An industrial machine made 9,096 cans of diet soda and 5times as many regular soda over the course of 53 minutes.Then the regular soda were placed into 2shipping boxes with each shipping box containing the same number of soda. How many regular sodas were in each shipping box?

When CG = 3 in., CH = 2 in. and GE = 5 in. the information made available in the question is not enough to solve for DH

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Examining the figure, shows that lines GH and DE should be parallel to create similar triangles

For similar triangles the sides are proportional and this can be used to solve for DH using the equation below'

CG / CE = CH / CD

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The complete question is attached

Answer:

72°

Step-by-step explanation:

4+2+6+8=20

360÷20=18

AC=4x18=72

Answer:

C. 8x²+x+3.

Step-by-step explanation:

A and B are not polynomials as they contain a division (A) and a square root (B).

D is a monomial ( just one term).

oc.8x²+x+3

Step-by-step explanation:

Which of the following is a polynomial?

OA. 5+x2²/X

OB. √x+2x-1

OC. 8x²+x+3

OD. 7x

The equation of the line in the slope-intercept form is: y = -2.00 x + 10.

The slope and provided point are both in the equation for the straight line.

The generic point (x, y) must satisfy the equation if we have a non-vertical land in a that passes through any point(x1, y1) has gradient m.

y-y₁ = m(x-x₁)

It is the necessary equation for a line in the form of a point-slope.

That gift card to the Coffee Café has been provided. = $10

Medium coffee = $2.00

customers

The quantity of coffees a consumer can purchase can be represented using a linear equation.

Slope formula

m = (8 - 10)/(1 - 0)

m = -2

Now consider the line's point-slope shape.

y-y₁ = m(x-x₁)

( y - 10) = -2.00 ( x - 0)

y = -2.00 x + 10

The slope: m = - 2.00

The equation of the line: y = -2.00 x + 10

The y-intercept is 10

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Step-by-step explanation:

11b + 5 = 38

11b = 33

b = 3 is the answer

Answer:

Step-by-step explanation:

Let's retype that as y = b^x.  The inverse of this function is log    y = x  

                                                                                                        b

which you could also write as  y = ln     x

                                                             b

If you had y = e^x, the inverse function would be y = ln x.

Note that if you let ln x be the input to y = e^x, the result would be just 'x,' which confirms that these two functions are inverses of one another.

The volume of the sculpture is 92.316 feet³.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is (1/3)πr²h.

We have,

Cone-shaped sculpture:

Height = 5 feet

Base circumference = 26.376

This means,

2πr = 26.376

r = 26.376/(2 x 3.14)

r = 4.2 feet

Now,

The volume of the sculpture.

= 1/3 x 3.14 x 4.2 x 4.2 x 5

= 92.316 feet³.

Thus,

92.316 feet³ is the volume of the sculpture.

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Answer:1.5

Step-by-step explanation:

Y=1/2 of x

Answer:

x = 3

Step-by-step explanation:

\( {5}^{2x} \ast {5}^{3} = {5}^{9} \\ {5}^{2x + 3} = {5}^{9} \\ 2x + 3 = 9 \\ (bases \: are \: equal \: so \: exponents \: will \: also \: \\ be \: equal) \\ 2x = 9 - 3 \\ 2x = 6 \\ x = \frac{6}{2} \\ \huge \red { \boxed{x = 3}}\)

the counting number just before C5F16 is 3,072.

The compound inequality that represents the range of the actual weight of the object is 125.4 ≤ w ≤ 126.2.

Part A: The absolute value inequality that describes the range of the actual weight of the object is:

|w - 125.8| ≤ 0.4

Part B: To solve the absolute value inequality, we can break it down into two separate inequalities:

w - 125.8 ≤ 0.4 and - (w - 125.8) ≤ 0.4

Solving the first inequality:

w - 125.8 ≤ 0.4

Add 125.8 to both sides:

w ≤ 126.2

Solving the second inequality:

-(w - 125.8) ≤ 0.4

Multiply by -1 and distribute the negative sign:

-w + 125.8 ≤ 0.4

Subtract 125.8 from both sides:

-w ≤ -125.4

Divide by -1 (note that the inequality direction flips):

w ≥ 125.4

Combining the solutions, we have:

125.4 ≤ w ≤ 126.2

The object is 125.4 ≤ w ≤ 126.2.

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61 percent of the 8th graders estimated they spend less than an hour a day on social media.

To find the percentage of 8th graders who estimated they spend less than an hour a day on social media, we need to calculate the proportion of 8th graders who answered "less" and then convert it to a percentage.

There were 12 + 19 = 31 8th graders in the sample.

Out of these 31 8th graders, 19 answered "less" and 12 answered "more".

So, the proportion of 8th graders who answered "less" is 19/31 = 0.61290323.

To convert this proportion to a percentage, multiply it by 100:

0.61290323 * 100 = 61.290323 (rounded to 2 decimal places).

Finally, rounding to the nearest whole number percent, we get:

61.290323 rounded to the nearest whole number percent = 61%

Therefore, 61% of the 8th graders estimated they spend less than an hour a day on social media.

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Answer:

I = $372.40

Step-by-step explanation:

Given the principal amount of $2,940, which is invested for 4 months at 3.8% interest rate:

Use the following simple interest formula to solve for the interest earned:

I = P × r × t

where:

I = interest earned

P = principal amount invested = $2,940

r = interest rate = 3.8% or 0.380

t = time = 4/12 months = ⅓ or 0.3333

Substitute to given values into the simple interest formula:

I = P × r × t

I = $2,940 × 0.380 × 0.3333

I = $372.40

Therefore, the simple interest earned in 4 months is $372.40.

We have the following:

The distributive property of multiplication over addition can be used when multiplying a number by a sum.

Answer:

3/10,1/2,4/5

this is because

if you make them all have common denominators they are:

8/10, 3/10, and 5/10

and you put them in order based on their numerators

For figure {0}, the number of tiles will be equal to 2.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph as shown in the image.

The line passes through point -

(3, 8) and (4, 10)

So, the slope of the line will be -

m = (10 - 8)/(4 - 3)

m = 2

y = 2x + c

For the point (3, 8), we can write -

8 = 6 + c

c = 2

For figure {0}, the number of tiles will be equal to 2.

Therefore, for figure {0}, the number of tiles will be equal to 2.

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69

How many bags of potatoes are on the van at the start.

The total number of bags the van have at the starting is 70.

Ratio is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another.

According to the given question.

The sacks of potatoes delivered in two different shops are in the ratio 3:7.

Also, one shop has 28 more bags than the other.

Let the number of bags of potatoes at one shop be x.

Then, the bags of potatoes in another shop = x + 28

Therefore,

\(\frac{x}{28 + x } =\frac{3}{7}\)

⇒ \(7x = 3(28 + x)\)

⇒ \(7x = 84 + 3x\)

⇒ \(4x = 84\)

⇒\(x = 21\)

So, the total number of bags

\(=x + (x + 28)\)

\(=2x + 28\)

\(= 2(21) + 28\)

\(= 42 + 28\)

\(= 70\)

Hence, the total number of bags the van have at the starting is 70.

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Answer:

Top : 24cm²

Bottom : 24cm²

Step-by-step explanation:

Surface area : Base × Height

Top :

3 × 8 = 24

Bottom :

3 × 8 = 24

Answer:

Step-by-step explanation:

we know ∠K is 90° by Thales theorem

then

180 = 90 + 4x-1 + 4x -5

96 = 8x

12 = x

x = 12

∠JLk = 4(12)-1

∠JLk = 47°

\(\dfrac{x!-(x-3)!}{23}=1\\x!-(x-3)!=23\\(x-3)!((x-2)(x-1)x-1)=23\\(x-3)!((x^3-x^2-2x^2+2x)-1)=23\\(x-3)!((x^3-3x^2+2x)-1)=23\)

23 is a prime number, therefore there are two possibilities:

\(\text{I.}\, (x-3)!=1 \wedge x^3-3x^2+2x-1=23\)

or

\(\text{II.}\, (x-3)!=23 \wedge x^3-3x^2+2x-1=1\)

\(\text{I.}\\(x-3)!=1\\x-3=0 \vee x-3=1\\x=3 \vee x=4\)

Now, we check if any of these solutions is also a solution to the second equation:

\(3^3-3\cdot3^2+2\cdot3-1=23\\27-27+6-1-23=0\\ -18=0\)

Therefore, 3 is not a solution.

\(4^3-3\cdot4^2+2\cdot4-1=23\\64-48+8-1-23=0\\0=0\)

Therefore, 4 is a solution.

\(\text{II.}\)

\((x-3)!=23\)

We know that \(3!=6\) and \(4!=24\), therefore there isn't any \(n\in\mathbb{N}\), for which \(n!=23\), so there's no solution.

So, the only solution is \(x=4\).

Answer:

The answer is A, All of the animals are vertebrates, and all are adapted to hot climate.

Step-by-step explanation:

Because i know for sure the owl has a backbone, and so does a puma and all live in hope weather so it has to be a

Answer: D: Square Root Of 5

Step-by-step explanation: 30/6 is 5, now fill in the sqrt symbol. Hope this helped. (This problem was one of the simpler, friendlier numbers.)

Answer:

5 ≥ p

Step-by-step explanation:

Add 5 to both sides:

0 ≥ p - 5

+5      + 5

________

5 ≥ p

Answer:

p <= 5

Step-by-step explanation:

Let's solve your inequality step-by-step.

0≥p−5

Step 1: Flip the equation.

p−5≤0

Step 2: Add 5 to both sides.

p−5+5≤0+5

p≤5

Answer:

p≤5

Answer:

x=2

x=4

Step-by-step explanation:

the range is x>0

Move the expression to the left side and change it's sign to get

log6(x^2+8)-log6(x)=1

using loga(x)-loga(y) = loga (x/y) to simplify log6(x^2+8/x)=1

convert it to exponential form to get x^2+8/x=6

multiply both sides of the equation by x to get x^2+8=6x

move variable to the left

x^2-6x+8

factor out x from the expression

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

factor out x-2

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

set both equal to 0 and get x=2 x=4

Answer:

w=5

Step-by-step explanation:

The equation of the line is x + 3y = 2

Linear equations are equations that have constant average rates of change.

The given parameters are

Slope, m = -1/3

Points (x, y) = (1, 1/3)

A linear equation is represented as

y = slope * (x - x₁) + y₁

Where

(x₁, y₁) = (1, 1/3)

Substitute (x₁, y₁) = (1, 1/3) and Slope, m = -1/3 in the equation y = slope * (x - x₁) + y₁

So, we have

y = -1/3* (x - 1) + 1/3

Multiply through by 4

So, we have

3y = -(x - 1) + 1

Remove the brackets

3y = -x + 1 + 1

So, we have

x + 3y = 2

Hence. the linear equation is x + 3y = 2

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Answer:

x = 2

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × breadth

given the rectangles have equal areas then equating the two areas gives

4x × 9 = 4(6x + 6) , that is

36x = 24x + 24 ( subtract 24x from both sides )

12x = 24 ( divide both sides by 12 )

x = 2

Answer:

approximately 28.26 square feet

Step-by-step explanation:

The formula for the area of a circle is A = pi(r)^2. So, the radius is half of the diameter, meaning it's 3 feet. Then we square it to get 9, and multiply by pi, or 3.14. This leads us to the approximated answer of 28.26 square feet.

The area is:

28.27 square feet

Work/explanation:

Since the tabletop is circular, we use the formula for a circle's area, which is: \(\bf{A=\pi r^2}\).

We have the diameter, and to find the radius, we divide the diameter by 2, which gives us 6 ÷ 2 = 3 feet, so the radius of the tabletop is 3 feet.

Now, here's a diagram for you;

\(\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 3\ ft}\end{picture}\)

Plug in the data:

\(\sf{A=\pi\times3^2}\)

\(\sf{A=\pi\times9}\)

\(\sf{A=28.27\:ft^2}\)

Dilations with a scale factor between 0 and 1 are called reductions. Multiply the coordinates by the scale factor to determine the new point

V ( 2,-4)

Multiply each point by 1/2 to determine V'

V' ( 1/2*2, 1/2 *-4) = (1,-2)