Joan has a prescription for 100 Theophylline capsules. Joan informs the pharmacist that she only has enough money to purchase ¼ of the prescription today. How many capsules will Joan pay for today?

Answer:

3/4

Step-by-step explanation:

We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(−5, −4), B(−7, 3) and C(3, −2) to the image triangle A'B'C' with vertices A' (−3.75, −3), B' (−5.25, 2.25) and C' (2.25, −1.5).

Center of dilation is at the origin.

To find the scale factor, we will divide the corresponding vertices of the image and pre-image.

A(−5, −4) ---> A' (−3.75, −3) = [tex]\frac{-3.75}{-5} , \frac{-3}{-4}=(\frac{3}{4} , \frac{3}{4})[/tex]

B(−7, 3) ---> B' (−5.25, 2.25) = [tex]\frac{-5.25}{-7} , \frac{2.25}{3}=(\frac{3}{4} , \frac{3}{4})[/tex]

C(3, −2) ---> C' (2.25, −1.5) = [tex]\frac{2.25}{3} , \frac{-1.5}{-2}=(\frac{3}{4} , \frac{3}{4})[/tex]

Therefore, the scale factor of the dilation is 3/4.

Answer: g(x) = x^4 - 9x^3 + 18x^2 + 32x - 96 which is choice C

=============================

Explanation:

Given roots: -2, 4, 4, 3

Based on that, we know that x = -2, x = 4, x = 4, and x = 3. The repeat x value of 4 is needed to help deal with a double root (multiplicity 2)

x = -2 leads to x+2 = 0, so (x+2) is one factor

x = 4 leads to x-4 = 0, making (x-4) another factor. We have two copies of (x-4) as a factor

x = 3 leads to x-3 = 0 so (x-3) is the last factor

Overall, the four factors are: (x+2) and (x-4) and (x-4) and (x-3)

Use the distributive property to expand everything out

g(x) = (x+2)(x-4)(x-4)(x-3)

g(x) = ( (x+2)(x-4) ) * ( (x-4)(x-3) )

g(x) = ( x^2 - 2x - 8 ) * ( x^2 - 7x + 12 )

g(x) = x^2( x^2 - 7x + 12 ) - 2x( x^2 - 7x + 12 ) - 8( x^2 - 7x + 12 )

g(x) = x^4 - 7x^3 + 12x^2 -2x^3 + 14x^2 - 24x - 8x^2 + 56x - 96

g(x) = x^4 - 9x^3 + 18x^2 + 32x - 96

which shows how I got choice C as the answer

To find the better buy, we can find how much they cost for an ounce and find it by comparison.

First option:

20/4.4

=$4.545454...

Second option:

16/3.68

=$4.3478...

As $4.3478..< $4.5454.., the second option is cheaper and therefore is the better buy.

Hope it helps!

The 20 ounces for $4.40 is the better deal at $0.22 per ounce, compared to the 16 ounces for $3.68 at $0.23 per ounce.

To determine which cereal is the better buy, we need to calculate the cost per ounce for each option. For the first option of 20 ounces at $4.40, the cost per ounce is:

[tex]\frac{0.44}{20} = 0.22 ~per ounce[/tex]

For the second option of 16 ounces at $3.68, the cost per ounce is:

[tex]\frac{3.68}{16} = 0.23[/tex]

Comparing these two costs per ounce, the 20 ounces for $4.40 is the better buy because it has a lower cost per ounce.

Answer:

$400,000

Step-by-step explanation:

We can write a proportion to find the total amount using the information given. A proportion is two equivalent ratios set equal to each other.

[tex]\frac{60}{100}=\frac{240000}{x}[/tex]

We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.

60x=100(240,000)

60x=24,000,000

y=400,000

Answer:

$400,000

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let b represent the number of boxes of cookies sold the first week. Then b+5 boxes were sold the second week, and 2(b+5) boxes were sold the third week. The total sold was ...

  b +(b+5) +2(b+5) = 431

  4b +15 = 431 . . . . . . simplify

  b = (431 -15)/4 = 104 . . . . . subtract 15, divide by the coefficient of b

First week: b = 104

Second week: b+5 = 109

Third week: 2(b+5) = 218

Answer:

B

Step-by-step explanation:

There are 8 possibilities: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. Of these 4 have at least two heads. Assuming a fair coin, the probability of tossing at least two heads is 4/8 or 1/2. The Answer would probably be 3/8 though.

C) 3/8

The probability of heads is 1/2, so the probability of not-heads is 1/2.

Then the probability of 2 heads and a tails is (1/2)²·(1/2) = 1/8.

There are 3 choose 2 = (3·2)/(2·1) = 3 ways that the pair of heads may appear among the three tosses. Thus the probability of 2 heads in 3 tosses is ...

... 3·(1/8) = 3/8

_____

Or you can simply count the favorable outcomes among the possible outcomes:

TTT TTH THT THH HTT HTH HHT HHH . . . . 3 of 8 are favorable.

Answer:

1. [tex]\Delta ADC\sim \Delta RTS[/tex] because [tex]\angle A\cong \angle R[/tex], [tex]\angle C\cong \angle S[/tex] and [tex]\angle D\cong \angle T[/tex]

Step-by-step explanation:

We have been given two triangles [tex]\Delta ADC[/tex] and [tex]\Delta RTS[/tex]. We are asked to find the relationship between these triangles.

By angle sum property let us find measure of angle C of triangle ADC.

[tex]m\angle C+m\angle D+m\angle A=180^{o}[/tex]

[tex]m\angle C+51.2^{o}+96.5^{o}=180^{o}[/tex]

[tex]m\angle C+147.7^{o}=180^{o}[/tex]

[tex]m\angle C=180^{o}-147.7^{o}[/tex]

[tex]m\angle C=32.3^{o}[/tex]

Let us find measure of angle T of triangle RTS.

[tex]m\angle T+m\angle R+m\angle S=180^{o}[/tex]

[tex]m\angle T+96.5^{o}+32.3^{o}=180^{o}[/tex]

[tex]m\angle T+128.8^{o}=180^{o}[/tex]

[tex]m\angle T=180^{o}-128.8^{o}[/tex]

[tex]m\angle T=51.2^{o}[/tex]

We can see that [tex]m\angle C=m\angle S[/tex], [tex]m\angle A=m\angle R[/tex] and [tex]m\angle D=m\angle T[/tex]. Therefore, [tex]\Delta ADC\sim \Delta RTS[/tex] and 1st option is the correct choice.

Answer:

16

D is correct.

Step-by-step explanation:

Coefficient: The coefficient is a number front of variable.

[tex]Expression: x^2+16y[/tex]

In the given expression there are two terms

x² and 16y

First term: x²

The coefficient of x² is 1

Second term: 16y

The coefficient of 16y is 16

Hence, The coefficient of 16 of the given expression.

2x² = 28 - x

2x²+x-28=0

2x²+8x-7x-28=0

2x(x+4)-7(x+4)=0

(x+4)(2x-7)=0

(2x-7)(x+4)=0

B.) (2x - 7)(x + 4) = 0

Answer:

P = 8x+4

Step-by-step explanation:

The perimeter of a rectangle is found by using the formula

P = 2(l+w)

We know l = 3x+3 and

w = x-1

Substitute these values in

P =2(3x+3 + x-1)

Combine like terms

P = 2(4x+2)

Distribute the 2

P = 8x+4

Answer:

The probability is 1/7 or 14.29%

Step-by-step explanation:

In order to find this, divide the number of marbles that are green by the total number.

8/56 = 1/7 = 14.29%

Answer:

144%

Step-by-step explanation:

We are told that Linnea's company's revenue in 2017 is 36/25 of its revenue in 2016..

To find the Linnea's company's revenue in 2017 as a percent of its revenue in 2016, we will have to figure out 36 is what percent of 25.    

[tex]\text{Percent}=\frac{36}{25}\times 100[/tex]  

[tex]\text{Percent}=36\times 4[/tex]      

[tex]\text{Percent}=144[/tex]  

Therefore, Linnea's company's revenue in 2017 is 144% of its revenue in 2017.

Answer:

35 mi^2

Step-by-step explanation:

Area of parallelogram = base x height

7 x 5 = 35

Answer:

Area = 35 mi^2

Step-by-step explanation:

Area = b*h

The base is 7 mi

The height is 5 mi

Area = 7*5

Area = 35 mi^2

Answer:

770 high-quality songs were downloaded

Step-by-step explanation:

A web music store offerst two versions:

There were 1290 for a total download size of 4403MB.

According to the information above, we have the following system of equations:

A + B =1290

2.1A + 4.3B = 4403

Where 'A' referst to the number of Standard songs and 'B' refers to the number of High Quality songs.

Solving the sistem of equations we get that:

A + B =1290 ⇒ A = 1290 - B

2.1A + 4.3B = 4403 ⇒ 2.1(1290 - B) + 4.3B = 4403

⇒ 2709 - 2.1B + 4.3B = 4403 ⇒ 2.2B = 1694 ⇒ B=770

Now, let's find the value of 'A':

A + B =1290 ⇒ A = 1290 - 770 ⇒ A = 520.

Therefore, 770 high-quality songs were downloaded.

Answer:

I'm not sure if those are the answer choices but your answer should be 5/2

Hope this helps

Step-by-step explanation:

Answer:

5/2

Step-by-step explanation:

Answer:

7<x<17

Step-by-step explanation:

a+b>x

5+12>x

17>x

5+x>12

x>7

12+x>5

x>-7 (ignore then since it is negative and you would use the one that makes the range smaller which is the one above)

Answer:

c

Step-by-step explanation:

Answer:

I think that there is a part of your question that is missing maybe? What is the method shown?

Step-by-step explanation:

Answer:

k = 3

Step-by-step explanation:

the equation relating x and y is

y = kx ← k is the constant of proportionality

to find use the given conditions

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{36}{12}[/tex] = [tex]\frac{9}{3}[/tex] = 3

Given:

A motorist traveled 250 miles on 11 gallons of gas.

To Find:

In the same vehicle, the distance that can be traveled in 16 gallons.

Answer:

Rounding to the nearest tenth, the distance traveled on 16 gallons of gas is 363.5 miles.

Step-by-step explanation:

We first find the number of miles that can be traveled on 1 mile of gas.

We do this by using the unitary method.

Given that in 11 gallons, 250 miles can be traveled in a certain vehicle.

So in 1 gallon, 250 ÷ 11 miles can be traveled. This is roughly equal to 22.72.

Next we will calculate how much distance he can go in 16 gallons. We multiply the distance traveled in 1 gallon by 16.

That is, in  16 gallons, the number of miles that can be traveled is 22.72 x 16 = 363.52.

Rounding to the nearest tenth, the distance traveled on 16 gallons of gas is 363.5 miles.

Answer:363.6miles

Step-by-step explanation:

sinB= 3/5 is correct

tanA= 4/3 is correct

and sinA= 4/5 is correct

hope this helps ^

Answer:

g(-1) = -1

g(1) =5

Step-by-step explanation:

g(x) = x^3 + (x + 1)^2

If x=-1  substitute this into the equation

g(-1) = (-1) ^3 + (-1+1)^2

g(-1) = 1+0  =-1

If x=1  substitute this into the equation

g(1) = (1)^3 + (1+1)^2 = 1+2^2 = 1+4 =5

Hi There!

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

Function: g(x) = x³ + (x + 1)²

Substitute: -1

Substitute: g(-1) = -1³ + (-1 + 1)²

Remember to follow PEMDAS.

Parenthese's: g(-1) = -1³ + (0)²

Exponents: g(-1) = -1 + 0

Simplify: g(-1) = -1

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

Function: g(x) = x³ + (x + 1)²

Substitute: 1

Substitute: g(1) = 1³ + (1 + 1)²

Remember to follow PEMDAS.

Parenthese's: g(1) = 1³ + (2)²

Exponents: g(1) = 1 + 4

Simplify: g(1) = 5

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

Hope This Helps :)

so, if you checked the link above, you know what we'll be doing, lemme run through it without much fuss.

[tex]\bf \stackrel{\textit{firstly some grouping}}{(x^2-4x)+(y^2+4y)=0}\implies (x^2-4x+\boxed{a}^2)+(y^2+4y+\boxed{b}^2)=0 \\\\[-0.35em] ~\dotfill\\\\ 2\cdot x\cdot \boxed{a}=4x\implies \boxed{a}=\cfrac{4x}{2x}\implies \boxed{a}=2 \\\\\\ 2\cdot y\cdot \boxed{b}=4y\implies \boxed{b}=\cfrac{4y}{2y}\implies \boxed{b}=2[/tex]

now, let's recall, we're simply borrowing from our very good friend Mr Zero, 0, so if we add whatever, we also have to subtract whatever.

[tex]\bf (x^2-4x+2^2-2^2)+(y^2+4y+2^2-2^2)=0 \\\\\\ (x^2-4x+2^2)+(y^2+4y+2^2)-4-4=0 \\\\\\ (x-2)^2+(y+2)^2-8=0\implies (x-2)^2+(y+2)^2=8 \\\\[-0.35em] ~\dotfill\\\\ \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] ~\dotfill\\\\ (x-2)^2+(y+2)^2=(\sqrt{8})^2\qquad \impliedby radius=\sqrt{8}[/tex]

Answer:

161

Step-by-step explanation:

We will use the math operation addition to find last year's number of floats. We know this year was 127 and was fewer than 34. So 127+34=last year's floats.

127+34=161

Answer:

Perimeter of the square MATH = 100.

Step-by-step explanation:

Given that MATH is a square, it means all sides would be equal to each other.

Given MA = 2x - 5 and AT = x + 10.

we know all sides are equal, so MA = AT.

2x - 5 = x + 10

2x = x + 10 + 5

2x = x + 15

2x - x = 15

x = 15

So, AT = x + 10 = 15 + 10 = 25.

Now the perimeter would be (MA + AT + TH + HM) = 4*AT = 4*25 = 100.

Hence, option D is the correct answer i.e. 100.

Answer:

100

Step-by-step explanation:

Sides of a square are congruent.

2x – 5 = x + 10

x = 15

Sides = 2(15) – 5 = 25

Perimeter = 25 + 25 + 25 + 25 = 100

Answer:

t = 6 4/25 hours

Step-by-step explanation:

The formula to find out how long it takes them to do the job is

1/m  + 1/ a  = 1 /t

where m is the time for Matthew to do the job

a is the time for Arianna to do the job

and t is the time for them to do the job together

m = 14 hours

a = 11 hours

Substituting what we know

1/14 + 1/11 = 1/t

Multiplying by 154t (14*11*t) so we can clear the fractions

154t*(1/14 + 1/11) = 1/t* 154t

 11t + 14t = 154

Combine like terms

25t = 154

Divide by 25

t = 154/25

t = 6 4/25 hours