Jennifer's bill for 6 cans of grape juice and 4 cans of apple juice was $13.10. When she got home she found out that she should have bought 4 cans of grape juice and 6 cans of apple juice. Although she mixed up the order, she did save 60 cents. What is the cost per can of apple and grape juice
Solve the system using substitution and elimination.
Convert your equations to slope intercept form and identify the variables for your x and y axes. Then graph.
SHOW ALL WORK

Answer:

b

Step-by-step explanation:

The set of equations that best represent the given information is B. a + b = 12, a = b + 8. This represents both conditions: the sum of the two numbers is 12 and a is 8 more than b.

The best representation of the given information is provided by option B. a + b = 12, a = b + 8. This is because it accurately portrays both conditions mentioned in the question. The first part of the equation, a + b = 12, represents the information that the sum of the two numbers a and b is 12. The second part of the equation, a = b + 8, represents the information that the first number, a, is 8 more than the second number, b.

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Answer:

[tex]y=8\cdot \left(\dfrac{1}{2}\right)^x.[/tex]

Step-by-step explanation:

If the graph of exponential function passes through the points (0,8) and (6,0.125), then the coordinates of these points sutisfy the equation [tex]y=a\cdot b^x:\\[/tex]

[tex]8=a\cdot b^0\Rightarrow a=8,\\ \\0.125=8\cdot b^6\Rightarrow \dfrac{1}{8}=8\cdot b^6,\\ \\b^6=\dfrac{1}{64},\\ \\b^6=\dfrac{1}{2^6}\Rightarrow b=\dfrac{1}{2}.[/tex]

Thus, the equation of exponential function is

[tex]y=8\cdot \left(\dfrac{1}{2}\right)^x.[/tex]

2 inches

The volume of a rectangular prism is length * width * height.

Substitute in the values to get 8 * 5 * height = 80.

Now, simplify to get 40 * height = 80.

Divide both sides of the equation by 40 to get height = 2.

This means the height of the rectangular prism is 2 inches.

A rectangular prism is a 3-dimensional shape; height, width, length. These three variables, when multiplied, will produce a volume for a rectangular prism. We are given everything we need but the height.

Given:

Volume, V = 80 in3

Length, L = 8in

Width, W = 5in.

Height, H = H in

8 inches * 5 inches * H inches = 80 inches3

40 inches2 * H inches = 80 inches 3

(divide each side by 40 inches2)

H inches = 2 inches.

The rectangular prism is 2 inches tall.

Answer:

(B) 3.6

Step-by-step explanation:

Coordinate of A = (-3, 9)

Coordinate of B = (-1, 6)

[tex]\text {Distance = }\sqrt{(- 3 - (-1) )^2 + (9 - 6)^2}[/tex]

[tex]\text {Distance = }\sqrt{(- 2 )^2 + (3)^2}[/tex]

[tex]\text {Distance = }\sqrt{13}[/tex]

[tex]\text {Distance = }3.6[/tex]

Answer:

B

Step-by-step explanation:

Calculate the distance using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = A(- 3,9) and (x₂, y₂ ) = B(- 1, 6)

d = [tex]\sqrt{-1+3)^2+(6-9)^2}[/tex]

  = [tex]\sqrt{2^2+(-3)^2}[/tex]

  = [tex]\sqrt{4+9}[/tex]

= [tex]\sqrt{13}[/tex] ≈ 3.6 → B

Answer:

0.65454545454 or -30/46 or 65.454545454%

Hope This Helps!   Have A Nice Day!!

Answer:

-36/55

Step-by-step explanation:

Answer:

6=1/2z

6÷1/2=1/2÷1/2z

6÷1/2=z

6×2/1 = z

z=12

The most efficient way to solve this problem is isolating the y in the first equation because:

6x + 3y = 27

3y = 27 - 6x

y = 9 - 2x

Since all the numbers have a common factor of 3, it can be easily simplified/reduce.

If you used any other variable, you would have gotten a fraction.

Now that you found y, you can substitute it into the other equation to solve for x.  

ANYWAYS, your answer is A

Answer:

A

Step-by-step explanation:

Jon should solve for y in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.

5•(9/15)+7= 9/3 +21/3= 30/3=10

it can be 2, 3, 4, 5, 6, or 7.

Answer:

[tex]\large\boxed{\dfrac{10}{5!\times2!}=\dfrac{1}{24}}[/tex]

Step-by-step explanation:

[tex]n!=1\cdot2\cdot3\cdot...\cdot n\\\\5!=1\cdot2\cdot3\cdot4\cdot5=120\\2!=1\cdot2=2\\\\\dfrac{10}{5!\times2!}=\dfrac{10}{120\cdot2}=\dfrac{1}{24}[/tex]

For this case we must find the value of "x" of the following equation:

[tex]x ^ 2-9 = 0[/tex]

So:

We add 9 to both sides of the equation:

[tex]x ^ 2-9 + 9 = 9\\x ^ 2 = 9[/tex]

We apply square root on both sides of the equation to eliminate the exponent on the left side:

[tex]x = \pm \sqrt {9}[/tex]

Thus, the solutions are:

[tex]x_ {1} = + 3\\x_ {2} = - 3[/tex]

ANswer:

[tex]x_ {1} = + 3\\x_ {2} = - 3[/tex]

Opcion C

ANSWER

C. $ 7.00

EXPLANATION

It was given that four students had the following amounts of money in their pockets: $3.14, $.67, $2.45, and $1.14.

To find the amount of money they have in total, we add all their monies together to get:

$3.14+$0.67+$2.45+$1.14

This will give us a total of $7.00

Answer:

7.40

Step-by-step explanation:

to get the total money for the four student you have to do addition.

3.14

2.45

1.14

+0.65 to get $7.40

Answer:

1. (-2,0)

2. (0,2)

I'm confirming the answer above. These are also the answers on Edge-nuity. I use Edge-nuity

Step-by-step explanation:

A local maximum occurs over the interval  (-2,0)  

A local minimum occurs over the interval  (0,2)

We may calculate the maximum of a continuous and twice differentiable function f(x) by first differentiating it with respect to x and then equating it to 0.

A local maximum occurs over the interval (-2,0)  

A local minimum occurs over the interval  (0,2)

Hence, local maximum and local minimum occurs at  (-2,0)  and (0,2).

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Answer:

The measure of  angle x is 90°

Step-by-step explanation:

Given the figure in which

∠1=88°, ∠6=89°

we have to find the value of x.

∠5=∠6=89°   (∵ Vertically opposite angles)

∠1+∠4=∠6  ( ∵ By exterior angle property)

88°+∠4=89°

∠4=89°-88°=1°

As AC=CB (both are radii of same circle)

∴ ∠4=∠3=1°

Now, by exterior angle property

x=∠5+∠3=89°+1°=90°

Hence, the measure of  angle x is 90°

Applying the angle of intersecting chords theorem, the value of x in the diagram showing the circle is: C. 90.

According to the angle of intersecting chords theorem, the measure of the angle formed at the point of intersection of two chords inside a circle equals half the sum of the intercepted arcs.

89 = 1/2(88 + x) [based on the angle of intersecting chords theorem]

2(89) = 88 + x

178 = 88 + x

178 - 88 = x

x = 90° (Option C).

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I believe that the answer is A 137-186,

that is the answer if you use  the Karvonen formula

Karvonen formula : target training HR = resting HR + (0.6 [maximum HR -resting HR]).

1. Resting Heart Rate (RHR) = your pulse at rest

2. Maximum Heart Rate (MHR) = 220- your age

3. Heart Rate Reserve (HRR)= Maximum Heart Rate - Resting Heart Rate  

sorry idk why my answer was deleted

Answer: That would be A mate 137-186

Step-by-step explanation:

Answer:

option d

13 , 173 , 29933

Step-by-step explanation:

Given in the question a function, f(x) = x² + 4

initial value x0 = -3

First iteration

f(x0) = f(-3) = (-3)² + 4 = 13

x1 = 13

Second iteration

f(x1) = f(13) = (13)² + 4 = 173

x2 = 173

Third iteration

f(x2) = f(173) = (173)² + 4 = 29933

x3 = 29933

Answer:

y = -1-x

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]-\dfrac{1}{2}(6x-5)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=\left(-\dfrac{1}{2}\right)(6x)+\left(-\dfrac{1}{2}\right)(-5)=-3x+2.5[/tex]

Final answer:

The expression equivalent to -1/2 (6x-5) is -3x + 2.5. The distributive property is used to multiply -1/2 with each term inside the parentheses.

Explanation:

The expression equivalent to -1/2 (6x-5) can be found by applying the distributive property of multiplication over addition and subtraction. This property allows us to multiply each term inside the parentheses by -1/2 to achieve the equivalent expression. Therefore, we proceed as follows:

Multiply 6x by -1/2 to get -3x.

Multiply -5 by -1/2 to get 5/2 or 2.5.

Putting it all together, the equivalent expression is -3x + 2.5. When simplifying expressions involving negative exponents or distributing negative factors, it's essential to carefully apply the multiplication to each term separately to avoid errors.

Final answer:

The initial velocity at which she threw the cap is 20 m/s.

Explanation:

Since the cap comes back to her hand at the same height, the initial vertical velocity of the cap is 0 m/s. The acceleration due to gravity is -10 m/s². Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can solve for the initial velocity. In this case, v = 0 m/s, a = -10 m/s², and t = 2.0 s. Plugging in these values, we get:

0 = u + (-10)(2.0)

0 = u - 20

u = 20 m/s

So the initial velocity at which she threw the cap is 20 m/s.

Answer:

150

Step-by-step explanation:

Answer:

[tex]\large\boxed{a.\ 7200\pi\ mm^2}[/tex]

Step-by-step explanation:

The formula of a surface area of a cylinder:

[tex]S.A.=2\pi r(r+H)[/tex]

r - radius

H - height

We have r = 40mm and H = 50mm. Substitute:

[tex]S.A.=2\pi(40)(40+50)=80\pi(90)=7200\pi\ mm^2[/tex]

Answer:

A) 6

Step-by-step explanation:

8 (6) = 48

130 + 48 = 178

13 (6) = 78

100 + 78 = 178

178 = 178

Step-by-step explanation:

[tex]\text{Use}\ \log_ab+\log_ac=\log_a(bc)\\\\\log(xy)=\log(x)+\log(y)\\\\\text{Where}\ x>0\ \text{and}\ y>0.[/tex]

Final answer:

To rewrite the logarithm log(xy), you apply the property that the logarithm of a product is equal to the sum of the logarithms of the individual factors, resulting in log x + log y.

Explanation:

The logarithm you are asked to rewrite is log(xy). According to the properties of logarithms, the logarithm of a product is equal to the sum of the logarithms of the individual factors. This means that log(xy) = log x + log y. This rule is useful for simplifying logarithmic expressions and is a direct consequence of how exponents work.

Another property to remember is that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. This is expressed as log(xy) = y × log x.

Remember, both properties are fundamental in working with logarithms and can be applied regardless of the base of the logarithm, whether it's log to the base 10, ln for natural logarithms (to the base e), or any other base.

Answer:

C.  2,160π

Step-by-step explanation:

took test

The linear velocity at the end of the blade is 13571.7 inches per minute by using the circumference of the circle that the blade makes to calculate the linear velocity at the end of the blade.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Here, The total distance in 1 minute is 60 times circumference of the circle made by the end of the blade of the lawnmower.

Since, The blade is 36 inches long, it can be taken as radius of that circle.

The circumference is thus calculated as;

⇒ linear velocity = 226.19 × 60

                           = 13571.7 inches per minute

Thus, The linear velocity at the end of the blade is 13571.7 inches per minute.

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Answer:

A

Step-by-step explanation:

To convert degrees to radians

radian measure = degree measure × [tex]\frac{\pi }{180}[/tex]

Hence

radian measure = 150° × [tex]\frac{\pi }{180}[/tex]

Cancel both 150 and 180 by 30, then

radian measure = 5 × [tex]\frac{\pi }{6}[/tex] = [tex]\frac{5\pi }{6}[/tex]

Final answer:

To convert 150 degrees to radians, multiply 150 by π/180 to get 5/6 * π or approximately 2.61799 radians.

Explanation:

To convert 150 degrees to radians, we use the fact that one complete revolution is 360 degrees which is equal to 2π radians (approximately 6.28318 radians). From this, we can derive that 1 degree is equal to π/180 radians. We multiply the value in degrees by π/180 to get the equivalent in radians.

150 degrees * π/180 radians/degree = 150/180 * π radians = 5/6 * π radians.

Therefore, 150 degrees is equal to 5/6 times π or approximately 2.61799 radians.

Answer:

23

Step-by-step explanation:

The word decreased indicates the use of subtraction, so to figure out our answer we do the opposite, -1 + 24 = 23, after that we then subtract, 23 - 24 = -1, there for your answer should be 23 - 24 = -1, or more simply the number that has to be decreased to make the statement true is 23

Question: A number decreased by 24 is -1

Answer: 23

Explanation: WORK BACKWARDS...

-1 + 24 = 23

WHEN WE CHECK BACK TO SEE IF THE ANSWER IS CORRECT:

23 - 24 = -1

Answer:

i am pretty sure its 1/5

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

P (minivan) = number of minivans / total number of vehicles

We have 3 minivans and 15 vehicles

P (minivan) = 3/15 = 1/5

Answer:

6 [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Substitute x = - [tex]\frac{1}{4}[/tex] into h(x)

h(- [tex]\frac{1}{4}[/tex]) = 6 - (3 × - [tex]\frac{1}{4}[/tex])

                                     = 6 - (- [tex]\frac{3}{4}[/tex])

                                     = 6 + [tex]\frac{3}{4}[/tex] = 6 [tex]\frac{3}{4}[/tex]

Answer:

h=3

Step-by-step explanation:

The given function is

[tex]g(x)=x^2-6x+14[/tex]

We add and subtract the square of half the coefficient of x to obtain;

[tex]g(x)=x^2-6x+(-3)^2-(-3)^2+14[/tex]

Identify the first three terms as a perfect square trinomial;

[tex]g(x)=(x-3)^2-9+14[/tex]

Simplify;

[tex]g(x)=(x-3)^2+5[/tex]

Comparing this to

[tex]g(x)=a(x-h)^2+k[/tex]

We have h=3 and k=5

Answer: h=3

the other answer on this page is right

Step-by-step explanation:

Answer:

[tex]2sin(x)*cos(x)*sec(x)*csc (x)=2[/tex]

Step-by-step explanation:

Remember the identities:

[tex]sec(x)=\frac{1}{cos(x)}\\\\csc(x)=\frac{1}{sin(x)}[/tex]

Ginven the expression:

[tex]2sin(x)*cos(x)*sec(x)*csc (x)[/tex]

You need to substitute [tex]sec(x)=\frac{1}{cos(x)}[/tex] and [tex]csc(x)=\frac{1}{sin(x)}[/tex] into it:

[tex]2sin(x)*cos(x)*sec(x)*csc (x)=2sin(x)*cos(x)*\frac{1}{cos(x)}*\frac{1}{sin(x)}[/tex]

Now, you need to simplify.

Remember that:

[tex]\frac{a}{b}*\frac{c}{d}=\frac{a*c}{b*d}[/tex]

And:

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

Then, you get:

[tex]=\frac{2sin(x)*cos(x)}{cos(x)*sin(x)}}=2[/tex]