Using the rational root theorem, identify all the possible rational roots of the equation x^4+25x^3-14x^2-19x+30

Question:

Consider a cookie recipe in which 1 1/2 cups of chocolate chips are needed to make 25 cookies. Lara wants to double the number of cookies. How many cups of chocolate chips should she use?

Answer:

[tex]Cups = 3[/tex]

Step-by-step explanation:

Given

[tex]Cups = 1\frac{1}{2}[/tex]

[tex]Cookies = 25[/tex]

Required

Number of cups when the cookies is doubled

When [tex]Cookies = 25[/tex], [tex]Cups = 1\frac{1}{2}[/tex]

So, when the number of cookies is doubled, the number of cups will also be doubled.

i.e.

[tex]Cookies = 25*2[/tex]

[tex]Cookies = 50[/tex]

and

[tex]Cups = 1\frac{1}{2} * 2[/tex]

Convert to improper fraction

[tex]Cups = \frac{3}{2} * 2[/tex]

[tex]Cups = \frac{3* 2}{2}[/tex]

[tex]Cups = \frac{6}{2}[/tex]

[tex]Cups = 3[/tex]

i.e. 3 cups are needed

[tex]\color{plum}m∠ABC = 71° [/tex]

Which means :

m∠ABC = ∠ADC (opposite angles of a parallelogram)

m∠ABC :

= 37° + 34°

= 71°

Thus, the measure of ∠ABC = 71°

Let us find the measures of the other angles as well :

m∠BCD + m∠ADC = 180°

m∠BCD + 71 = 180°

m∠BCD = 180 - 71

m∠BCD = 109°

Thus, the measure of∠BCD = 109°

m∠BCD = ∠BAD (opposite angles of a parallelogram)

m∠BAD = 109°

Thus, the measure of ∠BAD = 109°

Therefore, m∠ABC = 71°

Answer:

Step-by-step explanation:

Given isosceles trapezoid AB = CD

Angles B and C are congruent and angles A and D are congruent.

A and B, as well as C and D sum to 180 as supplementary angles, therefore:

Answer:

Step-by-step explanation:

5g. X% solution means there are Xg per 100mL. So 500mL at 1%: 5g

Answer:

The answer is b=128

Step-by-step explanation:

25+27=52

180-52=128

Answer:

∠A + ∠B + ∠C = 180°

⇒ 25° + 27° + ∠B= 180°

⇒ 52° + ∠B= 180°

Subtract both sides by 172°

⇒ 52° – 52° + ∠B = 180° – 52°

Therefore, ∠B = 128°

Answer:

Distance of RS = 14.4 units (Approx)

Step-by-step explanation:

Co-ordinate

R (-8, -6)

S (4, 2)

Find:

Distance of RS

Computation:

Distance = √(x1 - x2)² + (y1 - y2)²

Distance of RS = √(-8 - 4)² + (-6 - 2)²

Distance of RS = √144 + 64

Distance of RS = √208

Distance of RS = 14.4 units (Approx)

Answer:

Step-by-step explanation:

The least common multiple of 3 and 4 is 12. Divide the rectangle in twelfths.

⅓ = 4/12

¼ = 3/12

The Vertex is (-2,1)

And the focus is  (-2,3)

Answer:

On a standard running 400-meter track a mile is 4 laps… plus 9 more meters if you want to get all technical about it. A mile is specifically 1,609.3 meters.

Step-by-step explanation:

Answer:

a)

Therefore to compare this data effectively using the rates per driver is better off like for people who do not smoke their rate will be = 59 / 452 = 13.1% while for smokers of 61+ times = 50 / 156 = 32.1% and this rate will show clearly tat more accidents where caused by people who smoked 51+ times hence it should be used for graphical representation

b) attached below

Step-by-step explanation:

A) A  useful graph is must compare rates rather than counts of accidents in the four marijuana use classes

Using the rates on a graph is better for reference like saying; that 50 crashes were caused by those who smoke 51+ times and 59 crashes is caused by those who never smoke this statistics makes it seem like smoking has no effect on the amount of accidents

Therefore to compare this data effectively using the rates per driver is better off like for people who do not smoke their rate will be = 59 / 452 = 13.1% while for smokers of 61+ times = 50 / 156 = 32.1% and this rate will show clearly tat more accidents where caused by people who smoked 51+ times hence it should be used for graphical representation

B) accident rate for Non-smokers

 = (59/452) * 100 = 13.05

accident rate for smokers between 1-10 times

= ( 36/ 229 ) * 100 = 15.72

accidents rate for smokers between 11 - 50 times

=  ( 15/50 ) * 100 = 21.42

accidents rate for smokers 51+

 =  ( 50 / 156 ) * 100 = 32.05

attached below is the required graph

Answer:

Step-by-step explanation:

(-4,0)

Answer: x boletos de adulto

2x boletos de estudiante

x+2x=288

3x=288

x=288/3

x=96

adulto =96

estudiante 2*96=192

96+192=288

Step-by-step explanation: 96 y 192

Answer: 9x+6y ≤10  

Step-by-step explanation:

Let x= number of packs of hot dogs .

y =number of packs of hamburger.

Total expenditure = (Charge per hot dog) (number of packs of hot dogs ) +(Charge per hamburger) (number of packs of hamburger.)

i.e. Total expenditure =9x+6y  ( in $)

Jerry can spend a maximum of $100 on the food.

So, Total expenditure ≤ $100

i.e. 9x+6y ≤10  [Required inequality]

The inequality that represents this situation:9x+6y ≤10  

Answer:

y-7= 6(x-0)

Step-by-step explanation:

y-y1=m(x-x1) is the point slope form. The slope is substituted by the m while (x1,y1) are any coordinate on the plane. As you already have to coordinates (0,7) and the slope of 6 substitute it into the equation, to get y-7=6(x-0). Hope this helps!

Answer:

x=3 ,y=6

Step-by-step explanation:

4x+6y=44 eqni

4x+2y=28 eqn ii

now subtract it eqn i and ii

4x+6y=44

-4x+2y=28

or, 0 +4y=24

or, 4y=24

or , y=24/4

or,y=6

putting value of y in eqn i

4x+6y=44

4x+6×6=44

4x=44-36

4x=12

x=12/4

x=3

Answer:

the proportion of people who are sick after two weeks is 33.2%

Step-by-step explanation:

Given the data in the question;

Let there be 100 people in the city;

20% of them are sick( 20/100 × 100) = 20 people

so 80% are fine = ( 100 - 20 ) = 80

after one​ week, 40% of the people who were sick are still sick

40/100 × 20 = 8%

of the 80% of people who were well, 30% got sick after one week

30/100 × 80 = 24%

so after one week. 8% + 24% = 32% of the people were sick,

hence 68% are fine.

now, after second week 40% of sick and 30% of not sick people previously will be sick

∴ Total people who are sick after two weeks    

⇒ 40/100 × 32 + 30/100 × 68

= 12.8 + 20.4

= 33.2

Therefore, the proportion of people who are sick after two weeks is 33.2%

Answer: 3:2

Step-by-step explanation:

This is correct because 3:2 is equal to 6:4. 3:2 is 6:4 divided by 2.

Hope this helps ;)

Answer:

3:2

Step-by-step explanation:

Fiction to non-fiction.

6:4

Now, simplify. Divide both by 2.

6/2=3

4/4=2

3:2 is the ratio.

9514 1404 393

Answer:

  64°

Step-by-step explanation:

y° and the angle marked 64° are "alternate interior angles", so are congruent.

  y° = 64°

Answer:

y=4x-9                                                                      

Step-by-step explanation:

slope is rise/run

choose one point and do rise/run until you get to the next point

from the graph you can see the y-intercept is -9

Answer:

y=2x+-9

Step-by-step explanation:

this is the answer

Answer:

The first term is 9 and the second term is 5.5, and the third term is r.

Step-by-step explanation:

Hope this helps! ^^

Answer:

10x 8 is 80 so it will be 30+80

Answer:

y ⇒⇒⇒ monthly income

x ⇒⇒⇒ number of times app is opened

$20 per month and an additional $0.005 each time the app is opened

∴ y = 0.005 x + 20

The attached figure represents the graph of y

Step-by-step explanation:

The division 292,000 divide 100. results to 2920.

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers.

Given:

292,000 divide 100.

We know division with zero in the denominator is different and easy.

As, 292000 have three and 100 have two zeroes.

So, the two zero of hundred cancels out the two zeroes of  292000.

So, 292000/ 100

= 2920

Hence, the division results to 2920.

Learn more about Division here:

https://brainly.com/question/21416852

#SPJ2

Answer:

2 miles

Step-by-step explanation:

The total length of the trip is 464 miles

An equation is used to show the relationship between two or more numbers and variables.

Let x represent the total length of the journey.

Kylie fell asleep after they had travelled 306 miles and she fell asleep 34% of the way. Therefore:

(100% - 34%) of x = 306

66% of x = 306

0.66x = 306

x = 464 miles

The total length of the trip is 464 miles

Find out more on equation at:https://brainly.com/question/24868934

Answer:

x>0.5

Step-by-step explanation:

multiply by 0.25 on both sides

x>0.5

Step-by-step explanation:

fresco didn't Divo ratify jdndodnswjskd ksosbwjw

Answer:

There is no solution to this problem.

Step-by-step explanation:

The 1 digit number cannot be 1, since there would be no remainder.

The 1 digit number cannot be 2, since the remainder could be 0 or 1.

The 1 digit number cannot be 3, since the remainder could be 0, 1, or 2.

So, the 1 digit number must be greater than 3.  Let's start with 4.  Since the quotient is 307 (remainder 3), 4 x 307 is already more than 3 digits.

Step-by-step explanation:

We need to find an expression that is equivalent to 4×(8+3)

We know that,

4×(8+3) = 4(11) = 44

Option (1).

(4 • 8) + 3 = 32+3 = 35. It is incorrect

Option (2).

(8 + 3) • 4 = (11) 4 = 44. It is correct.

Option (3).

4 • (3 + 8) = 4(11) = 44. It is correct.

Option (4).

4 • 8 + 4 • 3 = 32+12 = 44. It is correct.

Hence, the correct options are (2), (3) and (4).

Answer:

the probability that sales will be less than 81,000 packages is 0.6681

Step-by-step explanation:

Given that;

Average sales μ = 87,000

standard deviation σ = 4,000

x' = 81,000

P( x < 81,000) = ?

so

P( x < 81,000) = P( x - μ / σ )

we substitute

P( x < 81,000) = P( 81,000 - 87000 / 4000 )

P( x < 81,000) = P(  - 6000 / 4000 ) = -1.5

from table;

P( z < 1.5 ) = 0.6681

Therefore the probability that sales will be less than 81,000 packages is 0.6681

Answer:

x/2 = 1/2x

Step-by-step explanation:

# of paintbrushes/ 2 piles = 1/2 # of paintbrushes

Answer:

x/2

Step-by-step explanation:

Since Lucy is taking the paintbrushes, x, and splitting them into 2 equally sized groups we can assume that this IS 1/2 the size of the original group.

We can show this claim by simply doing this equation: x/2, since she is splitting them into 2 groups that are equally sized, we are just dividing x by two.