Which statement about parallel lines is true

Answer:

Option (b) is correct.

The matrix A is [tex]\begin{pmatrix}-3&-14&7&18\\ -13&2&-5&-6\end{pmatrix}[/tex]

Step-by-step explanation:

Given : A matrix form,

[tex]A+\begin{pmatrix}3&9&-1&-8\\ \:16&-2&3&13\end{pmatrix}=\begin{pmatrix}0&-5&6&10\\ \:3&0&-2&7\end{pmatrix}[/tex]

we have to find the value of matrix A

Consider the given matrix form,

[tex]A+\begin{pmatrix}3&9&-1&-8\\ \:16&-2&3&13\end{pmatrix}=\begin{pmatrix}0&-5&6&10\\ \:3&0&-2&7\end{pmatrix}[/tex]

when A + B = C

Then A = C - B

That is

[tex]A=\begin{pmatrix}0&-5&6&10\\ \:3&0&-2&7\end{pmatrix}-\begin{pmatrix}3&9&-1&-8\\ \:16&-2&3&13\end{pmatrix}[/tex]

Subtract the elements in the matching position, we get,

[tex]A=\begin{pmatrix}0-3&\left(-5\right)-9&6-\left(-1\right)&10-\left(-8\right)\\ 3-16&0-\left(-2\right)&\left(-2\right)-3&7-13\end{pmatrix}[/tex]

Simplify, we get,

[tex]A=\begin{pmatrix}-3&-14&7&18\\ -13&2&-5&-6\end{pmatrix}[/tex]

Thus, The matrix A is [tex]\begin{pmatrix}-3&-14&7&18\\ -13&2&-5&-6\end{pmatrix}[/tex]

Answer:

1.a=2

2.  C  x=2  and x=-3

Step-by-step explanation:

The standard form for the quadratic function is  

ax^2 +bx+c

so  we need to rewrite the function to be in this form

2x^2 -10 = 7x

Subtract 7x from each side

2x^2 -7x-10 = 7x-7x

2x^2 -7x-10 = 0

a =2, b= -7  c=-10

2.  The quadratic formula is

-b ± sqrt(b^2 -4ac)

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

2a

2x^2 + 2x=12

Lest get the equation in proper form

2x^2 + 2x-12 = 12-12

2x^2 +2x-12 =0

a=2  b=2 c=-12

Lets substitute what we know

-2 ± sqrt(2^2 -4(2)(-12))

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

2(2)

-2 ± sqrt(4+96)

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

2(2)

-2 ± sqrt(100)

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

4

-2 ± 10

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

4

-2 + 10               -2-10

-----------   and  --------------

4                             4

8/4   and -12/4

2  and -3

Answer:

1987 + 1257 = 3247

Step-by-step explanation:

We are going to use a base number to start from. That number is 1,987 where the thousand is 1, the hundred is 9 and the ten is 8.

Then we are going to add 1,257 which will be 3,247. Thus we will have a new thousand which is 3 (formerly 1), a new hundred which is 2 (formerly 9), and finally, a new ten which is 5 (formerly 7).

1987 + 1257 = 3247 gives you a new thousand, a new hundred and a new ten.

Answer:

Step-by-step explanatcagion:

Answer:

Step-by-step explanation:

Sales of the chocolate ice cream is 45%, 30% for strawberry and 25% (100%-45%-30%) of vanilla.

Percentages of cone sales for chocolate, strawberry and vanilla are 75%, 60% and 40%respectively.

A. Probability chocolate chosen: 45%=0.45

B. Probability strawberry chosen: 30%=0.30

C. Probability vanilla chosen:25%=0.25

D. Probability ice cream on a cone: 75%×45%+60%×30%+40%×25%

                                                          =0.75×0.45+0.60×0.30+0.40×0.25

                                                          =0.3375+0.18+0.1

                                                          =0.6175

E. Probability ice cream in a cup: 1- Probability ice cream in a cone

                                                     =1-0.6175

                                                     =0.3825

Probability that the ice cream sold on a cone and was strawberry flavoured is : 30%×60%

=0.30×0.60

=0.18

Answer: 0.18.

Step-by-step explanation: Let us define the following events

A= event that chocolate chosen,

B=event that strawberry chosen,

C=event that vanilla chosen,

D=event of choosing ice-cream on a cone

and

E=event of choosing ice-cream on a cup.

Then, according to the given information, we have

P(A)=0.45, P(B)=0.30, P(C)=0.25, P(A\D)=0.75, P(B\D)=0.60 and P(C\D)=0.40.

Therefore, the probability that the ice-cream was sold on a cone and was strawberry flavour is given by

[tex]P(B\cap D)=P(B)\times 0.60\\\Rightarrow P(B\cap D)=0.30\times 0.60\\\Rightarrow P(B\cap D)=0.18.[/tex]

Thus, the required probability is 0.18.

Answer:

$273.60

Step-by-step explanation:

The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing.

i.e [tex]C\propto L\cdot D[/tex]

i.e [tex]C=k\cdot L\cdot D[/tex]

A 5 foot or 60 inches length with diameter 2 inches costs $48.00, so

[tex]\Rightarrow 48=k\times 60\times 2[/tex]

[tex]\Rightarrow k=\dfrac{48}{60\times 2}=0.4[/tex]

Now the equation becomes,

[tex]C=0.4\cdot L\cdot D[/tex]

So the cost of a 19 foot or 228 inches length with 3 inches diameter is,

[tex]C=0.4\times 228\times 3=\$273.60[/tex]

The equation for this problem is x=25(m)+40

If the value of x=240, then the value of m=8.

Answer:

see explanation

Step-by-step explanation:

the exterior angle of a triangle equals the sum of the 2 opposite interior angles, that is

2x + 4 = x + 60 ( subtract x from both sides )

x + 4 = 60 ( subtract 4 from both sides )

x = 56

exterior angle = 2x + 4 = (2 × 56) + 4 = 112 + 4 = 116°

Answer:

9,839 ft

Step-by-step explanation:

Answer:

Total wood required for the project will be 9 3/8 feet.

Step-by-step explanation:

As given in the question Quentin has lumber of length = 6 5/8

feet =53/8 feet.

Now Quentin needs more lumber = 2 3/4 feet =11/4 feet or 22/8 feet.

So we can get total wood required by adding these two figures

That is = 53/8 + 22/8

           = (53 +22)/8

           = 75/8

            = 9 3/8 feet

Answer:

[tex]The\ total\ wood\ will\ the\ project\ have\ used\ be\ 9 \frac{3}{8}.[/tex]

Step-by-step explanation:

As given

[tex]Quentin\ has\ 6 \frac{5}{8}\ feet\ of\ lumber\ but\ needs\ another\ 2 \frac{3}{4}\ feet\ to\ complete\ the\ project\ he's\ working\ on.[/tex]

i.e

 [tex]Quentin\ has\ \frac{53}{8}\ feet\ of\ lumber\ but\ needs\ another\ \frac{11}{4}\ feet\ to\ complete\ the\ project\ he's\ working\ on.[/tex]        

 [tex]Total\ wood\ will\ the\ project\ have\ used =\frac{53}{8} + \frac{11}{4}[/tex]

L.C.M of (8,4) = 8

Than

[tex]Total\ wood\ will\ the\ project\ have\ used =\frac{53 + 11\times 2}{8}[/tex]                              

[tex]Total\ wood\ will\ the\ project\ have\ used =\frac{53 + 22}{8}[/tex]       [tex]Total\ wood\ will\ the\ project\ have\ used =\frac{75}{8}[/tex]  

[tex]Total\ wood\ will\ the\ project\ have\ used = 9 \frac{3}{8}[/tex]  

[tex]Therefore\ the\ total\ wood\ will\ the\ project\ have\ used\ be\ 9 \frac{3}{8}.[/tex]

Answer:

Points X and Y lie on more than one plane.

Step-by-step explanation:

From the  figure attached we have to find the points which lie on more than one plane.

M and R :

These are the points which lie on only one plane painted in yellow color.

A and S

These points lie on a plane perpendicular to the plane painted in yellow color.

X and Y :

These points lie on both the planes, painted in yellow color and the plane perpendicular to this.

M and S :

Point M lies on a plane in yellow color and point S lies on a plane perpendicular to the yellow plane.

Therefore, points X and Y lie on more than one plane.

Answer:

The real part is -7

The imaginary part 8i

Step-by-step explanation:

A complex number is in the from a +bi

The real part is a and the imaginary part is bi

-7+8i

The real part is -7

The imaginary part 8i

Answer:

3.3 hours.

Step-by-step explanation:

We have been given that a scientist is testing a new antibiotic by applying the antibiotic to a colony of 10,000 bacteria. The number of bacteria decreases by 75% every two hours.

Since number of bacteria is decreasing exponentially, so we will use exponential decay function.

[tex]y=a*b^x[/tex], where,

a= Initial value,

b = For decay b is in form (1-r), where r is rate in decimal form.

Let us convert our given rate in decimal form.

[tex]75\%=\frac{75}{100}=0.75[/tex]

As number of bacteria is decreasing every 2 hours, so number of bacteria decreased in 1 hour will be x/2.

Upon substituting our given values in above formula we will get,

[tex]y=10,000(1-0.75)^{\frac{x}{2}}[/tex]

To find the number of hours it will take to for the bacteria colony to decrease to 1000, we will substitute y = 1,000 in our equation.

[tex]1,000=10,000(0.25)^{\frac{x}{2}}[/tex]

Let us divide both sides of our equation by 10,000.

[tex]\frac{1,000}{10,000}=\frac{10,000(0.25)^{\frac{x}{2}}}{10,000}[/tex]

[tex]0.1=(0.25)^{\frac{x}{2}}[/tex]  

Let us take natural log of both sides of our equation.

[tex]ln(0.1)=ln((0.25)^{\frac{x}{2}})[/tex]

[tex]ln(0.1)=\frac{x}{2}*ln(0.25)[/tex]

[tex]-2.302585=\frac{x}{2}*-1.386294[/tex]

[tex]x=\frac{-2.302585}{-1.386294}*2[/tex]

[tex]x=1.660964*2[/tex]

[tex]x=3.3219\approx 3.3[/tex]

Therefore, it will take 3.3 hours  for the bacteria colony to decrease to 1000.

Final answer:

It will take 4 hours for the bacteria colony to decrease from 10,000 to 1,000, considering a 75% decrease every two hours.

Explanation:

To find out how many hours it will take for the bacteria colony to decrease from 10,000 to 1,000 with a 75% decrease every two hours, we can use the formula for exponential decay: [tex]N = N0(1 - r)^t[/tex], where N is the final amount, N0 is the initial amount, r is the rate of decrease (expressed as a decimal), and t is the time in units of the rate's period (in this case, every two hours).

Here, N0 = 10,000, N = 1,000, and r = 0.75. Plugging the values into the formula gives [tex]1,000 = 10,000(1 - 0.75)^t.[/tex]Simplifying, we find [tex](1 - 0.75)^t = 0.1.[/tex]

Solving for t, we find that t equals 2 cycles or 4 hours, because the bacteria population decreases by 75% every 2 hours, and it takes 2 cycles for the population to reach 1,000 from 10,000.

1. EG = HJ (Given)

2. EG = EF + FG, HJ = HF + FJ (Seg. Add. Prop.)

3. EF + FG = HF + FJ (Subst. Prop.)

4. EF =  FJ (Given)

5. FG = HF (Subtraction Prop.)

It's challenging to demonstrate that FG equals HF as these may represent different elements or variables in different mathematics or physics contexts. At its simplest, FG seems to represent the gravitational force between two masses, and HF would need to represent the same force to hold true.

The equation given seems to pertain to gravitational forces where FG represents the gravitational force between two masses, electron and proton.

Given that FG = GMM where G is the gravitational constant (6.67×10-¹1 N·m²/kg²), m and M represent the masses of the electron and proton, to prove that FG=HF, it implies that HF represents the same gravitational pull.

However, without more detailed context or information, I can't further demonstrate or prove that FG does equal HF as these terms may refer to different elements or variables in different contexts of mathematics or physics problems.

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To calculate the amount that should be deposited today in an account that earns 3% compounded semiannually to accumulate to $8000 in three years, we can use the compound interest formula.

To calculate the amount that should be deposited today in an account that earns 3% compounded semiannually to accumulate to $8000 in three years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal, r is the interest rate, n is the number of compounding periods per year, and t is the number of years. In this case, the future value (A) is $8000, the interest rate (r) is 3% or 0.03, the number of compounding periods per year (n) is 2 (semiannual compounding), and the number of years (t) is 3. Plugging these values into the formula, we get:

A = P(1 + r/n)^(nt)

$8000 = P(1 + 0.03/2)^(2*3)

$8000 = P(1 + 0.015)^(6)

$8000 = P(1.015)^(6)

To find the value of P, we divide both sides of the equation by (1.015)^6: P = $8000 / (1.015)^6. Using a calculator, we find that P ≈ $7383.42. Therefore, approximately $7383.42 should be deposited today in the account.

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[tex]\bf \begin{cases} x=7\implies &x-7=0\\ x=-3\implies &x+3=0\\ x=2\implies &x-2=0 \end{cases}~\hspace{7em}(x-7)(x+3)(x-2)=\stackrel{y}{0} \\\\\\ (x^2-4x-21)(x-2)=y \\\\\\ x^3-4x^2-21x-2x^2+8x+42=y\implies x^3-6x^2-13x+42=y[/tex]

Answer:

Point B is Point A reflected across the y-axis.

Step-by-step explanation:

Answer:

B is A reflected across the y-axis; only the signs of the x-coordinates of A and B are different.

Step-by-step explanation:

When a point is reflected across the y-axis, the x-coordinate of the point is negated.  Algebraically,

(x, y)→(-x, y)

Point A is located at (-1, -3.5) and point B is located at (1, -3.5).  The only difference between the two points is that the x-coordinate is negated; this means it is a reflection through the y-axis.

To find the equation of a line perpendicular to a given line, find the negative reciprocal of the slope and use the point-slope form of a line.

To find the equation of a line that is perpendicular to the given line and passes through the given point, we first need to determine the slope of the given line. The given line has a slope of -1/5, which is the negative reciprocal of the slope we want for the perpendicular line. The negative reciprocal of -1/5 is 5/1 or 5. Now we have the slope of the perpendicular line and a point it passes through (-2, 7), we can use the point-slope form of a line to find the equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.

Substituting the values, we get: y - 7 = 5(x - (-2))
y - 7 = 5(x + 2)
y - 7 = 5x + 10
y = 5x + 10 + 7
y = 5x + 17

Therefore, the equation of the line that is perpendicular to the given line and passes through the given point (-2, 7) is y = 5x + 17. Option B is the correct answer.

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The correct answer is B. y=5x+17.

To write the equation of a line that is perpendicular to the given line y-3=-1/5(x+2) and that passes through the point (-2, 7), first, we need to find the slope of the given line and then determine the slope of the perpendicular line, which will be the negative reciprocal of the given line's slope. The slope of the given line is -1/5, so the slope of the line perpendicular to it will be 5 (since the negative reciprocal of -1/5 is 5).

Next, we use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point through which the line passes. Plugging in our slope of 5 and the point (-2, 7), the equation becomes:

y - 7 = 5(x - (-2))

Expand and simplify to solve for y:

y - 7 = 5x + 10

y = 5x + 17

The correct answer is B. y=5x+17.

Answer:

y = -.75 x

Step-by-step explanation:

To determine if y varies directly with x, we look at y/x and see if it is a constant

y/x = 2.25/-3 = -.75

     = -.75/1 = -.75

     =-3/4 = -.75

Since it is a constant, it has direct variation.  The constant of variation is -.75

y = -.75 x

Answer:

105.35

Step-by-step explanation:

:)

Answer:

d=1

Step-by-step explanation:

If North is i and South is -i

East is 1 and West is -1

The robot is facing East as it enters the maze, it will have a starting value of 1

Answer:

The value of d at the start of the maze will be 1 because 1 represents East .

Answer:

x= -2

Step-by-step explanation:

The distance from one end of the line  to the other is -3x-1.

Counting on the number line we count 6 units.  Setting them equal we get

-3x-1 = 5

Add 1 to each side

-3x-1+1 = 5+1

-3x = 6

Divide each side by -3

-3x/-3 = 6/-3

x = -2

Answer:

The correct option is B.

Step-by-step explanation:

From the given figure it is nices that the length of sides AB, BC and AC are 20, 22 and 35. The line AD is angle bisector.

Let the missing value be x.

The Triangle Angle Bisector Theorem states that the angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

Since AD is angle bisector, therefore

[tex]\frac{AB}{AC}=\frac{BD}{CD}[/tex]

[tex]\frac{20}{35}=\frac{22-x}{x}[/tex]

[tex]20x=35(22-x)[/tex]

[tex]20x=770-35x[/tex]

Add 35x both sides.

[tex]55x=770[/tex]

Divide both sides by 55.

[tex]x=\frac{770}{55}[/tex]

[tex]x=14[/tex]

Therefore, second option is correct.

Answer: 15

Step-by-step explanation:

Using synthetic division:

-5  |  1    9     17    -8    50

    |  ↓   -5   -20   15   -35            

       1     4   -3      7     15  ← this is the remainder

Check:

f(x) = x⁴ + 9x³ + 17x² - 8x + 50

f(-5) = (-5)⁴ + 9(-5)³ + 17(-5)² - 8(-5) + 50

      = 625 - 1125 + 425 + 40 + 50

      = 15

Answer:

5 x 2 inside the parenthesis

Step-by-step explanation:

We need an order of operations to ensure we always arrive at the correct answer. It gives us a consistent way to work with numbers. We use the mnemonic device like PEMDAS to remember the correct order.

P-parenthesis

E-exponents

M-multiplication

D-division

A-add

S-subtract.

We apply them left to right doing inner operations before outer operations.

There fore our first step is in the parenthesis and multiplication because it is the inner most operations. 5 x 2 inside the parenthesis.

Answer:

a = 8

Step-by-step explanation:

Put the given information into the function equation and solve for a.

f(x) = a/(x-h) +k . . . . for (h, k) = (4, 2) and (x, y) = (12, 3)

3 = a/(12 -4) +2 . . . . . . . givens substituted in

1 = a/8 . . . . . . subtract 2

8 = a . . . . . . . multiply by 8

1 ║ 1               2                  -3               2

                       1                   3               0

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

       1              3                   0              [tex]\boxed{2}[/tex]

⇒ The Remainder is 2

The question is asking how many different outfit combinations William can form if he has 5 shirts and 7 pants. It's a simple multiplication of the two numbers (5*7) resulting in 35 different combinations. Therefore, William could wear a different outfit for 35 days without repeating.

The subject of this question is combinatorics, a branch of mathematics concerned with counting, both as a means and an end. In this specific context, we are looking at the number of different combinations that William can wear with the clothes he has. Since each shirt can be worn with any pair of pants, this translates into a simple product calculation.

William has 5 different shirts and 7 different pairs of pants. So, the total number of combinations of outfits he can put together is calculated by multiplying these numbers together. Hence, 5 shirts * 7 pants = 35 combinations.

This means that if William chooses a different combination each day, he could go for 35 days without wearing the same outfit twice.

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Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

P(tail) = [tex]\frac{1}{2}[/tex]

P(2) = [tex]\frac{1}{6}[/tex]

P(tail and 2 ) = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{12}[/tex]

Answer: No, we can't find a unique price for an apple and an orange.

Step-by-step explanation:

Since we have given that

Cost of 4 apples and 4 oranges = $10

Cost of 6 apples and 6 oranges = $12

We need to find the unique price for an apple and an orange.

According to question, our equations will be

[tex]4x+4y=\$10\\\\6x+6y=\$12[/tex]

since it is equation of parallel lines, as

[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}\\\\\frac{4}{4}=\frac{6}{6}\neq \frac{10}{12}[/tex]

Hence, No, we can't find a unique price for an apple and an orange.