For a class picnic two teachers went to the same store to the purchase drinks. one teacher purchased 18 juice boxes and 32 bottles of water and spent $19.92. the other teacher purchased 14 juice boxes and 26 bottles of water and spent $15.76 write a system of equations to represent the costs of a juice box j and a bottle of water w.​

Answer:

it would take her 7 days

Step-by-step explanation:

Answer:

7 days

Step-by-step explanation:

90-118=(-28)

28° to go.

12°/3 days = 4° per day

28/4=7. 7 days

Answer:

first number is 2, second number is 2

Step-by-step explanation:

If the first number is 'a' and second number is 'b'. We can use simultaneous equations

9a + 4b = 26

3a + 4b = 14

therefore by taking the second equation from the first

6a = 12

a = 2 (first number)

as a = 2

(3 x 2) + 4b = 14

6 + 4b = 14

4b = 8

b = 2 (second number)

By setting up a system of equations, we find that the two mystery numbers are both 2. This conclusion is reached by first eliminating the variable representing the second number and then solving for the first number, which turns out to be 2. Subsequently, the value of the second number is also determined to be 2.

We can solve for the two mystery numbers by setting up a system of linear equations based on the information given:

9 times the first number plus 4 times the second number equals 26.

3 times the first number plus 4 times the second number equals 14.

Let's designate the first number as x and the second number as y. Then, we can express the problem using equations:

9x + 4y = 26 (1)

3x + 4y = 14 (2)

Next, we'll solve this system of equations. We can start by subtracting equation (2) from equation (1), which will remove y from the equations, as the coefficients before y are the same:

(9x + 4y) - (3x + 4y) = 26 - 14

6x = 12

After simplifying the equation, we find that:

x = 12 / 6

x = 2

Now that we have the value for x, we can substitute it back into either (1) or (2) to find y:

9(2) + 4y = 26

18 + 4y = 26

4y = 26 - 18

4y = 8

y = 8 / 4

y = 2

Therefore, the first number is 2 and the second number is also 2.

We have

[tex]a^b\cdot a^c=a^{b+c}[/tex]

[tex]a^b\div a^c=a^{b-c}[/tex]

So, in your case, we have

[tex]4^{-\frac{11}{3}}\div 4^{-\frac{2}{3}} = 4^{-\frac{11}{3}+\frac{2}{3}} = 4^{-\frac{9}{3}}=4^{-3} = \dfrac{1}{4^3} = \dfrac{1}{64}[/tex]

Answer:

Option D. 1/64

Step-by-step explanation:

We have to simplify the following expression

[tex]4^{-\frac{11}{3} }[/tex] ÷ [tex]4^{-\frac{2}{3} }[/tex]

= [tex]\frac{4^{-\frac{11}{3} } }{4^{-\frac{2}{3} } }[/tex]

= [tex][4^{-\frac{11}{3}}[/tex] × [tex]4^{\frac{2}{3}}][/tex] [since [tex]\frac{1}{A-1}[/tex]=a]

= [tex]4^{(-\frac{11}{3}+\frac{2}{3})}[/tex] [since [tex]a^{b}[/tex] × [tex]a^{c}[/tex] = [tex]a^{(b+c)}[/tex]]

= [tex]4^{-\frac{9}{3}}[/tex]

= [tex]4^{-3}[/tex]

= [tex]\frac{1}{4^{3} }[/tex]  [[tex]a^{-1}=\frac{1}{a}[/tex]]

= [tex]\frac{1}{64}[/tex]

Option D. 1/64 is the answer.

Answer:

8  15/16 inches

Step-by-step explanation:

Multiply 3  1/4 inches by 2  3/4:

13      11

---- * ----- = 146/16 inches, or 8.9375 inches, or 8  15/16 inches.

 4       4

Answer:  The required enlarged height of the photo is [tex]8\dfrac{15}{16}~\textup{inches}.[/tex]

Step-by-step explanation:  Given that a customer wants you to enlarge a photo to [tex]2\dfrac{3}{4}[/tex] its current height and the photo’s current height is [tex]3\dfrac{1}{4}[/tex] inches.

We are to find the enlarged height of the photo in inches.

The enlarged height of the photo is given by

[tex]2\dfrac{3}{4}\times \textup{current height of the photo}\\\\\\=\dfrac{11}{4}\times3\dfrac{1}{4}\\\\\\=\dfrac{11}{4}\times\dfrac{13}{4}\\\\\\=\dfrac{143}{16}\\\\=8\dfrac{15}{16}.[/tex]

Thus, the required enlarged height of the photo is [tex]8\dfrac{15}{16}~\textup{inches}.[/tex]

Answer:

Step-by-step explanation:

All you have to do here is to divide polynomial f(x) = (x + 16)/x by polynomial g(x) = 2x / (x + 4), simplify the result and label the quotient properly.  Recall that division by a fraction involves inverting the divisor fraction and then multiplying.

               (x + 16)       (x + 4)      (x + 16)(x + 4)

(f/g)(x) = ------------- * ----------- = --------------------

                    x              2x                 2x^2

Note that this quotient is true for all x except x = 0.

y=2x+20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.

Answer:

A

Step-by-step explanation:

Answer:

Area = 575m²  Perimeter = 94

Step-by-step explanation:

Trust me I'm right

Answer:

Area of the Figure: 575 m

Perimeter of the Figure: 94 m

Step-by-step explanation:

That shape can easily be divided into a right triangle and a rectangle.

•••To solve the area for the rectangle:

base x height

17 * 25 = 425 m

•••To solve the area for the right triangle:

1/2 x base x height

1/2 x 15 x 20 = 150 m

•••Perimeter of the figure:

Add all the sides.

17 + 17 + 25 + 15 + 20 = 94 m

Answer:

6mph and 4mph

Step-by-step explanation:

because 2:3 is some as 3x:x in terms of speed

Answer: The speed of her walking is 4 mph and the speed of her jogging is 6 mph.

Step-by-step explanation:

Since we have given that

Time taken by Lorena to walk the path = 30 minutes

Time taken by Loren to jogs the path = 20 minutes

Let the speed of her walking be 'x'.

Let the speed of her jogging be 'x+2'.

Since distance would remain same, so it becomes,

[tex]30x=20(x+2)\\\\30x=20x+40\\\\30x-20x=40\\\\10x=40\\\\x=\dfrac{40}{10}\\\\x=4\ mph[/tex]

Hence, the speed of her walking is 4 mph and the speed of her jogging is 6 mph.

Answer:

19 m

Step-by-step explanation:

This is Geometric progression with

[tex]\left \{ {{u_1=1,\: u_2 =2} \atop {u_n=2^{n-1}u_1} \right.[/tex]

Then the fomular of sum is

[tex]S=u_1\frac{2^n-1}{2-1} =1\times(2^n-1)=2^n-1\\To\: save\: 1 \:million\: then \; our \:sum \: will \: be\: 1000000\\Hence,\\2^n-1=1000000\\2^n=1000001\\n=log_{2}{1000001}\approx19,9\\Thus, it\:would \;be \:19 \:months \:before\: we\: saved \:1000000 \:pounds[/tex]

Answer:

[tex]x^{2}+(y+2)^{2}=9[/tex]

Step-by-step explanation:

The center of the circle is (0, -2). The dark-filled circle is the center and lies 2 units below the origin on the y-axis.

On the other hand, the radius of the circle is 3 units. If we count from the dark-filled circle, we have 3 complete squares to the left, to the right.

Now the standard equation of a circle with center (a, b) and radius r units is given by the formula;

[tex](x-a)^{2}+(y-b)^{2}=r^{2}[/tex]

Substituting the values obtained;

[tex]x^{2}+(y+2)^{2}=9[/tex]

and is our standard equation of the given circle

Answer:

86 4/7, C.

Step-by-step explanation:

14x6= 84

       +

6 x 3/7 = 2 4/7

86 4/7

Answer:

multiply 14 over 7 to get the number as one fraction. after adding three to that product, you get 101/7. Multiply that by 6/1 to get 606/7, then divide 606 by 7 to get 86 4/7 hours every 6 months.

Step-by-step explanation:

Answer:

1017.36 square inches

Step-by-step explanation:

The globe is in the shape of a sphere. As we given the diameter of the globe

d = 18 inches

We have to find the radius of globe first

[tex]Radius=r=\frac{d}{2}\\r=\frac{18}{2}\\r=9\ inches[/tex]

The formula for finding the surface area is:

[tex]Surface\ Area=4\pi r^{2}\\Putting\ the\ values\ of \pi \ and\ r\\Area=4*3.14*(9)^{2} \\=4*3.14*81\\=1017.36\ square\ inches[/tex]

Hence, the surface area is 1017.36 square inches ..

Answer:

B and D

Step-by-step explanation:

if they had letters it would be

A     B

C     D

options B and D are similar

Answer:

II and IV

Step-by-step explanation:

We are given that four figures

We have to find two similar figures.

Similar figures: Two triangle are called similar when the ratio of corresponding sides are equal and corresponding angles are equal.

In Second and fourth figure

Each angle of second figure  is equal to its  corresponding angle of fourth figure.

Ratio of corresponding sides

[tex]\frac{6}{12}=\frac{1}{2}[/tex]

[tex]\frac{2.5}{5}=\frac{1}{2}[/tex]

[tex]\frac{6.5}{13}=\frac{1}{2}[/tex]

[tex]\frac{6}{12}=\frac{2.5}{5}=\frac{6.5}{13}[/tex]

Hence, second and fourth figure are similar to each other.

Answer:

3y+4x=5

Step-by-step explanation:

step 1

Find the slope

we have

(–7, 11) and (8, –9)

m=(-9-11)/(8+7)

m=-20/15

m=-4/3

step 2

Find the equation of the line into point slope form

we have

m=-4/3

point (-7,11)

substitute

y-11=-(4/3)(x+7) ----> equation of the line into point slope form

Multiply by 3 both sides

3y-33=-4(x+7)

3y-33=-4x-28

3y+4x=33-28

3y+4x=5 -----> equation of the line into standard form

Answer:

The first and 4th option

Step-by-step explanation:

Just took it on edge

Answer:

Chicago's temperature < Phoenix's temperature

Step-by-step explanation:

Because -1°F is less than 40°F.

Answer:

a*b = 8

Step-by-step explanation:

a-b =2

Let b= 2

a-2 =2

Add 2 to each side

a-2+2 =2+2

a =4

We want to find a*b

4*2 = 8

a*b = 8

First substitute 2 in for b to get a - (2) = 2.

Now isolate a by adding 2 to both sides to get a = 4.

Since a = 4, substitute 4 in for a and 2 in for b to get 4 × 2.

Multiplying, 4 × 2 gives us a product of 8.

So the value of a × b is 8.

Answer:

[tex]\large\boxed{A=9x^2-6xy+y^2}[/tex]

Step-by-step explanation:

The formula of an area of a square:

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

s - side length

We have s = 3x - y. substitute:

[tex]A=(3x-y)^2[/tex]           use (a - b)² = a² - 2ab + b²

[tex]A=(3x)^2-(2)(3x)(y)+y^2=9x^2-6xy+y^2[/tex]

Answer:

The amount of medicine in the patient's blood after 20 minutes is 2.6906 milligrams

Step-by-step explanation:

The amount of medicine in the patient's blood after 20 minutes will given by;

f(20)

since we are informed that the amount f(t) of a certain medicine in a patient's bloodstream t minutes after being taken is given by f(t);

We simply substitute t = 20 in the function f(t);

[tex]f(20)=\frac{60(20)}{20^{2}+46 }=2.6906[/tex]

Answer:

Step-by-step explanation:

Since the formula is given, we only need to substitute 20 for t to find the answer.

60t/t sq. + 46 we substitute 20 for x:

60(20)/ 20x20 +46

1200/446 which equals

2.6905 milligrams

Answer:

[tex]\large\boxed{B.\ x=\dfrac{5+\sqrt{21}}{2},\ C.\ x=\dfrac{5-\sqrt{21}}{2}}[/tex]

Step-by-step explanation:

[tex]\text{Use the quadratic formula:}\\\\ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\================================\\\\\text{We have}:\\\\x^2+1=5x\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\x^2-5x+1=0\\\\a=1,\ b=-5,\ c=1\\\\b^2-4ac=(-5)^2-4(1)(1)=25-4=21\\\\x=\dfrac{-(-5)\pm\sqrt{21}}{2(1)}=\dfrac{5\pm\sqrt{21}}{2}[/tex]

Answer:

b and c Apex answers

[tex]4x^{2} -4x - 1 = 0[/tex]

To solve for the zeros you can use the quadratic formula:

[tex]\frac{-b plus/minus\sqrt{b^{2}-4ac } }{2a}[/tex]

a = 4

b = -4

c = -1

[tex]\frac{-(-4) plus/minus\sqrt{(-4)^{2}-4(4)(-1) } }{2(4)}[/tex]

[tex]\frac{4 plus/minus\sqrt{16+16 } }{8}[/tex]

[tex]\frac{4plus/minus\sqrt{32} }{8}[/tex]

[tex]\frac{4plus/minus4\sqrt{2 } }{8}[/tex]

[tex]\frac{1 plus/minus\sqrt{2} }{2}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

The quadratic equation 4x^2 - 4x - 1 = 0 can be solved by using the quadratic formula -b ± √b² - 4ac / 2a. After substituting the coefficients into the formula, we get 4 ± √((-4)^2 - 4 * 4 * -1) / 2 * 4. These roots are the solution to the equation.

The subject of the question is the solution of a quadratic equation which can be found using the quadratic formula. For the given equation 4x^2 - 4x - 1 = 0, the values of a, b, and c as per the general quadratic equation (ax^2 + bx + c = 0) are a = 4, b = -4 and c = -1. The quadratic formula to solve for x is -b ± √b² - 4ac / 2a.

Substituting the given values in to the formula we get the solution for x: 4 ± √((-4)^2 - 4 * 4 * -1) / 2 * 4, which can further be solved to get the two roots of the quadratic equation.

https://brainly.com/question/30398551

#SPJ3

Answer:

total resistance is 54.54 ohms

Step-by-step explanation:

In parallel circuits, current can take various paths so the resistance are not added simply like that in series circuit, instead the reciprocal of total resistance in parallel circuit is calculated by adding the reciprocals of all the resistors connected parallel in circuit.

Given:

Resistor r1= 100

resistor r2 = 200

resistor r3= 300

The three resistors are connected in parallel  so the total resistance will be calculated by:

1/R= 1/r1 +1/r2 +1/r3

Putting the values of r1, r2, r3 in above we get

1/R= 1/100 + 1/200 +1/300

  = 0.01 + 0.005 + 0.0033

  = 0.0183

Taking reciprocal of both sides:

R=54.54

Hence total resistance is 54.54 ohms!

Final answer:

The total resistance of three resistors rated at 100 Ω, 200 Ω, and 300 Ω connected in parallel is approximately 54.64 Ω. This is calculated using the reciprocal formula for parallel resistances.

Explanation:

When you have a circuit with resistors connected in parallel, the total (or equivalent) resistance of the circuit is found by using the reciprocal formula:

Rtotal = 1/(1/R1 + 1/R2 + 1/R3)

For the given resistors of 100 Ω, 200 Ω, and 300 Ω in parallel, you calculate the total resistance like this:

Rtotal = 1/(1/100 Ω + 1/200 Ω + 1/300 Ω)
= 1/(0.01 Ω-1 + 0.005 Ω-1 + 0.0033 Ω-1)
= 1/(0.0183 Ω-1)
= 54.64 Ω

The total resistance of the circuit would therefore be approximately 54.64 Ω.

Answer:

a.

                         R-------8/38--------RR

R------9/39--------B-------13/38-------RB

                          G------17/38--------RG

                          R-------9/38--------BR

B--------13/39------B-------12/38-------BB

                           G-------17/38-------BG

                             R-----9/38--------GR

G---------17/39-------B------13/38-------GB

                              G------16/38-------GG

b).

RB=9/39 × 13/38=3/38

BR= 13/39 × 9/38 =3/38

BG= 13/39 × 17/38=17/114

GB= 17/39 × 13/38=17/114

=3/38 +3/38+17/114+ 17/114 =26/57

Answer:

sin(150°) = 1/2

Step-by-step explanation:

* Lets study how we can solve this problem

- At first the measure of the angle is 150°

- Ask your self in which quadrant can you find this measure

* To know the answer lets revise the four quadrants

# First quadrant the measure of all angles is between 0° and 90°

  the measure of any angle is α

∴ All the angles are acute

∴ All the trigonometry functions of α are positive

# Second quadrant the measure of all angles is between 90° and 180°

  the measure of any angle is 180° - α

∴ All the angles are obtuse

∴ The value of sin(180° - α) only is positive ⇒ sin(180° - α) = sinα

# Third quadrant the measure of all angles is between 180° and 270°

  the measure of any angle is 180° + α

∴ All the angles are reflex

∴ The value of tan(180° + α) only is positive ⇒ tan(180° + α) = tanα

# Fourth quadrant the measure of all angles is between 270° and 360°

  the measure of any angle is 360° - α

∴ All the angles are reflex

∴ The value of cos(360° - α) only is positive ⇒ cos(360° - α) = cosα

* Now lets check the angle of measure 150

- It is an obtuse angle

∴ It is in the second quadrant

∴ the value of sin(150) is positive

∴ sin(150°) = sinα

∵ 180 - α = 150 ⇒ isolate α

∵ α = 180° - 150° = 30°

∴ sin(150°) = sin(30°)

∵ sin(30°) = 1/2

∴ sin(150°) = 1/2

ANSWER

[tex]\sin(150 \degree) = \frac{1}{2} [/tex]

EXPLANATION

The principal angle for 150° is 30°.

The terminal side of 150° is in the second quadrant.

In this quadrant the sine ratio is positive.

This implies that;

[tex] \sin(150 \degree)= \sin(30 \degree) [/tex]

On the unit circle,

[tex] \sin(30 \degree) = \frac{ 1 }{2} [/tex]

Therefore

[tex]\sin(150 \degree)= \sin(30 \degree) = \frac{1 }{2} [/tex]

Answer:

$5,000

Step-by-step explanation:

Create a proportion:

11/100 = 550/x

100(550)/11

5,000= x

You have to form a proportion: [tex]\frac{part}{whole}[/tex]

Meals are only 11% for the vacation budget. This means that meals would go over 100% like this:

[tex]\frac{11}{100}[/tex]

You also know that you have $550 for meal (your part) but you want to know what your total vacation budget is(your whole)[tex]\frac{x}{550}[/tex] (x), so you would set it up like this

Now you sent them equal to solve for x:

[tex]\frac{11}{100} = [tex]\frac{550}{x}[/tex]

cross multiply:

11x = 55,000

x = 5,000

This means that your total vacation budget is $5,000

Hope this helped!

Answer:

10r⁵ + 2r⁴ + 5r²

Step-by-step explanation:

A = 90r⁶ + 28r⁵ + 2r⁴ + 45r³ + 5r²

Factor our r²:

A = r² (90r⁴ + 28r³ + 2r² + 45r + 5)

Factor 2r² from the first three terms and 5 from the last two:

A = r² (2r² (45r² + 14r + 1) + 5 (9r + 1))

Factor the trinomial:

A = r² (2r² (5r + 1)(9r + 1) + 5 (9r + 1))

Factor out 9r+1:

A = r² (2r² (5r + 1) + 5) (9r + 1)

Distribute the 2r²:

A = r² (10r³ + 2r² + 5) (9r + 1)

Distribute the r²:

A = (10r⁵ + 2r⁴ + 5r²) (9r + 1)

The area is width times length, and the width is 9r + 1.

WL = (10r⁵ + 2r⁴ + 5r²) (9r + 1)

(9r + 1) L = (10r⁵ + 2r⁴ + 5r²) (9r + 1)

L = 10r⁵ + 2r⁴ + 5r²

The length of the pool is 10r⁵ + 2r⁴ + 5r².

Answer:

1,2,20

take away 14 from 8 = 6

add 6 to 14 = 20

Hope I helped!

NOTE: MARK BRAINLIEST!!!! plz....

Answer:

8,4  

14,7

6,3

Step-by-step explanation:

Answer:

It will reach 0 degrees celcius at 5:20AM i believ

Step-by-step explanation:

If you divide 8 by 1.5 you bet 5 and 1/3

5 1/3 turns to 5:20 AM

ANSWER

[tex](g \circ \: f)(0) = - 216[/tex]

EXPLANATION

The functions are:

[tex]f(x) = 2x - 6[/tex]

[tex]g(x) = {x}^{3} [/tex]

[tex](g \circ \: f)(x) =g(f(x))[/tex]

[tex](g \circ \: f)(x) =g(2x - 6)[/tex]

We substitute f(x) into g(x) to obtain:

[tex](g \circ \: f)(x) =(2x - 6)^{3} [/tex]

We now substitute x=0 to obtain;

[tex](g \circ \: f)(0) =(2(0) - 6)^{3} [/tex]

[tex](g \circ \: f)(0) =(- 6)^{3} [/tex]

This simplifies to:

[tex](g \circ \: f)(0) = - 216[/tex]

The answer is:

The population in 2015 will be 1,412,415.

Since from the statement we know that the population is increasing, we know that we are working with an exponential growth problem.

We can calculate the exponential growth using the following equation:

[tex]Population(t)=StartPopulation(1+growthpercent)^{t}[/tex]

Where,

P, is the population after t (years, months, days or hours)

Start Population, is the starting population.

Growth percent, is the percent of growth

t, is the time elapsed (years, months, days or hours)

So, we are given the following information:

[tex]StartPopulation=478434\\\\GrowthPercent=7(percent)=\frac{7(percent)}{100}=0.07\\\\TimeElapsed=2015-1999=16years[/tex]

Now, substituting and calculating, we have:

[tex]Population(t)=StartPopulation(1+growthpercent)^{t}[/tex]

[tex]Population(t)=478434(1+0.07)^{16}=141241.5=1412415[/tex]

Hence, the population in 2015 will be 1,412,415.

Have a nice day!

Answer:

Let x be the number of questions he gets right. Let y be the number of questions he gets wrong.

Then:

x + y = 25

4x - 1y = 65

Adding these two equations gives:

5x = 90

y = 25 - 18 = 7 wrong answers

* Hopefully this helps:) Mark me the brainliest:)!!!

~ 234483279c20~

The number of right questions is 18

Let the number of right questions be x, and the wrong questions be y

So, we have the following equations

x + y = 25

4x - y = 65

Add both equations

5x =90

Divide both sides by 5

x = 18

Hence, the number of right questions is 18

Read more about system of linear equations at:

https://brainly.com/question/13729904