please Help will mark brainliest !!1!Use the linear combination method to solve the system of equations. Explain each step of your solution. 2x -3y = 13 x+2=- 4

Answer:

-2             7

-1             -6

Step-by-step explanation:

I used a calculator.

¡Hola! ¡Ojalá esto ayude!

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La fórmula para calcular el área de cualquier triángulo es:

base multiplicada por la altura y dividida por dos.

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Bh / 2.

Answer:

D) 53 Degrees.

Step-by-step explanation:

Things we need to establish beforehand: We know that Lines OZ and OX are equal because they are both radii of the circle. We can make an Iscoceles traingle by drawing a line between ZX. We know angle YZO and angle YXO is a right angle because YZ and XY are tangent to the circle. The Arc angle is the same angle as angle ZOX.

1) Find angles OZX and OXZ. these will be 26.5, because 180-127 is 53, which is the sum of the two angles. the two angles are the same, so divide 53 by 2.

2) Find Angles XZY and ZXY. We know that YZO is a right angle, and both XZY and OZX make up this right angle so XZY + OZX = 90. OZX is 26.5, so 90-26.5=XZY. XZY = ZXY, so both angles equal 63.5.

3) Now that we have two angles of triangle XYZ, we can find angle XYZ.     180-(XZY+ZXY)=XYZ, so (180-(63.5+63.5)=53. Angle XYZ=53.

Answer:

D. 11.8 cm.

Step-by-step explanation:

This is a 30-60-90 triangle, which means that the hypotenuse is 2x, the short leg is x, and the long leg is x[tex]\sqrt{3}[/tex].

In this case, the hypotenuse is 5.

5 / 2 = 2.5. That is the short leg.

The long leg is 2.5 * [tex]\sqrt{3}[/tex] = 4.330127019.

5 + 2.5 + 4.330127019 = 7.5 + 4.330127019 = 11.83012702, which is about D. 11.8 cm.

Hope this helps!

Answer:

0.0035289

Step-by-step explanation:

From the question;

mean annual salary = $63,500

n = sample size = 31

Standard deviation = $6,200

Firstly, we calculate the z-score of $60,500

Mathematically;

z-score = x-mean/SD/√n = (60500-63500)/6200/√(31) = -2.6941

So we want to find the probability that P(z < -2.6941)

We can get this from the standard normal table

P( z < -2.6941) = 0.0035289

Answer:

9 in.

Step-by-step explanation:

Given that the line 10 in. and line 4 in. are parallel, then the two triangles are similar.

As such, the ratio of the sides would give the same results.

Hence,

4/6 = 10/(6 + x)

cross multiplying

4(6 + x) = 60

Dividing both sides by 4

6 + x = 15

collecting like terms

x = 15 - 6

= 9

Answer:

[tex]a^9 + b^ 5 + c^{13}[/tex]

Step-by-step explanation:

[tex](a^5 \times a^4)+(b^2 \times b^3) + (c^7 \times c^6)[/tex]

When bases are same and it is multiplication, then add the exponents.

[tex](a^{5+4})+(b^{2+3})+(c^{7+6})[/tex]

[tex](a^9)+(b^ 5) + (c^{13})[/tex]

Apply rule : [tex](a^b)=a^b[/tex]

[tex]a^9 + b^ 5 + c^{13}[/tex]

Answer:

[tex]a^9+b^5-c^{13[/tex]

Step-by-step explanation:

[tex](a^5*a^4) + (b^2*b^3)-(c^7*c^6)[/tex]

When bases are same, powers are to be added.

=> [tex](a^{5+4})+(b^{2+3})-(c^{7+6})[/tex]

=> [tex]a^9+b^5-c^{13[/tex]

Answer:

For me, ill say there are many ways it can be done.

First, u can pick at random. Or u can decide to do it boys and girls

Step-by-step explanation:

Answer:  60

Step-by-step explanation:

Formula to calculate sample size (n):

[tex]n=(\dfrac{\sigma\times z^*}{E})^2[/tex]

, where [tex]\sigma[/tex] = population standard deviation, E Margin of error , z* = critical value for the confidence interval.

As per given , we have

E =5

[tex]\sigma=15[/tex]

Critical value for 99% confidence = 2.576

Then,

[tex]n=(\dfrac{15\times2.576}{5})^2\\\\\Rightarrow\ n=59.721984\approx60[/tex]

So, Required sample size = 60 .

Answer:

[tex]\boxed{\sf k=6}[/tex]

Step-by-step explanation:

[tex]\sf kx (x-2)+6=0[/tex]

Expand brackets.

[tex]\sf kx^2 -2kx+6=0[/tex]

This is in quadratic form.

[tex]\sf ax^2 +bx+c=0[/tex]

Since this is for equal roots:

[tex]\sf b^2 -4ac=0[/tex]

[tex]\sf a=k\\b=-2k\\c=6[/tex]

[tex]\sf (-2k)^2 -4(k)(6)=0[/tex]

[tex]\sf 4k^2-24k=0[/tex]

[tex]\sf 4k(k-6)=0[/tex]

[tex]\sf 4k=0\\k=0[/tex]

[tex]\sf k-6=0\\k=6[/tex]

Plug k as 0 to check.

[tex]\sf \sf 0x^2 -2(0)x+6=0\\6=0[/tex]

False.

So that means k must equal 6.

Answer:

The answer is below

Step-by-step explanation:

Let x represent the big buses and y represent small buses. The large buses can carry 30 students and the small buses can carry 15 students. The total number of students are 450, this can be represented by the inequality:

30x + 15y ≤ 450

They are only 20 drivers, therefore only 20 buses can be used. It is represented by:

x + y ≤ 20

They  are only 19 small buses and 18 large buses:

x ≤ 18

y ≤ 19

After plotting the graph, the minimum solution to the graph are at:

A (15,0), B(18,0), C(10, 10), D(18, 2).

The cost function is given as:

The total cost of operating one large bus is $225 a day, and the total cost of operating one small bus is $100 per day.

​

F(x, y) = 225x + 100y

At point A:

F(x, y) = 225(15) + 100(0) = $3375

At point B:

F(x, y) = 225(18) + 100(0) = $4050

At point C:

F(x, y) = 225(10) + 100(10) = $3250

At point D:

F(x, y) = 225(18) + 100(2) = $4250

The minimum cost is at point C(10, 10) which is $3250

Complete Question

A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 ​respondents, 12 ​% chose chocolate​ pie, and the margin of error was given as plus or minus 5 percentage points.What values do ​ [tex]\r p , \ \r q[/tex], ​n, E, and p​ represent? If the confidence level is 90​%, what is the value of [tex]\alpha[/tex] ​?

Answer:

a

   [tex]\r p[/tex] is the sample proportion   [tex]\r p = 0.12[/tex]

   [tex]n[/tex] is the  sample size is  [tex]n = 500[/tex]

   [tex]E[/tex] is the  margin of error is [tex]E = 0.05[/tex]

   [tex]\r q[/tex] represents the proportion of those that did not chose chocolate​ pie i.e                        [tex]\r q = 1- \r p[/tex]

b

   [tex]\alpha = 10\%[/tex]

Step-by-step explanation:

Here

    [tex]\r p[/tex] is the sample proportion   [tex]\r p = 0.12[/tex]

   [tex]n[/tex] is the  sample size is  [tex]n = 500[/tex]

    [tex]\r q[/tex] represents the proportion of those that did not chose chocolate​ pie i.e  

      [tex]\r q = 1- \r p[/tex]

      [tex]\r q = 1- 0.12[/tex]

      [tex]\r q = 0.88[/tex]

     [tex]E[/tex] is the  margin of error is [tex]E = 0.05[/tex]

Generally [tex]\alpha[/tex] is the level of significance and it value is mathematically evaluated as

     [tex]\alpha = ( 100 - C )\%[/tex]

Where  [tex]C[/tex] is the confidence level which is given in this question as  [tex]C = 90 \%[/tex]

So  

    [tex]\alpha = ( 100 - 90 )\%[/tex]

    [tex]\alpha = 10\%[/tex]

Answer:

[tex]x = -5[/tex]

Step-by-step explanation:

We can simplify this equation down until x is isolated.

[tex]2x - 3 + 3x = -28[/tex]

We can combine the like terms of x.

[tex]5x - 3 = -28[/tex]

Add 3 to both sides.

[tex]5x = -25[/tex]

Now we can divide both sides by 5.

[tex]x = -5[/tex].

So x = -5.

Hope this helped!

Answer:

x=-5

Step-by-step explanation:

first combine like terms

5x-3=-28

add on both sides

5x=-25

divide

x==-5

Answer: min = 12, Q1 =17,  median =23.5 , Q3 = 30, max = 37 .

Step-by-step explanation:

The five-number summary for this data set consists  of  min, Q1,

median, Q3, max.

Given data: 12, 15, 17, 20, 22, 25, 27, 30, 33, 37, which is already arranged in a order.

Minimum value = 12

Maximum value = 37

since , number of observations = 10 (even)

So , Median = Mean of middle most terms

Middle most terms = 22, 25

Median =[tex]\dfrac{22+25}{2}=23.5[/tex]

First quartile ([tex]Q_1[/tex])= Median of first half ( 12, 15, 17, 20, 22)

= middle most term

= 17

Third quartile ([tex]Q_3[/tex]) = Median of second half (25, 27, 30, 33, 37)

= middle most term

= 30

Hence, five-number summary for this data set :

min = 12, Q1 =17,  median =23.5 , Q3 = 30, max = 37 .

Answer:

(0,0), (-4,0), (0,-5).

Step-by-step explanation:

Note: Matrices are not in proper format.

Consider the given matrix is

[tex]T=\begin{bmatrix}0&4&0\\0&0&5\end{bmatrix}[/tex]

It means vertices are (0,0), (4,0) and (0,5).

Transformation matrix is

[tex]A=\begin{bmatrix}-1&0\\0&-1\end{bmatrix}[/tex]

To find the coordinates of the transformed triangle multiply both matrices and calculate matrix AT.

[tex]AT=\begin{bmatrix}-1&0\\0&-1\end{bmatrix}\begin{bmatrix}0&4&0\\0&0&5\end{bmatrix}[/tex]

[tex]AT=\begin{bmatrix}\left(-1\right)\cdot \:0+0\cdot \:0&\left(-1\right)\cdot \:4+0\cdot \:0&\left(-1\right)\cdot \:0+0\cdot \:5\\ 0\cdot \:0+\left(-1\right)\cdot \:0&0\cdot \:4+\left(-1\right)\cdot \:0&0\cdot \:0+\left(-1\right)\cdot \:5\end{bmatrix}[/tex]

[tex]AT=\begin{bmatrix}0&-4&0\\ 0&0&-5\end{bmatrix}[/tex]

It means coordinates of the transformed triangle are (0,0), (-4,0), (0,-5).

Answer:

A

Step-by-step explanation:

E2020

Answer:

  5

Step-by-step explanation:

The limit of f(x) at x=-1 is 5 when approached from the left or right. Since those limits are the same, the limit exists and is ...

  [tex]\boxed{\lim\limits_{x\to-1}f(x)=5}[/tex]

Answer:  see below

Step-by-step explanation:

1) Foci is plural for Focus.  Since a hyperbola has two focus points, they are referred to as foci.  The foci is where the sum of the distances from any point on the curve to the foci is constant.

2) When determining the equation of a hyperbola you need the following:

    a)  does the hyperbola open up or to the right?

    b)  what is the center (h, k) of the hyperbola?

    c)  What is the slope of the asymptotes of the hyperbola?

3) The equation of a hyperbola is:

[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1\qquad or\qquad \dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=1[/tex]

Answer:

623

Step-by-step explanation:

Given that margin of error (E) = 3 unit, standard deviation (σ) = 29, sample size (n) = ?

a) The confidence (C) = 99% = 0.99

α = 1 - C = 1 - 0.99 = 0.01

α/2 = 0.01 / 2 = 0.005

From the normal distribution table, The z score of α/2 (0.005) is the critical value and it corresponds to the z score 0.495 (0.5 - 0.005) which is 2.58.

[tex]critical\ value = z_{\frac{\alpha}{2} }=z_{0.005}=2.58\\[/tex]

b) The margin of error (E) is given as:

The minimum sample size (n) is 623

Answer:

The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.

Step-by-step explanation:

A trapezoid is a quadrilateral that is symmetrical and whose bases are of different length and in every quadrilateral the sum of internal angles is equal to 360º. The bigger base has the pair of adjacent angles of least measure, whereas the smaller base has the pair of adjancent angles of greatest measure.

Since the sum of the angles adjacent to bigger base is 120º, the value of each adjacent angle ([tex]\alpha[/tex]) is obtained under the consideration of symmetry:

[tex]2\cdot \alpha = 120^{\circ}[/tex]

[tex]\alpha = 60^{\circ}[/tex]

The sum of the angles adjacent to smaller base is: ([tex]\alpha = 60^{\circ}[/tex])

[tex]2\cdot \alpha + 2\cdot \beta = 360^{\circ}[/tex]

[tex]2\cdot \beta = 360^{\circ} - 2\cdot \alpha[/tex]

[tex]\beta = 180^{\circ}-\alpha[/tex]

[tex]\beta = 180^{\circ} - 60^{\circ}[/tex]

[tex]\beta = 120^{\circ}[/tex]

The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.

Answer:

101.98 yards.

Step-by-step explanation:

Please refer to the diagram that I drew (sorry for the messiness; I do not own a stylus and so I was using my mouse to try to draw it).

Since the triangle is a right triangle, you can use SOH CAH TOA. In this case, you are trying to figure out the opposite length, but you are given the adjacent. So, we will use tangent to solve this (TOA = Tangent, Opposite over Adjacent).

The angle is 22.6 degrees, and the tangent of the angle is equivalent to the opposite length, x, divided by the adjacent length, 245 yards.

tan(22.6) = x / 245

x / 245 = tan(22.6)

x = tan(22.6) * 245

x = 0.4162598242 * 245

x = 101.9836569

So, you are about 101.98 yards from the cabin.

Hope this helps!

Answer:

y=-192

Step-by-step explanation:

Answer:

i) A = (3, 3), B = (12, 6), C = (6, 52) : Not orthogonal, ii) A = (-10, 5), B = (12, 16), C = (6, 52) : Not orthogonal, iii) A = (-8, 3), B = (12, 8), C = (18, 4) : Not orthogonal, iv) A = (12, -14), B = (-16, 21), C = (-11, 25) : Orthogonal, v) A = (-12, -19), B = (20, 45) : Impossible orthogonality, vi) A = (30, 20), B = (-20, -15) : Impossible orthogonality.

Step-by-step explanation:

The statement indicates that segments AB and BC must be orthogonal. Vectorially speaking, this can be expressed by using the following expression from Linear Algebra:

[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = 0[/tex]

[tex](AB_{x}, AB_{y})\bullet (BC_{x},BC_{y}) = 0[/tex]

[tex]AB_{x}\cdot BC_{x} + AB_{y}\cdot BC_{y} = 0[/tex]

Now, let is evaluate each choice:

i) A = (3, 3), B = (12, 6), C = (6, 52)

[tex]\overrightarrow {AB} = \vec B - \vec A[/tex]

[tex]\overrightarrow {AB} = (12, 6) - (3, 3)[/tex]

[tex]\overrightarrow {AB} = (12-3, 6-3)[/tex]

[tex]\overrightarrow {AB} = (9, 3)[/tex]

[tex]\overrightarrow {BC} = \vec C - \vec B[/tex]

[tex]\overrightarrow {BC} = (6, 52) - (12, 6)[/tex]

[tex]\overrightarrow {BC} = (6 - 12, 52 - 6)[/tex]

[tex]\overrightarrow {BC} = (-6, 46)[/tex]

[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = (9, 3)\bullet (-6, 46)[/tex]

[tex]\overrightarrow{AB} \bullet \overrightarrow {BC} = (9)\cdot (-6) + (3) \cdot (46)[/tex]

[tex]\overrightarrow{AB}\bullet \overrightarrow {BC} = 84[/tex]

AB and BC are not orthogonal.

ii) A = (-10, 5), B = (12, 16), C = (6, 52)

[tex]\overrightarrow {AB} = \vec B - \vec A[/tex]

[tex]\overrightarrow {AB} = (12, 16) - (-10, 5)[/tex]

[tex]\overrightarrow {AB} = (12+10, 16-5)[/tex]

[tex]\overrightarrow {AB} = (22, 11)[/tex]

[tex]\overrightarrow {BC} = \vec C - \vec B[/tex]

[tex]\overrightarrow {BC} = (6, 52) - (12, 16)[/tex]

[tex]\overrightarrow {BC} = (6 - 12, 52 - 16)[/tex]

[tex]\overrightarrow {BC} = (-6, 36)[/tex]

[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = (22, 11)\bullet (-6, 36)[/tex]

[tex]\overrightarrow{AB} \bullet \overrightarrow {BC} = (22)\cdot (-6) + (11) \cdot (36)[/tex]

[tex]\overrightarrow{AB}\bullet \overrightarrow {BC} = 264[/tex]

AB and BC are not orthogonal.

iii) A = (-8, 3), B = (12, 8), C = (18, 4)

[tex]\overrightarrow {AB} = \vec B - \vec A[/tex]

[tex]\overrightarrow {AB} = (12, 8) - (-8, 3)[/tex]

[tex]\overrightarrow {AB} = (12+8, 8-3)[/tex]

[tex]\overrightarrow {AB} = (20, 5)[/tex]

[tex]\overrightarrow {BC} = \vec C - \vec B[/tex]

[tex]\overrightarrow {BC} = (18, 4) - (12, 8)[/tex]

[tex]\overrightarrow {BC} = (18 - 12, 4 - 8)[/tex]

[tex]\overrightarrow {BC} = (6, -4)[/tex]

[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = (20, 5)\bullet (-6, -4)[/tex]

[tex]\overrightarrow{AB} \bullet \overrightarrow {BC} = (20)\cdot (-6) + (5) \cdot (-4)[/tex]

[tex]\overrightarrow{AB}\bullet \overrightarrow {BC} = -140[/tex]

AB and BC are not orthogonal.

iv) A = (12, -14), B = (-16, 21), C = (-11, 25)

[tex]\overrightarrow {AB} = \vec B - \vec A[/tex]

[tex]\overrightarrow {AB} = (-16,21) - (12, -14)[/tex]

[tex]\overrightarrow {AB} = (-16-12, 21+14)[/tex]

[tex]\overrightarrow {AB} = (-28, 35)[/tex]

[tex]\overrightarrow {BC} = \vec C - \vec B[/tex]

[tex]\overrightarrow {BC} = (-11,25) - (-16, 21)[/tex]

[tex]\overrightarrow {BC} = (-11+16, 25-21)[/tex]

[tex]\overrightarrow {BC} = (5, 4)[/tex]

[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = (-28,35)\bullet (5, 4)[/tex]

[tex]\overrightarrow{AB} \bullet \overrightarrow {BC} = (-28)\cdot (5) + (35) \cdot (4)[/tex]

[tex]\overrightarrow{AB}\bullet \overrightarrow {BC} = 0[/tex]

AB and BC are orthogonal.

v) A = (-12, -19), B = (20, 45)

It is not possible to determine the orthogonality of this solution, since point C is unknown.

vi) A = (30, 20), B = (-20, -15)

It is not possible to determine the orthogonality of this solution, since point C is unknown.

Answer:

Step-by-step explanation:

Given the statement "subtract y from 5", we are to express the statement mathematically. Expressing mathematically is as shown;

5 - y

Since we are removing the value of a variable y from 5, the variable we are subtracting will come last in the expression.  For example say, we want to subtract 5 from 10, since we are taking out 5 from 10, the value of 5 will come last in the expression i.e 10 - 5 not 5 - 10.

According to the statement in question, we can see that we are to subtract y from 5, therefore y will come last in our expression and will be expressed as 5 - y

Answer:

We conclude that the true average stopping distance exceeds this maximum value.

Step-by-step explanation:

We are given the following observations that are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions.;

X = 32.1, 30.9, 31.6, 30.4, 31.0, 31.9.

Let [tex]\mu[/tex] = true average stopping distance

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 30      {means that the true average stopping distance exceeds this maximum value}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 30      {means that the true average stopping distance exceeds this maximum value}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                              T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean stopping distance = [tex]\frac{\sum X}{n}[/tex] = 31.32 ft

            s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 0.66 ft

            n = sample size = 6

So, the test statistics =  [tex]\frac{31.32-30}{\frac{0.66}{\sqrt{6} } }[/tex]  ~  [tex]t_5[/tex]

                                    =  4.898

The value of t-test statistics is 4.898.

Now, at 0.01 level of significance, the t table gives a critical value of 3.365 at 5 degrees of freedom for the right-tailed test.

Since the value of our test statistics is more than the critical value of t as 4.898 > 3.365, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the true average stopping distance exceeds this maximum value.

Answer:

[tex]\large \boxed{\sf \ \ 9 \text{ and } 22 \ \ }[/tex]

Step-by-step explanation:

Hello,

We can write that, x being the second number

(4 + 2*x) *x = 198

Let's solve this equation.

[tex](4+2x)x=198\\\\4x+2x^2=198 \\\\\text{*** subtract 198 from both sides ***}\\\\2x^2+4x-198 = 0\\\\\text{*** The product of the zeroes is -198/2=-99=-11*9 and their sum is -4/2=-2 ***}\\\\2x^2+4x-198=2(x-9)(x+11)=0\\\\x=9 \ \ or \ \ x=-11[/tex]

We are looking for positive number so the solution is 9.

And the first number is 4 + 2 * 9 = 4 + 18 = 22

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

22 and 9

Step-by-step explanation:

Let the positive number be x.

Let the other number be y.

x = 2y + 4

xy = 198

Substitute x as 2y + 4 in the second equation.

(2y+4)y = 198

2y² + 4y = 198

2y² + 4y - 198 = 0

2(y-9)(y+11) = 0

y-9=0 or y+11=0

y=9

y=-11

The product is 198, so y is positive.

x(9)=198

x=22

Answer:

Part A: no solution

Part B: Distributive property of multiplication over addition.

Step-by-step explanation:

Part A:

4x + 2(x – 3) = 4x + 2x – 11

4x + 2x - 6 = 6x - 11

6x - 6 = 6x - 11

-6 = -11

Since -6 = -11 is a false statement, there is no solution.

Number of solutions: 0

Part B:

Property used: Distributive property of multiplication over addition.

Part A: Here are the steps I used to solve this equation-

4x + 2(x – 3) = 4x + 2x – 11

4x + 2x - 6 = 6x - 11

6x - 6 = 6x - 11

-6 = -11

Since -6 = -11 is a false statement, there is no solution.

The final number of solutions: 0

Part B: I used the distributive property of multiplication over addition.

Answer:

[tex]\large \boxed{\sf \ \ 6 \ and \ 11 \ \ }[/tex]

Step-by-step explanation:

Hello,

Let's note a and b the two numbers.

a = b - 5

[tex]a^2+b^2=157[/tex]

We replace a in the second equation and we solve it

[tex](b-5)^2+b^2=157 \\ \\ \text{*** develop the expression ***} \\ \\b^2-10b+25+b^2=157 \\ \\ \text{*** subtract 157 from both sides ***} \\ \\2b^2-10b+25-157=2b^2-10b-132=0 \\ \\ \text{*** divide by 2 both sides ***} \\ \\b^2-5b-66=0[/tex]

It means that the sum of the two roots is 5 and the product is -66.

because

     [tex](x-\alpha )(x-\beta )=x^2-(\alpha +\beta )x+\alpha \beta \\ \\ \text{ where } \alpha \text{ and } \beta \text{ are the roots }[/tex]

And we can notice that 66 = 6 * 11 and 11 - 6 = 5

So let's factorise it !

    [tex]b^2-5b-66=0 \\ \\b^2+6b-11b-66=0 \\ \\b(b+6)-11(b+6)=0 \\ \\(b-11)(b+6) =0 \\ \\ b=11 \ or \ b=-6[/tex]

It means that the solutions are

(6,11) and (-6,-11)

I guess we are after positive numbers though.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

  0.12 g/cm³

Step-by-step explanation:

Density is the ratio of mass to volume. The volume of the brownie is the cube of its side dimension:

  V = s³ = (5 cm)³ = 125 cm³

Then the density is ...

  ρ = M/V = (15 g)/(125 cm³) = 0.12 g/cm³

The density of the brownie is 0.12 g/cm³.