Find "x" so that a line drawn through the given points has the given slope. (Sketching the
problem may be helpful.)_
Given: A(x,6) B(2,4)
m=1/3

Answer:

a. k = 24 b. y = [tex]Ae^{4t} + Be^{6t}[/tex]

Step-by-step explanation:

a. Find the value of the constant k

Since  [tex]y = e^{4t}[/tex] is a solution of d²y/dt² -10dy/dt + ky = 0, then  [tex]y = e^{4t}[/tex] must satisfy the equation.

So, d²y/dt² =  [tex]16e^{4t}[/tex] and dy/dt =  [tex]4e^{4t}[/tex]

So, d²y/dt² -10dy/dt + ky = 0

[tex]16e^{4t}[/tex] - 10([tex]4e^{4t}[/tex]) + k([tex]e^{4t}[/tex]) = 0

[tex]16e^{4t}[/tex] - [tex]40e^{4t}[/tex] + [tex]ke^{4t}[/tex] = 0

 - [tex]24e^{4t}[/tex] + [tex]ke^{4t}[/tex] = 0

- [tex]24e^{4t}[/tex] =  -[tex]ke^{4t}[/tex]

So, k = 24

b. Find the general solution to this equation.

Since k = 24, our equation is

d²y/dt² -10dy/dt + 24y = 0

The characteristic equation is thus

m² - 10m + 24 = 0

Factorizing this we have

m² - 6m - 4m + 24 = 0

m(m - 6) - 4(m - 6) = 0

(m - 6)(m - 4) = 0

m - 6 = 0 or m - 4 = 0

m = 6 or m = 4

Since we have real roots for the characteristic equation, then, the general solution is

y = [tex]Ae^{4t} + Be^{6t}[/tex]

Based on the random numbers given, the probability that 5 random digits will have at least 3 even digits is D. 3/5.

Based on the given numbers, the numbers that have at least 3 even digits are 6.

They are: 46370, 53480, 49126, 89212, 88241, and 37808.

The probability out of 5 of at least 3 even numbers is:

= Number of 3 digit numbers / Total random numbers

= 6 / 10

= 3 / 5

Find out more on probability and random numbers at https://brainly.com/question/251701.

#SPJ1

Answer:

9/10

Step-by-step explanation:

Guy above is wrong, I took it just now.

Answer:

Step-by-step explanation:

Answer:

z=3

Step-by-step explanation:

1.−6z−4=−22

2. +4 to both sides

3.-6z=−18

4. Divide -6 by both sides

5. -6z/-6 = -18/-6

6. x=3

Answer:

Make x equal 0 in the equation of the graph (the equation in the form of y=mx+b)

Step-by-step explanation:

Then, solve the equation for y.

Answer:

6. O+ to A+ donors = 90 to 45; 90 : 45 and 90/45

7. AB- donors to AB+ donors = 4 to 6; 4 : 6 and 4/6

8. B+ to total donors = 20 to 195; 20 : 195 and 20/195

9. O- donors to A- donors = 9 to 21; 9 : 21 and 9/21

10. B- donors to B+ donor = 0 to 20; 0 : 20 and 0/20

11. O- donors to total donors = 9 to 195; 9 : 195 and 9/195

12. A+ donors and B+ donors to AB+ donors = 65 to 6; 65 : 6 and 65/6

13. A- donors and B- donors to AB- donors = 21 to 4; 21 : 4 and 21/4

14. the ratio 90/9 is a comparison of O+ donors to O- donors

Step-by-step explanation:

A ratio is a relationship where for every x unit of one quantity there are y units of another quantity. A ratio can be written in three ways:

x to y

x:y, or

x/y

For the given questions;

6. O+ to A+ donors = 90 to 45; 90 : 45 and 90/45

7. AB- donors to AB+ donors = 4 to 6; 4 : 6 and 4/6

8. B+ to total donors = 20 to 195; 20 : 195 and 20/195

9. O- donors to A- donors = 9 to 21; 9 : 21 and 9/21

10. B- donors to B+ donor = 0 to 20; 0 : 20 and 0/20

11. O- donors to total donors = 9 to 195; 9 : 195 and 9/195

12. A+ donors and B+ donors to AB+ donors

A+ donors and B+ donors to = 45 + 20 = 65

therefore, A+ donors and B+ donors to AB+ donors = 65 to 6; 65 : 6 and 65/6

13. A- donors and B- donors to AB- donors

A- donors and B- donors = 21 + 0= 21

therefore, A- donors and B- donors to AB- donors = 21 to 4; 21 : 4 and 21/4

14. O+ donors = 90; O- donors = 9

therefore, the ratio 90/9 is a comparison of O+ donors to O- donors

Answer:

The value of 8x - 30 is 74 when solved.

Step-by-step explanation:

Subtract 12 on both sides to get 13 as your x value.  Plug in 12 on the x value of 8x to get 104 when multiplied.  Subtract 30 to get 74 as your result.

Answer:

593.14 m

Step-by-step explanation:

Given that :

Length of rig visible above water surface (sea. Level) = 74.98m

Length of rig below surface of water (sea level) = 518.16 m

The total height of the rig:

The surface of water is usually regarded as a zero point ;

Hence. The total height of rig will be the sum of the height above sea level and the length below water surface

=(74.98 + 518.16) m

= 593.14 m

Answer:

C. y - 5= 5/3 ( x - 3 )

Step-by-step explanation:

I used a graphing calculator

Answer:

13

Step-by-step explanation:

Answer:

6) C. amount left in her money

7) C. Php1 500, Php403 and 3 cans of paints

8) A. Php291

9) B. Php1 170

10) D. Php840

Step-by-step explanation:

Alona bought 3 cans of paint for Php403 p er can. She gave the salesclerk Php1 500. How much change did she get?

6.) What is asked in the problem?

Aloha was asked of her change. This means the amount that is left after buying the 3 cans of paint. Hence, option C is correct.

C. amount left in her money

7. )What are the given facts?

The given facts in the question are

The 3 cans of paint that cost Php 403 and the amount she paid the clerk which is Php 1500

Hence, Option C. Is correct.

C. Php1 500, Php403 and 3 cans of paints

8. )How much change did she get?

The amount for change she got is calculated as.

Php 1 500 - 3(Php 403)

= Php 1 500 - Php 1 209

= Php 291

The amount of change she got is Php 291

Option A. Php291 is correct

9.) Lilia has six Php100 bills, seven Php50 bills and eleven Php20 bills. How much does she have?

The question above can be interpreted as:.

Six Php100 bills

= 6 (Php100)

= Php 600

Seven Php50 bills

7 (Php50)

= Php 350

Eleven Php20 bills

11 (Php20)

= Php 220

The amount she she has is calculated as:

Php 600 + Php 350 + Php 220

= Php 1 170

Hence, Option B. Php1 170 is correct

10.) Mang Jose is a tricycle driver. He charges Php10 for every passenger he transports. The tricycle carries 4 passengers each trip. How much does he earn for 21 trips?

We are told that:

He charges Php10 for every passenger he transports. The tricycle carries 4 passengers each trip.

Hence, the cost for each trip is

Php 10 × 4 passengers

= Php 40

Hence:

1 trip = Php 40

21 trips = x

Cross Multiply

x = 21 trips × Php 40

x = Php 840

Option D. Php840 is correct

Answer:

Regular Polygons

Polygons can also be classified as equilateral, equiangular, or both. Equilateral polygons have congruent sides, like a rhombus. Equiangular polygons have congruent interior angles, like a rectangle. When a polygon is both equilateral and equiangular, it is called a regular polygon.

Answer:

Equilateral = all sides are the same length

Equiangular = all angles are the same length

Step-by-step explanation:

Answer: The required simple interest = $240

Step-by-step explanation:

Formula for simple interest:

Interest = Principal x rate x time

Given: Principal = $800

rate of interest = 5% = 0.05

Time = 6 years

Interest = 800 x 0.05 x 6 = $240

Hence, the required simple interest = $240

Answer:

480

Step-by-step explanation:

Answer:

8 grams

Step-by-step explanation:

4+4+4+8=20

4+8+8=20

Answer:

D. 8 grams

Step-by-step explanation:

Based on the information given regarding the inheritance pattern, the chance that the child would also be affected or would be a carrier is 50% respectively.

It should be noted that pedigree analysis simply means the study of heredity and inheritance of genes.

It is used by doctors to analyze the inheritance pattern, and observe any genetic disorder. In this case, the male is affected by the chromosome XY. Similarly, the male married the female, having X-linked recessive disorder.

In this case, the chance that the child would also be affected is 50%, and the chance that the child would be a carrier is 50%.

Learn more about inheritance on:

https://brainly.com/question/9365566

Answer:

% 50

% 50

False

Step-by-step explanation:

Answer:Jada will get same shade as Perfect Purple Water

Step-by-step explanation:

STEP 1

To get the right  recipe for Perfect purple water, every new mixture must have an equivalent ratio as the ideal mixture

The ideal mixture is given as

8ml  blue water and 3 ml red water.

Step 2

Andre mixes 16ml blue water with 9ml red water

[tex]\frac{8ml}{3ml}[/tex] is not equivalent to [tex]\frac{16ml}{9ml}[/tex]

Because dividing Andre's mixture  by a common value  will  not give  the equivalent ratio of the ideal recipe

[tex]\frac{16ml}{9ml}[/tex]  [tex]\frac{/}{/}[/tex]  [tex]\frac{3}{3}[/tex] =[tex]\frac{5.3ml}{3ml}[/tex]  

Jada mixes 24ml blue water with 9ml red water

[tex]\frac{8ml}{3ml}[/tex] is equivalent to [tex]\frac{24ml}{9ml}[/tex]

Because dividing Jada's mixture  by a common value  gives the equivalent ratio of the ideal recipe

[tex]\frac{24ml}{9ml}[/tex]  [tex]\frac{/}{/}[/tex]  [tex]\frac{3}{3}[/tex] =[tex]\frac{8ml}{3ml}[/tex]  

This shows that Jada got the right recipe and will get  same shade as Perfect Purple Water but in a higher quantity, 3 times the right recipe for  Perfect Purple Water

Answer:

The slope is m=1/2

Step-by-step explanation:

hope this helps you.

Answer:

The first one

Step-by-step explanation:

Note the brackets means absolute value so the order of the first one goes like this

-1, 3/2, 2, 3, 3.5

Thus it's from least to greatest

Answer:

39

Step-by-step explanation:

1. Use the Pythagorean theorom: a^2+b^2=c^2.

C is the missing side here, which is the hypotenuse of the triangle. The other two sides and be put into the equation either way. Doesn't matter the order.

15^2 + 36^2 =c^2

2. Evaluate 15^2 and 36^2 and add the results.

15^2 = 225

36^2 = 1,296

225+1,296= 1,521

3. Take the square root of the answer.

√1521 = 39

Answer:

3.75

Step-by-step explanation:

the unit range is 610 so 2287.5/610

Answer:

Step-by-step explanation:

y -30 plus 30 = 84 plus 30

y = 114

Your welcome BiThhhh

Answer:

y-114

Step-by-step explanation:

Answer:

ummmm.......

Step-by-step explanation:

Step-by-step explanation:

I guess its 1/3 ??........

Answer:

B

Step-by-step explanation:

The total change in position is represented by a number with a magnitude of 155 feet.

Hope this helps!

xoxo,

cafeology

Answer:

a+(n-1)d is the formula to calculate

Answer:c

Step-by-step explanation:

its 8 less which would be -8 and then you have to divide p by 2 because its half so it would be p/2-8

Answer:

Step-by-step explanation:

(C) [tex]\frac{p}{2} - 8[/tex]

See attachment for math work and answer.