratio.

And it shows this symbol (/)

Answer:

The answer is D.

Step-by-step explanation:

Rational number is a number that can be written in the form of fraction, a/b .

Integer is a positive or negative number.

Answer:

Probability ≈ 0.0714

Step-by-step explanation:

Consider permutation and combination;

[tex]Total Combinations - 8C4,\\8C4 = 8! / 4! * ( 8 - 4 )!,\\8 * 7 * 6 * 5 / 4!,\\\\Total Combinations = 70,\\\\Combinations of Dance Classes - 5C4,\\5C4 = 5! / 4! * ( 5 - 4 )!,\\5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1,\\\\Dance Classes = 5,\\\\Probability - 5 / 70 = 0.0714,\\Conclusion; Probability = ( About ) 0.0714[/tex]

Answer: -1/2

You get y = 2x - 5, so the slope is 2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is -1/2.

Answer:

Step-by-step explanation:

7x + 3 = 3x + 35

4x + 3 = 35

4x = 32

x = 8

Answer:

22.360679775

Step-by-step explanation:

i used a calulator on the web

Answer:

±10 sqrt(5)

Step-by-step explanation:

sqrt(500)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(100*5)

sqrt(100) sqrt(5)

±10 * sqrt(5)

Answer:

A is the answer

Step-by-step explanation:

5(2x+1)<10

10x+5<10

     -5  -5

____________

     10x<5

   ——   —-

    10      10

———————-

    x < 1/2

Answer:

a.x<1/2

Step-by-step explanation:

5(2x+1)<10

2x+1< 5/10

2x+1<2

2x<2−1

2x<1

x< 1/2

mark brianliest if my answer suit your question

Answer: A Collecting data

Step-by-step explanation:

just did the quiz

Answer:

p ( 15p - 7)

Step-by-step explanation:

15 p^2 - 7p

The only common term is p so factor out p

p ( 15p - 7)

____________________________

15p^2-7p

take the common,

Ans: p(15p-7)

hope it helps

Good luck on your assignment

__________________________

Answer:

15 days

Step-by-step explanation:

5 x 21 = 105

105/7 = 15

Answer:

15 days

Step-by-step explanation:

As the number of people in that family increases the time taken reduces, so the time is in inverse proportion to the number of people in that family.

Let the number of days taken by a family of 7 to finish a quantity of food be x.

⇒ [tex]\frac{x}{21}[/tex] = [tex]\frac{1}{\frac{7}{5} }[/tex]

⇒ [tex]\frac{x}{21}[/tex] = [tex]\frac{5}{7}[/tex]

⇒ x = [tex]\frac{21 * 5}{7}[/tex]

x = 15

∴ It would take a family of 7 15 days to finish a quantity of food.

Hope this helps!!!

Answer & Step-by-step explanation:

18 - (2x + 1)

Distribute the negative sign (-) to 2x + 1.

18 - 2x - 1

Put -2x in the beginning of the expression and combine like terms.

-2x + 17

So, the answer to 18 - (2x + 1) is -2x + 17.

Answer:

52 people

Step-by-step explanation:

Answer:

4+x

Step-by-step explanation:

you combine your like terms so you take 6x-3x and you end up with 3x than you take that 3x and subtract the 2x from it so you are left with just x so that would be 4+x

Answer:

The correct statement is (C).

Step-by-step explanation:

The data for the number of hours per week they spend working at part-time jobs by 20 juniors and seniors at Delmar high school is:

Juniors: 20, 10, 20, 10, 15, 0, 0, 10, 20, 15

Seniors: 20, 20, 10, 10, 0, 0, 0, 10, 0, 10

Compute the mean of both the data:

[tex]\mu_{J}=\frac{1}{n}\sum\limits^{n}_{i=1}{x_{iJ}}[/tex]

     [tex]=\frac{1}{10}\times [20+10+20+10+15+0+0+10+20+15]\\\\=\frac{120}{10}\\\\=12[/tex]

[tex]\mu_{S}=\frac{1}{n}\sum\limits^{n}_{i=1}{x_{iS}}[/tex]

     [tex]=\frac{1}{10}\times [20+ 20+10+10+0+0+0+10+0+10]\\\\=\frac{80}{10}\\\\=8[/tex]

Compute the range of both the data:

[tex]Range_{J}=Max._{J}-Min._{J}[/tex]

            [tex]=20-0\\=20[/tex]

[tex]Range_{S}=Max._{S}-Min._{S}[/tex]

            [tex]=20-0\\=20[/tex]

It can be seen that the range of both the data is same, i.e. 20.

Thus, the correct statement is (C).

Answer:

There are 54 total sweets  

Step-by-step explanation:

Alex: Stephen : Bridget : total

4:          1          :      1       : 4+1+1 = 6

Alex gets 36

36/4 = 9

Multiply each number by 9

Alex: Stephen : Bridget : total

4*9:          1*9   :      1*9    :    6*9

36:               9 :         9     :   54

There are 54 total sweets  

Answer:

Division

Step-by-step explanation:

Answer:

division

Step-by-step explanation:

when you divide you split into even groups

Answer: 20.058

Step-by-step explanation:

401.16 x 0 05

= 20 058

Answer:

-2 = not in domain

0= in domain

3= in domain

Answer:

Let's find the explicit rule for this arithmetic sequence. We have:

aₙ = a₁ + (n - 1) * d

   = 18 + 12 * (n - 1)

   = 12n + 6.

The 73rd term is 12 (73) + 6 = 882.

Answer:

$11.25 / hr

Step-by-step explanation:

36x+40x=855

76x=855

x=11.25