Alex determines that there are 5 chocolate candies per cubic inch. If there are 150 chocolate candies in a jar, what is the volume of the jar?
A) 30 in3
B) 75 in3
C) 500 in3
D) 750 in3

Final answer:

After calculating the cost per ounce for both packages, the 10.5-ounce package, with a unit price of $0.284 per ounce, is the better deal compared to the 27.8-ounce package, which has a unit price of $0.323 per ounce.

Explanation:

To determine which package has the better unit price, you calculate the cost per ounce for each package and compare them. First, divide the total cost of each package by the number of ounces it contains.

For the 10.5-ounce package at $2.98:

$2.98 ÷ 10.5 ounces = approximately $0.284 per ounce

For the 27.8-ounce package at $8.99:

$8.99 ÷ 27.8 ounces = approximately $0.323 per ounce

Now, compare the unit prices. The 10.5-ounce package has a lower unit price of $0.284 per ounce compared to the 27.8-ounce package with a unit price of $0.323 per ounce, making the 10.5-ounce package the better deal based on unit price.

The graph described by the student shows a solid vertical line through the point (5, 0), with shading to the left. This corresponds to the inequality 'x less than or equal to 5'.

The student is asking about a graph of an inequality which features a solid vertical line that passes through the point (5, 0). The graph has shading to the left of this line. A vertical line in coordinate geometry represents all points where the x-coordinate is a specific value, and if the shading is to the left, it indicates that the x-values are less than or equal to that specific value of the vertical line.

Therefore, the correct inequality that matches the described graph is x less than or equal to 5 (`x ≤ 5`). The other options do not correctly represent a vertical line or the indicated shading direction.

Answer:

The answer is (r + 3)(r - 3)

Step-by-step explanation:

There need to be two number that add together to get 0

and two number that multiply together to get -9

3 + -3 = 0

3 · -3 = -9

= (r + 3)(r - 3)

Answer:

x= 1

Step-by-step explanation:

- = negative. so negative 2 blank + 7 equals 14.

x is 1 because the more you add positively to a negative number the close it gets to zero. negative 21 + 7 is negative 14 but I you got an 8ntegr the n it would be 14.

The graph of the function -2x + 7y = 14 is attached

From the question, we have the following parameters that can be used in our computation:

-2x + 7y = 14

We start by making the variable y the subject

-2x + 7y = 14

So, we have

7y = 2x + 14

Divide through by 7

y = 2/7x + 2

And it also means that the equation is a linear equation

A linear equation is represented as

y = mx + c

Where

m = slope

i.e. m = 2/7

Hence, the equivalent equation to plot is y = 2/7x + 2

See attachment for graph

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Answer:

y= 2x-4   ,   y= -1/2x +3    , y= -2/3x+2

Step-by-step explanation:

slope intercept form: y=mx+b

y-2x=-4

add 2x to both sides

y= 2x-4

y-3= -1/2x

add 3 to both sides

y= -1/2x +3

2x+3y=6

subtract 2x from both sides

3y= -2x+6

divide both sides by 3

y= (-2x+6)/3

y= -2/3x+2

NOTES:

Slope-Intercept form is y = mx + b  ; where m is the slope and b is the y-intercept.

To convert an equation into slope-intercept form, solve for y

******************************************************************************************

Answer: y = 2x - 4

Step-by-step explanation:

y - 2x = -4

  +2x    +2x  

y       = 2x - 4

********************************************************************************************

Answer: y = [tex]-\frac{1}{2}x[/tex] + 3

Step-by-step explanation:

y - 3 = [tex]-\frac{1}{2}x[/tex]

  +3          +3  

y       = [tex]-\frac{1}{2}x[/tex] + 3

********************************************************************************************

Answer: y = [tex]-\frac{2}{3}x[/tex] + 2

Step-by-step explanation:

2x + 3y = 6

-2x         -2x  

        3y = -2x + 6

        ÷3    ÷3  ÷3  

          y = [tex]-\frac{2}{3}x[/tex] + 2

Answer:

The answer is approximately about 23.5 feet about the ground touching the wall.

Step-by-step explanation:

The ladder makes a right triangle with the wall and ground, therefore you use pythagorean theorem. If you draw what is being described, you can see that the 24 ladder is the hypotenuse or "c", while the ground and wall are "a" and "b" for the equation.

you set it up like so:

√(24²-5²) = a²

which will result in √(551) or ≈23.5 feet

The number of feet above the ground where the ladder touches the wall is 23.47 ft.

The information above forms a right angle triangle. The base of the right angle triangle is 5 ft and the hypotenuse of the right angle triangle is 24 ft.

Let's find the height of the triangle to know how many feet above the ground where the ladder touches the wall.

Using Pythagoras theorem,

where

c =hypotenuse

a and b are either adjacent side or opposite sides.

Therefore,

b² = 24² - 5²

b² = 576 - 25

b = √551

b = 23.4733891886

b ≈ 23. 47 ft.

Therefore, the feet above the ground where the ladder touches the wall is 23.47 feet.

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Answer:

y = 3.5x

Step-by-step explanation:

The equation for a straight line is  

y = mx +b

We know that when

x₁ = 2, y₁ = 7 and when

x₂ = 5, y₂ = 17.5

Step 1. Determine the slope

m = (y₂ - y₁)/(x₂ - x₁)       Substitute values

m = (17.5 – 7)/(5 – 2)    Remove parentheses

m = 10.5/3

m = 3.5

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

Step 2. Determine the y-intercept.

y = 3.5x + b     Insert x₁ and y₁

7 = 3.5×2 + b

7 = 7 + b          Subtract 7 from each side

b = 0

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

Step 3. Write the equation

y = mx + b

y = 3.5x + 0

y = 3.5x

The equation is y = 3.5x.

Answer:

3. aₙ = -9n +7

4. d = -2.4

5. a₆ = 45

6. aₙ = 133 + 4n

Step-by-step explanation:

Question 3.

a₁ = -2; aₙ = aₙ₋₁ - 9

The explicit rule for an arithmetic sequence is

        aₙ = a₁ + d(n -1 )

         d = aₙ - aₙ₋₁

        aₙ = aₙ₋₁ - 9     Subtract aₙ₋₁ from each side

aₙ - aₙ₋₁ = -9

         d = -9

For this sequence,  

aₙ = -2 – 9(n - 1)     Remove parentheses

aₙ = -2 - 9n + 9      Combine like terms

aₙ = -9n + 7

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

Question 4

d = aₙ - aₙ₋₁

a₂ - a₁ = 6.2 – 8.6 = -2.4

a₃ - a₂ = 3.8 – 6.2 = -2.4, etc.

The common difference is

d = -2.4

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

Question 5

aₙ = 8n – 3     Substitute the value of n

a₆ = 8×6 – 3

a₆ = 48 - 3

a₆ = 45

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

Question 6

a₁ = 137; d = 4

aₙ = a₁ + d(n -1 )

aₙ = 137 + 4(n -1 )

aₙ = 137 + 4n -4

aₙ = 133 + 4n

Answer:

$27.83

Step-by-step explanation:

26.50 x .05 = 1.325  (round up to 1.33 since the 5 is 5 or greater)  

26.50 + 1.33 = 27.83  

Amount of tax will be 1.33

Answer:

27.83

Step-by-step explanation:

Graham and Max will meet at the same altitude after approximately 22 minutes.

Explanation:

To find out how many minutes it will take Graham and Max to meet at the same altitude, we need to set up an equation.

Let's assume that after t minutes, Graham and Max will meet at the same altitude. This means that the altitude of Graham is equal to the altitude of Max.

Equation: 14,040 - 50t = 12,500 + 20t

To find t, we can solve this equation:

14,040 - 50t = 12,500 + 20t

Subtract 20t from both sides: 14,040 - 70t = 12,500

Subtract 12,500 from both sides: 14,040 - 12,500 - 70t = 0

Combine like terms: 1,540 - 70t = 0

Subtract 1,540 from both sides: -70t = -1,540

Divide by -70 on both sides: t = -1,540/-70

Simplify: t ≈ 22 minutes

Therefore, it will take approximately 22 minutes for Graham and Max to meet at the same altitude.

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Answer:

Tate has 7x pennies.

Step-by-step explanation:

Tate has 2x pennies because Mia has x pennies and Tate has twice the pennies of Mia so

5+2x= 7x

Answer:

Slope (m) = 0.2 and y-intercept (b) = 3.5.

Step-by-step explanation:

We are given weather equation y=0.2x +3.5 for finding the amount of accumulated snow y in inches x hours after 5 P.M. on a certain day.

We need to identify the slope and y- intercept of the graph of the equation .

Let us compare given equation y=0.2x +3.5 by slope-intercept form y=mx+b, we get

Slope (m) = 0.2 and y-intercept (b) = 3.5.

Answer:

C. b^27

Step-by-step explanation:

By the definition of exponents

[tex](b^9)^3=b^9*b^9*b^9[/tex]

And since for any real numbers [tex]r,x,[/tex] and [tex]y[/tex]

[tex]r^x*r^y=r^{(x+y)}[/tex]

This makes

[tex](b^9)^3=b^9*b^9*b^9=b^{{9+9+9}}=\boxed{b^{27}}[/tex]

Which is choice C.

Alternatively, we could use the identity

[tex](r^x)^y=r^{xy}[/tex]

in which case

[tex](b^9)^3=b^{(9*3)}= \boxed{b^{27}}[/tex]

which is the same answer.

Answer:b²⁷

Step-by-step explanation:

Answer:

[tex]n=241[/tex]

Step-by-step explanation:

We are given

[tex]5x^2+nx+48[/tex]

Let's assume it can be factored as

[tex]5x^2+nx+48=(5x-s)(x-r)[/tex]

now, we can multiply right side

and then we can compare it

[tex]5x^2+nx+48=5x^2-5rx-sx+rs[/tex]

[tex]5x^2+nx+48=5x^2-(5r+s)x+rs[/tex]

now, we can compare coefficients

[tex]rs=48[/tex]

[tex]5r+s=-n[/tex]

[tex]n=-(5r+s)[/tex]

now, we can find all possible factors of 48

and then we can assume possible prime factors of 48

[tex]48=-+(1\times 48)[/tex]

[tex]48=-+(2\times 24)[/tex]

[tex]48=-+(3\times 16)[/tex]

[tex]48=-+(4\times 12)[/tex]

[tex]48=-+(6\times 8)[/tex]

Since, we have to find the largest value of n

So, we will get consider larger value of r because of 5r

and because n is negative of 5r+s

so, we will both n and r as negative

So, we can assume

r=-48 and s=-1

so, we get

[tex]n=-(5\times -48-1)[/tex]

[tex]n=241[/tex]

Answer:the answer would be a i just did it but correct me if i was wrong

Step-by-step explanation:

Answer:

b. $3,000.00

Step-by-step explanation:

Daniel buys one bond each with a par value of $1,000 from Grath Oil, Ombor Medical Supplies, and Dwyn Horticulture.

Grath Oil bonds are selling at 120.514

Ombor Medical Supplies bonds are selling at 90.773

Dwyn Horticulture bonds are selling at 101.180.

These values have nothing to do here as we only have to find the face value.

The face value of 1 bond is $1000 so, the face value of 3 bonds will be = [tex]1000\times3=3000[/tex] dollars.

[tex]a-the\ side\ of\ square\\a^2-the\ area\ of\ square\\\\a+3-the\ one\ side\ of\ rectangle\\a-2-the\ second\ side\ of\ rectangle\\(a+3)(a-2)-the\ area\ of\ rectangle\\\\\text{The equation:}\\\\(a+3)(a-2)=a^2+30\qquad\text{use distributive property}\\\\(a)(a)+(a)(-2)+(3)(a)+(3)(-2)=a^2+30\\\\a^2-2a+3a-6=a^2+30\qquad\text{subtract}\ a^2\ \text{from both sides}\\\\a-6=30\qquad\text{add 6 to both sides}\\\\\boxed{a=36}\\\\Answer:\ \boxed{36\ cm}[/tex]

[tex]1/4(20-4a)=6-a \ /\cdot4\\20-4a=24-4a\\-4a+4a=24-20\\0=4\\false[/tex]

Final answer:

To solve 8(5x+9x+6)=160, we first combine like terms to simplify the expression within the parentheses to 14x+6, and then use the distributive property to further simplify and solve the equation. This order of operations ensures clarity and accuracy in solving the equation.

Explanation:

The question involves solving the algebraic expression 8(5x+9x+6)=160. The first step in simplifying and solving an equation like this is to combine like terms within the parentheses. Combining like terms (5x+9x) simplifies the expression inside the parentheses to 14x+6. This simplification makes the equation easier to manage and understand. The next step is to use the distributive property which allows us to multiply the number outside the parenthesis (in this case, 8) by each term inside the parenthesis individually (14x and 6). After distributing, we get 112x + 48 = 160, from which we can solve for x by isolating the variable.

The order of operations is crucial here; combining like terms before using the distributive property ensures the equation remains manageable and reduces the potential for errors. After these steps, we can subtract 48 from both sides and divide by 112 to find the value of x that satisfies the equation.

Answer:

[tex]\frac{1}{81}[/tex]

Step-by-step explanation:

Law of exponent

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

1) Applying the above rule, we have

[tex]9^{-2} = \frac{1}{9^{2} }[/tex]

= [tex]\frac{1}{9*9}[/tex]

= [tex]\frac{1}{81}[/tex]

f(2) This means that x is 2, so you can plug in 2 for "x" in the equation

f(x) = 3x - 12

f(2) = 3(2) - 12

f(2) = 6 - 12

f(2) = -6

Your answer is D

Answer:

D. -6

Step-by-step explanation:

Hi!!! You have to substitute 2 for f(x) & for the x next to 3!!!

f(x) = 3x- 12

f(2) = 3(2) - 12

= 6 - 12

= 6 -12

= -6

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (7, -1) and (9, -9). Substitute:

[tex]d=\sqrt{(9-7)^2+(-9-(-1))^2}=\sqrt{2^2+(-8)^2}=\sqrt{4+64}=\sqrt{68}\\\\=\qrt{4\cdot17}=\sqrt4\cdot\sqrt{17}=\boxed{2\sqrt{17}}[/tex]

The distance between the points (7, -1) and (9, -9) is calculated using the distance formula and simplifies to [tex]2\sqrt{17}[/tex] units.

To find the distance between two points in simplest radical form, we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]. For the points (7, -1) and (9, -9), the calculation is as follows:

First, find the difference in the x-coordinates: 9 - 7 = 2.

Next, find the difference in the y-coordinates: -9 - (-1) = -8.

Now, square each difference: (2)^2 = 4 and (-8)^2 = 64.

Add these squares together: 4 + 64 = 68.

Finally, take the square root of the sum: [tex]\sqrt{68}[/tex].

This radical simplifies to [tex]\sqrt{4 * 17} = 2\sqrt{17}[/tex], which is in simplest radical form.

Therefore, the distance between the points (7, -1) and (9, -9) is [tex]2\sqrt{17}[/tex] units.

Answer:

D. multiplication property

Step-by-step explanation

Am not so sure but i think its that

Statement: Two planes intersect to form a point

This is false. Two planes intersect to form a single straight line.

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

Statement: two lines intersect to form a point

This is true assuming the two lines have different slopes

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

Because the first statement is false, the overall argument is false.

Final answer:

The intersection of two planes is a line, not a point, which makes the statement false. Two lines intersecting in a point is true provided they are not parallel.

Explanation:

The statement that the intersection of two planes is a point is false. According to geometric principles, specifically the line of intersection of two planes, when two planes intersect, they do so along a line, not just a single point. This line of intersection is represented by the points where their respective great circles cross. The intersection of two lines, however, is indeed a point, provided that the lines are not parallel. This is in agreement with Theorem 1, which states that two straight lines of a plane have either one point or no point in common; similarly, two planes have no point in common or a straight line in common.

Relevant Theorems on Intersections

Theorem 1 and Theorem 2 outline the foundational concepts regarding intersections in geometry. Understanding these theorems helps explain why two intersecting planes result in a line and not a single point.

Answer:

35q-384 = 225q-189

Step-by-step explanation:

since its 384 subtracted from 35 times q it will be 35q-384 and then it says "is" which is an equal sign (=) and then q times 225 which is 225q decreased by 189 which is 225q-189 so it will be 35q-384 = 225q-189

Answer:

a. x+y=10, 2x+3y=24

b.this systems of equations have a unique solution since there is only one value for x and one value for y where each equation is present in. There is no same slope or y-intercept

c. 4 magnet gift boxes

Step-by-step explanation:

Answer:

22.5 miles

Step-by-step explanation:

first divide 75 by sixty and that will be your traveled per minute then multiply that by 18 and that is you answer. Good luck, please mark me brainliest.

Constant speed is the speed of the object witch does not changes with the time. With constant speed the body traveled the same distance for the each time interval. The distance traveled by the car in 18 minutes is 22.5 miles.

The car traveled with the constant speed is 75 miles in 60 minutes.

Constant speed is the speed of the object witch does not changes with the time. With constant speed the body traveled the same distance for the each time interval.

As the car traveled with the constant speed is 75 miles in 60 minutes. Let x the total miles traveled by  the car in one minutes is.

[tex]x=\dfrac{75}{60}[/tex]

[tex]x=\dfrac{5}{4}[/tex]

Thus the the total miles traveled by the car in one minutes is 5/4 miles. Let n be the total miles traveled by the car in 18 minutes. Thus,

[tex]x=\dfrac{5}{4}\times 18[/tex]

[tex]x=\dfrac{45}{2}[/tex]

[tex]x=22.5[/tex]

Hence the distance traveled by the car in 18 minutes is 22.5 miles.

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Answer:

x = 10

Step-by-step explanation:

First, we need to isolate all the x's on one side. To do this we need to move the -20 over to the other side making it a +20:

3.5x + 1/2x = 40 + 20 - 2x

Add the x's and the 40 and 20:

4x = 60 - 2x

Move the -2x over to the other side making it a +2x:

4x + 2x = 60

6x = 60

Divide both sides by 6:

x = 10

So x = 10

Answer:

10

Step-by-step explanation:

3.5(x) + -20 + 1/2(x) = 40 - 2x

3.5x - 20 + x/2 = 40 - 2x

3.5x + x/2 + 2x = 40 + 20

6x = 60

x = 60/6

    = 10