Given the infirmation in the diagram, which theorem best justifies why lines j and k must be parallel

Answer:

As both Louis and Heidi runs at the same speed, both are running at equal speed of 1.33 miles per hour.

Step-by-step explanation:

We will calculate speed of both the person in miles per hour and then compare the speeds.

Speed = distance/time

_____________________________________

For Heidi

Distance = 1/3 miles

time = 1/4 hour

speed = 1/3  ÷ 1/4 = 4/3 miles per hour = 1.33 miles per hour

_______________________________________

For Louis

Distance = 2/3 miles   (here it was given 23 miles but it appears to be 2/3 of a miles )

time = 1/2 hour

speed = 2/3  ÷ 1/2 = 4/3 miles per hour = 1.33 miles per hour

______________________________________________________

As both Louis and Heidi runs at the same speed, both are running at equal speed of 1.33 miles per hour.

Answer:

Step-by-step explanation:

Given that:

OA = 7 cm, AB = 6 cm. ∠A = 90°, OA = OC = 7 cm

Using Pythagoras theorem: OB² = OA² + AB²

OB² = 6² + 7²=85

OB = √85 = 9.22 cm

to find ∠O, we use sine rule:

[tex]\frac{AB}{sin(O)}=\frac{OB}{sin(A)}\\ \\sin(O)=\frac{AB*sin(A)}{OB}=\frac{6*sin(90)}{9.22} =0.65 \\\\O=sin^{-1}0.65=40.6^o[/tex]

AOC is a minor sector with radius 7 cm and angle 40.6

The Area of the triangle OAB = 1/2 × base × height = 1/2 × OA × AB = 1/2 × 7 × 6 = 21 cm²

Area of sector OAC = [tex]\frac{\theta}{360}*\pi r^2=\frac{40.6}{360}*\pi *7^2=17.37 \ cm^2[/tex]

Area of shaded region = The Area of the triangle OAB - Area of sector OAC = 21 - 17.37 = 3.63 cm²

Perimeter of arc AC = [tex]\frac{\theta}{360}*2\pi r=\frac{40.6}{360}*2\pi *7=4.96\ cm[/tex]

CB = OB - OC = 9.22 - 7 = 2.22

Perimeter of shaded region = AB + CB + arc AC = 6 + 2.22 + 4.96 = 13.18 cm

Answer:

yes, the base is 4

Step-by-step explanation:

Answer:

3/14

Step-by-step explanation:

En esta pregunta, nos preocupa calcular la fracción de los estudiantes que no asisten a los talleres.

Para obtener la fracción que no asiste a los talleres, lo que debemos hacer es sumar las fracciones de cada uno de los talleres y restar el total de 1.

Matemáticamente eso sería;

1- (2/7 + 1/10 + 2/5)

Agregando los términos en el paréntesis, tenemos;

(20+ 7 + 28) / 70 = 55/70 = 11/14

Restando esto de 1, tenemos; 1-11 / 14 = 3/14

Answer:

Compound interest is best defined as:

Earning interest on interest.

Compound interest is earning interest on interest.

Compound interest is an interest accumulated on the principal and interest together over a given time period. The interest accumulated on a principal over a period of time is also accounted under the principal. Further, the interest calculation for the next time period is on the accumulated principal value. Compound interest is the new method of calculation of interest used for all financial and business transactions across the world. The power of compounding can easily be understood, when we observe the compound interest values accumulated across successive time periods.

Compound Interest = Interest on Principal + Compounded Interest at Regular Intervals

The compound interest is calculated at regular intervals like annually(yearly), semi-annually, quarterly, monthly, etc; It is like, re-investing the interest income from an investment makes the money grow faster over time! It is exactly what the compound interest does to the money. Banks or any financial organization calculate the amount based on compound interest only.

as, we know that Compound interest is an interest accumulated on the principal and interest together over a given time period.

So, we can also write Earning interest on interest.

learn more about compound interest here:

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Answer: 0.49 ± 0.0237

Step-by-step explanation: A interval of a 99% confidence interval for the population proportion can be found by:

[tex]p_{hat}[/tex] ± z.[tex]\sqrt{\frac{p_{hat}(1-p_{hat})}{n} }[/tex]

[tex]p_{hat}[/tex] is the proportion:

[tex]p_{hat}[/tex] = [tex]\frac{1455}{2957}[/tex]

[tex]p_{hat}[/tex] = 0.49

For a 99% confidence interval, z = 2.576:

0.49 ± 2.576.[tex]\sqrt{\frac{0.49(1-0.49)}{2957} }[/tex]

0.49 ± 2.576.[tex]\sqrt{\frac{0.49*0.51}{2957} }[/tex]

0.49 ± 2.576.(0.0092)

0.49 ± 0.0237

For a 99% confidence interval, the proportion will be between 0.4663 and 0.5137 or 0.49 ± 0.0237

Answer:

x = 3 and y = 2

Step-by-step explanation:

Start by multiplying the first equation by "-3" so we can cancel the term with denominator (x+y) when we combine:

[tex]\frac{(-3)\,5}{x+y} -\frac{(-3)\,2}{x-y} =(-3)(-1)\\\frac{-15}{x+y} +\frac{6}{x-y} =3[/tex]

which now added term by term to the second equation gives:

[tex]\frac{-15}{x+y} +\frac{6}{x-y} =3\\\frac{15}{x+y} +\frac{7}{x-y} =10\\ \\\frac{13}{x-y} =13[/tex]

Now we solve for x-y by cross multiplying:

[tex]\frac{13}{13}=x-y\\ x-y=1\\x=y+1[/tex]

Now we use this substitution for x  back in the first equation to solve for the unknown y:

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

and now that we know that y = 2, we use the substitution equation to solve for x:

[tex]x=y+1\\x=2+1\\x=3[/tex]

Answer:

C 375 this your answer

Hope it will help

Answer:

B) 592

Step-by-step explanation:

483, 759, 264, 837,?

Erase commas.

483759264837

Separate into two-digit groups:

48, 37, 59, 26, 48, 37

There is a common pattern:

48 - 11 = 37 + 22 = 59 - 33 = 26 + 22 = 48 - 11 = 37

The next term:

37 + 22 = 59 (add 22)

59 - 33 = 26 (subtract 33)

5926

Answer:

The answer to your question is given in the attached photo.

Step-by-step explanation:

To determine the answer to the question,

First, we shall determine the value 3A.

This is obtained by multiplying matrix A by 3 as shown in the attached photo.

Next, we shall carry out the operation 3A – B as shown in the attached photo.

Answer:

After 24 hours, there will be 4191 bacteria present in the culture.

Step-by-step explanation:

Initial number of bacteria = 300

amount in 10 hrs = 3 x 300 = 900

time taken = 10 hours

Bacterial growth is exponential, ans so we use the equation

N = N'[tex]e^{kt}[/tex]

where N is the final amount

N' is the initial amount

k is the growth constant

t is the time

For this first case, we have

900 = 300 x [tex]e^{k*10}[/tex]

3 = [tex]e^{10k}[/tex]

take natural log of both sides, we'll have

ln 3 = ln [tex]e^{10k}[/tex]

1.0986 = 10k

k = 1.0986/10 = 0.10986

using the growth constant above, we calculate for a day which is 24 hours

N = N'[tex]e^{kt}[/tex]

N = 300 x [tex]e^{0.10986*24}[/tex]

N = 300 x [tex]e^{2.637}[/tex]

N = 300 x 13.97

N = 4191 bacteria

Answer:

x=5/a-b+3

Step-by-step explanation: Since we don't know a or b, we'll leave them as is. Shift all terms with x to the left and keep 5 on the right (ax+3x-bx)=5. x is a factor of that, so you'd change it to x(a-b+3)=5. Then, divide by (a-b+3). If a and b had set values, then just add all the x values and solve.

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Lets do this step by step.

Simplify 5 by ( b - x)

Apply the distributive property.

[tex]5b + 5 ( -x ) = 2b + ax[/tex]

Multiply -1 by 5.

[tex]5b - 5x = 2b + ax[/tex]

Subtract ax from both sides of the equation.

[tex]5b - 5x - ax = 2b[/tex]

Move all terms not containing x  to the right side of the equation.

Subtract 5b from both sides of the equation.

[tex]-5x - ax = -3b[/tex]

Subtract 5b from 3b.

[tex]-5x - ax = -3b[/tex]

Factor x out of -5x - ax .

[tex]x ( -5 - a ) = -3b[/tex]

Divide each term by = -3b.

Divide each term in x ( -5 - a) = -3b by - 5 -a.

[tex]\frac{x( -5 - a)}{-5 - a} = \frac{-3b}{-5 - a}[/tex]

Cancel the common factor of -5 - a.

[tex]x = \frac{-3b}{-5 - a}[/tex]

Simplify [tex]\frac{-3b}{-5 - a}[/tex]

[tex]x = \frac{3b}{5 + a}[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

2/xy

Step-by-step explanation:

you have to do the math but im not very sure on this

Answer:

50 square units

Step-by-step explanation:

When graphed you have a width  of 5 and a length of 10 so multiply them together to get 50

Answer:

Step-by-step explanation:

I have this question too. I think it is 45. sorry if its incorrect

Answer:

39 investors contributed $6,000, and 21 investors contributed $12,000.

Step-by-step explanation:

Let's say that x investors contributed $6,000, and y investors contributed $12,000.

x + y = 60

6,000x + 12,000y = 486,000

x + 2y = 81

x + y = 60

y = 21

x + 21 = 60

x = 39

So, 39 investors contributed $6,000, and 21 investors contributed $12,000.

Hope this helps!

Answer:

1. f(-1) = -6

2. f(0) = -5

3. f(1) = -4

4. f(2) = -3

5. f(5) = 0

6. f(8) = 3

Step-by-step explanation:

1. f(-1)=-1-5=6

substitute the x value into the equation.

2. f(0)=0-5=-5

3. f(1)=1-5=-4

4.f(2)=2-5=-3

5. f(5)=5-5=0

6. f(8)=8-5=3

Answer:

Step-by-step explanation:

m1=40

Taking m3

m3=40 ×3

m3= 120

Answer: [tex]y=\frac{2}{5}, \frac{6}{5}[/tex]

Step-by-step explanation:

When answering a problem like this, you first isolate the absolute value.  TO do this, first subtract 8 from both sides, to get –2|4–5y|=-4.  Then divide both sides of the equation to get |4–5y|=2.  The next thing you do is split the equation into 4-5y=2 and 4-5y=-2, because the contents of the absolute value could be negative or positive, and simplifying both into y = 2/5, and y = 6/5y.

Hope it helps <3

Answer: 4n - 20

Step-by-step explanation: We can use the distributive property.

The distributive property tells us that if were given an expression

such as 4(n - 5), we can multiply the 4 by both the n and the -5.

So our answer is just 4n - 20.

Answer:

1,110

Step-by-step explanation:

calculator

Answer:

Graph A is the one that represents the given piecewise function.

Step-by-step explanation:

Notice that the Domain of the given function has been partitioned in three sections:

[tex]-2\leq x<0\,\,; \,\,\,x = 0\,\,;\,\,\,0<x\leq 2[/tex]

in the first section we have that the function responds to [tex]f(x)=x-1[/tex], which is a line of positive slope (ascending line) equal to "1", and y-intercept at y= -1.

This line should therefore start at the point (-2, -3) (when x = -2) and end at y almost equal to -1, when x approaches the value zero; and an empty dot should be seen in the position (0, -1)

For x = 0 we should see a solid dot located at the position (0, 1) on the plane.

And finally for the third section we should see a horizontal segment (that represents a constant value of 3, starting with an empty dot at the point (0, 3), and ending on a solid dot located at (2, 3).

This is what we see represented by the graph labeled A in the list of answer options.

Answer:

B

Step-by-step explanation:

Answer:6/16 or 3/8

Step-by-step explanation:

I did it

Answer: 3/16

Step-by-step explanation:

The expression a/b ÷ c/d = ad/bc is A. true.

To show that if a/b and c/d are rational expressions, then a/b ÷ c/d = ad/bc

Rational expressions are expressions of the form a/b where a and b are integers and b ≠ 0

If the rational expression a/b is to be divided by c/d, we take the reciprocal of the expression on the right side of the division sign.

So, L.H.S = a/b ÷ c/d

= a/b × 1/(c/d)

= a/b × d/c

= ad/bc

= R.H.S

Since L.H.S = R.H.S.

a/b ÷ c/d = ad/bc

So, the expression a/b ÷ c/d = ad/bc is A. true.

Learn more about rational expressions here:

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Answer:

x=4

Step-by-step explanation:

x²-16=0

x²=0+16

x²=16

x=√16

x=4

Answer:

Marcelo acertou 22 questões.

Step-by-step explanation:

Vamos representar

Questões que acerta = a

Questões que erra = b

a + b = 30 .......... Equação 1

a = 30 - b

o aluno ganha 3 pontos por cada questão que realizar, mas perde 2 pontos por cada questão que ocorrerá.

Matematicamente:

3 × a - 2 × b = 50

3a - 2b = 50 pontos ............. Equação 2

Substitua 30 - b por a na Equação 2

3 (30 - b) - 2b = 50

90 - 3b - 2b = 50

90 - 5b = 50

Colete termos semelhantes

90 - 50 = 5b

5b = 40

b = 40/5

b = 8

Questões que erra = b

Marcelo, portanto, perdeu 8 questões.

Dizem-nos que ele respondeu todas as 30 questões. Portanto, se ele perdeu 8 questões, o número de questões acertadas é representado pela Equação 1

a + b = 30 .......... Equação 1

a + 8 = 30

a = 30 - 8

a = 22 questões.

Portanto, ele acertou 22 questões.

Answer:

1:2

Step-by-step explanation:

The area of ΔFED must be 1/4th of the entire area and so must the area of ΔBCD because B and F are the midpoints. Therefore, the area of ABDF is 1 - 1/4 - 1/4 = 1/2 of ACDE's are so the ratio is 1:2.

Answer:

11 bags

Step-by-step explanation:

725 jelly beans evenly into 29 plastic containers:

725/29=25  jelly beans in each plastic containers

275/25=11  Jim found eleven bags

Answer:

11 containers

Step-by-step explanation:

His mom evenly divided the jelly beans into containers. There are 725 jelly beans and 29 containers. To find how many jelly beans are in each container, divide 725 by 29.

725/29

25

There are 25 jelly beans in every container.

After the hunt, Jim had 275 jelly beans. There are 25 beans in each container. To find the number of containers, we can divide 275 by 25.

275/25

11

He found 11 containers.

Answer:

y = -x/4 + 9/2

Step-by-step explanation:

The diagonal AC is the perpendicular bisector of BD.

The centre of the square, P, through which both diagonal pass through is at the average of the coordinates of B(2,6) and D(0,-2)

P ((2+0)/2, (6-2)/2) = P(1,2)

The slope of BD,

m = (yd-yb)/(xd-xb) = (-2-6)/(0-2) = -8/-2 =4

Slope of AC

m' = -1 / m = -1/4

Using the point slope form of the line AC, slope m' through P(1,2)

y-yp = m'(x-xp)

y-2 = -(1/4)(x-1)

Simplify and isolate y

y = -x/4 + 1/4 +2 = -x/4 + 9/2

Answer:

It decreases from 45° to 40°

Step-by-step explanation:

The secant angle GBJ is half the difference of the measure of its intercepted arcs, that is

∠ B = [tex]\frac{1}{2}[/tex] (CDF - GHJ) = [tex]\frac{1}{2}[/tex](130 - 40)° = [tex]\frac{1}{2}[/tex] × 90° = 45°

If arc GHJ is now 50°, then

∠ B = [tex]\frac{1}{2}[/tex](130 - 50)° = [tex]\frac{1}{2}[/tex] × 80° = 40°

That is ∠ B decreases from 45° to 40°

Answer:

D

Step-by-step explanation:

If you put the equation into a graphing calculator it will give ou a function than is a straight line that is stretched vertically by 3 units