Clara is taking a medicine for a common cold. The table below shows the amount of medicine f(t), in mg, that was present in Clara's body after time t:


t (hours) 1 2 3 4 5
f(t) (mg) 236.5 223.73 211.65 200.22 189.41


Heidi was administered 300 mg of the same medicine. The amount of medicine in her body f(t) after time t is shown by the equation below:

f(t) = 300(0.946)t

Which statement best describes the rate at which Clara's and Heidi's bodies eliminated the medicine?

Clara's body eliminated the antibiotic faster than Heidi's body.

Clara's body eliminated the antibiotic at the same rate as Heidi's body.

Clara's body eliminated the antibiotic at half of the rate at which Heidi's body eliminated the antibiotic.

Clara's body eliminated the antibiotic at one-fourth of the rate at which Heidi's body eliminated the antibiotic.

Answer:

The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution is correct.

Step-by-step explanation:

1) The system of linear equations 6x - 5y = 8 and 12x - 10y = 16 has no solution.

Solve these linear equations simultaneously

Step 1 : Find y in terms of x from any one equation

6x - 5y = 8

y = 8 - 6x

        -5

Step 2 : Substitute y in terms of x from step 1 in the second equation.

16x - 6y = 22

16x - 6 (8 - 6x) = 22

              -5

80x - 48 + 36x = 22 x -5

94x = 43

x = 0.457

This statement is incorrect as it does have a solution.

2) The system of linear equations 7x + 2y = 6 and 14x + 4y = 16 has an infinite number of solutions.

Solve these linear equations simultaneously

Step 1 : Find y in terms of x from any one equation

7x + 2y = 6

y = 6 - 7x

        2

Step 2 : Substitute y in terms of x from step 1 in the second equation.

14x + 4y = 16

14x + 4(6 - 7x) = 16

              2

14x + 12 - 14x = 16

0 ≠ 4

This statement is not true as there are no solutions.

3) The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution.

Solve these linear equations simultaneously

Step 1 : Find x in terms of y from any one equation

8x - 3y = 10

x = 10 + 3y

        8

Step 2 : Substitute x in terms of y from step 1 in the second equation.

16x - 6y = 22

16(10 + 3y) - 6y = 22

       8

20 + 6y - 6y = 2

0 ≠ -18

This statement is true because there are no solutions

4) The system of linear equations 9x + 6y = 14 and 18x + 12y = 26 has an infinite number of solutions.

Solve these linear equations simultaneously

Step 1 : Find x in terms of y from any one equation

9x + 6y = 14

x = 14 - 6y

        9

Step 2 : Substitute x in terms of y from step 1 in the second equation.

18x + 12y = 26

18 (14 - 6y) + 12y = 26

        9

8 - 12y + 12y = 26

0 ≠ 18

This statement is incorrect because there are no solutions. It does not have infinite number of solutions.

!!

Answer:

Step-by-step explanation:

The true statement is the third one, because that system of equations has no solutions. This is because those lines are parallel, see image attached.

We can demonstrate this by solving the system:

[tex]\left \{ {{8x-3y=10} \atop {16x-6y=22}} \right.[/tex]

If we multiply the first equation by -2, we would have

[tex]\left \{ {{-16x+6y=-20} \atop {16x-6y=22}} \right\\0x+0y=2\\0=2[/tex]

When this happens, means that the system has no solution, that is, the lines that represents those linear equations, are parallel.

Therefore, the right answer is the third option.

Answer:

16C14 = 120

Step-by-step explanation:

we need to find the value of the combination 16C14.

The formula used is [tex]nCr= \frac{n!}{r!(n-r)!}[/tex]

in the given question

n = 16

and r = 14

Putting values and solving:

[tex]16C14= \frac{16!}{14!(16-14)!}\\16C14= \frac{16!}{14!2!}\\16!\,\,can\,\,be\,\,written\,\,as\,\, 16*15*14!\\16C14= \frac{16*15*14!}{14!2!}\\16C14= \frac{16*15}{2*1}\\16C14= \frac{240}{2}\\16C14 = 120[/tex]

So, 16C14 = 120

Answer:

120

Step-by-step explanation:

Using the definition of n[tex]C_{r}[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex]

where n ! = n(n - 1)(n - 2)...... × 3 × 2 × 1

16[tex]C_{14}[/tex]

= [tex]\frac{16!}{14!2!}[/tex]

= [tex]\frac{16(15)14!}{14!(2)(1)}[/tex] ← cancel 14 !

= [tex]\frac{16(15)}{2}[/tex] = [tex]\frac{240}{2}[/tex] = 120

To solve this plug in 9 for b and solve for a like so...

3a + 9 = 54

9 must be combined with 54. To do this you must subtract 9 from both sides. This will cancel out 9 from the left and bring it over to the right

3a + (9 - 9) = 54 - 9

3a + 0 = 45

3a = 45

Now we must isolate the a. To do this you have to divide 3 to both sides. This will make 3 on the left side 1 and bring 3 over to the other side

3a/3 = 45/3

1a = 15

a = 15

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

(A) 10

Step-by-step explanation:

Let age of Marco's be "x" years

then according to question

Yolanda age will be "2x - 5"

Also in the question it is given that age Yolanda is 15 years.

then, 2x - 5 = 15

Adding 5 both sides of the equation, we will get

        2x = 20

Dividing both sides of the equality by 2, we get

         x = 10

therefore, Age of Marcus will be 10years

Option (A) is the correct option.

Answer:

[tex]x=\frac{7}{5}[/tex]

Step-by-step explanation:

The question states product so we know that we're multiplying.

A number and 5, and since the unknown variable is now [tex]x[/tex] we have [tex]5x[/tex] so far.

Then we need to make it so that it is 2 more.

[tex]5x+2[/tex]

Equals 9.

[tex]5x+2=9[/tex]

Solve for the unknown number.

[tex]5x=7[/tex]

[tex]x=\frac{7}{5}[/tex]

Transforming the problem into the equation 5x + 2 = 9, where 'x' is the unknown number, we solve for 'x' by subtracting 2 from both sides and then dividing by 5, yielding 'x' = 7/5, or 1.4.

The mathematics problem described can be solved using simple algebra. The problem is stated as: two more than the product of a number and 5 equals 9. If we use the variable 'x' to represent the unknown number, then we can write the algebraic equation to represent this problem as 5x + 2 = 9. The next step would be to solve this equation to find the value of 'x'. In order to isolate 'x', you would first subtract 2 from both sides of the equation, yielding 5x = 7. To find 'x', you would then divide both sides of the equation by 5. The solution to the equation, and therefore the value of the unknown number 'x', would thus be 7/5 or 1.4.

https://brainly.com/question/32436021

#SPJ2

To find the midpoint, add the two X values and divide by 2 and add the two Y values and divide by 2.

-1 + 5 = 4/2 = 2

5 +5 = 10 /2 = 5

Midpoint = (2,5)

Answer:

(2,5)

Step-by-step explanation:

The points are on the same y, which is 5, so we only have to find the distance between the x values.

Distance formula = [tex]M = \frac{x_{1} + x_{2} }{2}[/tex]

[tex]M = \frac{-1 + 5}{2}[/tex]

Mid = \frac{4}{2} [tex]

Mid = 2

Answer:

x = -1

Step-by-step explanation:

x + 2.5 = 1.5

- 2.5   -2.5

x = -1

Answer:

45-2(h-1)<32

Step-by-step explanation:

This is a problem related to arithmetic progression. The formula we use is that of for nth term

[tex]a_{n}=a+(n-1)d[/tex]

Here

[tex]a=45 , d=-2 ,n=h , a_{n}=a_{h}[/tex]

[tex]a_{h}=45+(h-1)(-2)\\a_{h}=45-2(h-1)\\[/tex]

Now we have to analyse a situation when our temperature comes below 32

or

[tex]a_{h}<32[tex]

[tex]45-2(h-1)<32\\45-2h+2<32\\45-2h<32-2\\45-2h<30\\[/tex]

This is our inequality

Solving this

[tex]45-2h<30\\-2h<30-45\\-2h<-15\\h>7.5\\[/tex]

Hence in 8th hours the temperature will be below 32F

Answer:

4 weeks and 2 days

Step-by-step explanation:

There are 7 days in one week.

To convert 30 days into weeks and days, divide 30 by 7.

The biggest number you can divide it by is 4 [without going over 30]

7 x 4 = 28.

30 - 28 = 2.

So 30 days = 4 weeks and 2 days.

I hope this helps! :)

Answer:

4 weeks and 2 days

Step-by-step explanation:

Answer:

f(x) = x

Step-by-step explanation:

note : slope is positive 1, so the x term must be positive

also note the graph intersects the curve at y = 0, which means that they y-intercept is zero .

if we substitute this into the general equation for a line

y = mx + b, where m = +1 and b = 0,

we get y = x

or f(x) = x (in function form)

Answer:

x = - 14, x = - 4

Step-by-step explanation:

Given

(x + 9)² = 25 ( take the square root of both sides )

x + 9 = ± [tex]\sqrt{25}[/tex] = ± 5

Subtract 9 from both sides

x = - 9 ± 5, that is

x = - 9 - 5 = - 14 or x = - 9 + 5 = - 4

Answer:

B) 2x² = 3x

Step-by-step explanation:

Answer:

Option 2 - [tex]x^2=3x[/tex]                

Step-by-step explanation:

Given : Susan wants to make 2 square flags to sell at a crafts fair. The fabric she wants to buy is 3 meters wide. she doesn't want any fabric left over.

To find : What's the least amount of fabric she should buy?

Solution :

If  she doesn't want any fabric left over.

The fabric purchased should have same area of the flags.

So, let x be the length of 1 side of the flag.

Area of the flag is

[tex]A=s^2[/tex]

[tex]A=x^2[/tex]

Area of 2 square flags is [tex]A=2x^2[/tex]

Now, Area of fabric is

[tex]A=l\times b[/tex]

[tex]A=x\times 3[/tex]

[tex]A=3x[/tex]

According to question,

Area is same so,

[tex]x^2=3x[/tex]

Therefore, Option 2 is correct.

Answer:

The length is 39.6 feet.

Step-by-step explanation:

Since the area is lw, we make this an equation. The width is already known, it's 26.2. So make a single variable equation: 26.2w=1037.52

dividing both sides by 26.2 gives you the answer of 39.6.

Hope this helps!

We know that - Area of a Rectangle is given by : Length × Width

Here : Length = u  and  Width = 26.2 ft

Given : Area of the Rectangle = 1037.52 ft²

[tex]:\implies[/tex]  u × 26.2 = 1037.52

[tex]\mathsf{\implies u = \dfrac{1037.52}{26.2}}[/tex]

[tex]:\implies[/tex]  u = 39.6 ft

bearing in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf y+2=\cfrac{1}{2}(x-4)\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( y+2 \right)=2\left( \cfrac{1}{2}(x-4) \right)}\implies 2y+4=2(x-4) \\\\\\ 2y+4=2x-8\implies 2y=4x-12\implies -4x+2y=-12\implies 4x-2y=12[/tex]

Answer:

36π cubic inches

Step-by-step explanation:

Volume of sphere:

V = 4/3 πr^3

Given: r = 3 in.

Plug in

V = 4/3 π (3^3)

V = 4/3 π (27)

V = 36 π

Answer

36π cubic inches

Answer with explanation:

 Radius of the Sphere (r)= 3 inches

Volume of the sphere

                  [tex]=\frac{4*\pi *r^3}{3}\\\\\rightarrow \frac{4*\pi *3^3}{3}\\\\\rightarrow 4*\pi *3^2\\\\=36\pi \text{Cubic inches}[/tex]  

→→→Option B: 36 π Cubic inches          

Answer: 348 kiwis.

Step-by-step explanation:

You need to analize the information provided in the exercise.

First: You know that you can put 6 trays in crates.

Second: Each one of these trays holds 58 kiwis.

Therefore, in order to calculate the number of kiwis that the crates contain when it is full, you need to multiply the total number of trays you can put in crates by the number of kiwis each tray can hold.

Then:

[tex]number\ of\ kiwis=(6)(58\ kiwis)\\\\number\ of\ kiwis=348\ kiwis[/tex]

Answer:

[tex]\boxed{2.7 \times 10^{3}}[/tex]

Step-by-step explanation:

[tex]\dfrac{4 \times 10^{9}}{1.5 \times 10^{6}}[/tex]

1. Divide the coefficients and the exponentials separately

[tex]\dfrac{4 \times 10^{9}}{1.5 \times 10^{6}} = \dfrac{4}{1.5} \times \dfrac{10^{9}}{10^{6}}[/tex]

2. Divide the coefficients

[tex]\dfrac{4}{1.5} \approx 2.7[/tex]

3. Divide the exponential terms

Subtract the exponent in the denominator from the exponent in the numerator.

[tex]\dfrac{10^{9}}{10^{6}} = 10^{(9 - 6)} = 10 ^{3}[/tex]

4. Rejoin the new coefficient and the new exponential

[tex]\dfrac{4 \times 10^{9}}{1.5 \times 10^{6}} \approx \boxed{\mathbf{2.7 \times 10^{3}}}[/tex]

Answer:

2.7 x 10(3)

Step-by-step explanation:

Answer:

It increases

Step-by-step explanation:

if b increases and the only other part of the equation is a constant it should increase as well. for example (the first value is b and the second is b-1) : (1,0) (2,1) (3,2) (4,3) (5,4)...

Answer:

The value increases

Step-by-step explanation:

Thinking process:

Let the expression be: b - 1

Let's say the value of b was 0, then the function will be: 0 - 1 = -1

Let the value of b be increased to 1, the expression will be 1 - 1 = 0

Let the value of b be increased to 2, the expression will be 2 - 1 = 1

Let the value of b be increased to 3, the expression will be 3 - 1 = 2

From the simulation, as the value of b increases, the net value becomes large.

Answer:  y < 1

Step-by-step explanation:

[tex]\begin{array}{c|c||l}\underline{x; x<-3}&\underline{y=2x+2}&\\-5&2(-5)+2=-8&\\-4&2(-4)+2=-6&\\-3&2(-3)+2=-4&\text{approaching but not including -4}\\&&&\underline{x; x=-3}&\underline{\qquad y=x\qquad}&\\-3&-3&\\&&&\\\underline{x; x>-3}&\underline{y=-x-2}&\\-3&-(-3)-2=1&\text{approaching but not including 1}\\-2&-(-2)-2=0&\\-1&-(-1)-2=-1&\end{array}[/tex]

The first function has the range of y < -4

The second function has the range of y = -3

The third function has the range of y < 1

The largest y-value is 1 and the smallest y-value is -∞, therefore the range (y-values) are from -∞ to 1 → y < 1

Answer:

y=-6

y=-4

y=-3

y=0

Step-by-step explanation:

Answer:

$16.75

Step-by-step explanation:

$25×.33=$8.25

$25-$8.25=$16.75

Answer:

30

Step-by-step explanation:

20% = 20/100= 1/5

It is 1/5 of the number 150

Taking the problem what is 20% of 150

Is means equals and of means multiply

what is 20% of 150

W = 20% * 150

Change 20% to a decimal

W = .20 * 150

W = 30

Answer:

20% of 150 is 30

Step by Step Solution:

To find percentage of any number, we must change the percent to a decimal.

Step 1: Move the decimal place in 20% to the left by two place so that it ends up being .20

Step 2: Now that 20% is now .20, We simply 150 by .20

Conclusion: 20% of 150 is 30

The smallest possible value for the sum of the squares of two numbers differing by 1 is 0.5. This is obtained by setting one number as x and the other as x + 1, and then minimizing the function f(x) = x² + (x + 1)².

The difference of two numbers is 1 implies that if we set one number as x, then the other would be x + 1. To find the smallest possible value for the sum of their squares, you need to minimize the function f(x) = x² + (x + 1)².

Completing the square, this simplifies to 2(x² + 1)². Setting the derivative of this expression, 4x(x² + 1), equal to zero and solving for x, we obtain x = 0 or x = -1. Testing these values within the function f(x), we find that the minimum value is when x = -0.5 and x + 1 = 0.5 and the sum of their squares equals 0.5.

Although one can handle an equation containing an unknown square which produces two solutions, in this problem, the meaningful solution is that the smallest possible value for the sum of their squares is 0.5.

https://brainly.com/question/28284783

#SPJ2

Answer:

300 teenagers

Step-by-step explanation:

Let

x -----> the number of children

y ----> the number of teenagers

z ----> the number of adults

we know that

x+y+z=1,200 ----> equation A

4x+5y+6z=5,300 ---> equation B

y/x=3/8

y=(3/8)x ----> equation C

Substitute equation C in equation A and equation B and solve for x,z

x+y+z=1,200 ----> x+(3/8)x+z=1,200 ---> (11/8)x+z=1,200 -----> equation D

4x+5y+6z=5,300 --> 4x+5(3/8)x+6z=5,300 --> (47/8)x+6z=5,300 --> equation E

Solve the system of equations D and equation E by graphing

(11/8)x+z=1,200 -----> equation D

(47/8)x+6z=5,300 --> equation E

The solution is the intersection point both graphs

The intersection point is (800,100)

see the attached figure

therefore

x=800 children

z=100 adults

Find the value of y

y=(3/8)x  ----> y=(3/8)800=300 teenagers

Answer:

x= 6

Step-by-step explanation:

You need to set up a proportion

12/8 = 9/x

Then you do Cross Product Property

8*9=72

12*x=12x

12x=72

divide 72 by 12

72/12=6

x=6

Answer:

A

Step-by-step explanation:

The ratios of corresponding sides are equal, that is

[tex]\frac{XZ}{DF}[/tex] = [tex]\frac{XY}{DE}[/tex], that is

[tex]\frac{12}{8}[/tex] = [tex]\frac{9}{x}[/tex] ( cross- multiply )

12x = 72 ( divide both sides by 12 )

x = 6

x = DE = 6 → A

Answer:

20 minutes

Step-by-step explanation:

Both will meet again at start point after LCM(60,80) seconds.

That is 240 seconds.

in time slower car completes one lap, faster one covers 1 +20/80 lap, that is 1.25 laps. After 20 laps faster by slower car car will be 5 laps ahead, time =20*60 = 1200s = 20 minutes

Answer:

f(4) =123

Step-by-step explanation:

first your going to put in 4 for every w

then, think of PEMDAS.

after you solve your parenthesis, then exponents Multiply/devide Then, add/subtract.

2(4)^3 -5

2* 64 -5

128 - 5

123 = f(4)