A pool fills up 3 gallons of water in one minute. How many pints does it fill in one minute?

The perimeter of frame is given 70 cm.

There are two frames given.

For first frame , calculating the perimeter .

For second frame, calculating the perimeter.

Hence the first frame is suitable for for a photo with a perimeter of 70 cm.

This is the frame which is suitable.

In this case we have two functions. The first one is the volume of the balloon and the other is the value of the radius. Both functions depend on the variable time.

Finding the functions to solve the problem, we have:

Let us replace the second function in the first one to get a composite function. Doing so, we have:

Now, we can replace t=11 to find the value of the volume.

The answer is 12248.9 cm3 (Rounding to the nearest tenth of a centimeter).

To find out if the point (1,0) satisfy the equation we plug x=1 and y=0 into the equation:

since this is not true we conclude that th

1) [tex]BC \parallel EF, \angle 1=\angle 3[/tex] (given)

2) [tex]\angle 2=\angle 3[/tex] (corresponding angles)

3) [tex]\angle 1=\angle 2[/tex] (transitive property)

4) [tex]AB \parallel DE[/tex] (converse of corresponding angles theorem)

f(x) = 4

this line is

O vertical

O horizontal

O diagonal

O impossible to graph

Answer:

Length between two points is given as √(x1-x2)²+(y1-y2)², where x and y are the coordinates of the points.

Distance = √(1-(-7))²+(-3-2)²

= √8²+(-5)²

= √64+25

= √89

= 9.43

= 9.4 (nearest tenth)

Answer: C. $29,746.08

Step-by-step explanation:

The amount of weight lost will be equal to 4.72%.

Percentage may be defined as a form of expressing a number as a fraction of hundred. To find the percentage of a number we divide the number by the total amount and then multiply the answer with hundred. The initial weight of the casting was 148 lb and the final weight is 141 lb. To find the percentage we use the formula

Percentage lost = [(Final weight - Initial weight)/Initial weight] × 100

Percentage lost = [(141 - 148)/148] × 100

Percentage lost = ( -7/148) × 100

Percentage lost = -0.0472 × 100

Percentage lost = -4.72% and since we write the absolute value therefore, Percentage lost = 4.72%.

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To find the unit rate (amount per hour) you divide the given amount into the given number of hours:

Then, the unit rate is $16.15/hour

The slope of a line perpendicular to the line 6x + 8y = -128 is 4/3.

Given,

The equation of a line = 6x + 8y = -128

We have to convert this into standard form of linear equation, y = mx + b :

So,

6x + 8y = -128

Add -6x to both sides,

6x + 8y - 6x = -6x - 128

Now,

8y = -6x - 128

Divide 8 on both sides

8y/8 = (-6x - 128) / 8

We get,

y = -6/8x - 16

Here, this is in standard form of linear equation.

Here slope of line, m₁ = -6/8

We have to find the slope of line(m₂) which is perpendicular to the given line.

If the line is perpendicular, the slope(m₂) will be the negative reciprocal of the slope(m₁) of the given line.

That is,

Slope of line, (m₂)= -(m₁) =  - (-8/6) = 8/6 = 4/3

That is, the slope of the line which is perpendicular to the given line is 4/3.

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Answer:

3000

Step-by-step explanation:

Parentheses - (9 + 1) = 10

Exponents - 10 x 10 = 100

Multiplication - 10 x 100 = 1000 then 1000 x 3 = 3000

D

A

S

If we round to the nearest tenth, it would be 8.5 because the hundredth digit is less than 5.

Answer:

[tex]\frac{3}{5}[/tex]

Step-by-step explanation:

2 feet is equivalent to 24 inches.  (12 inches make a foot 2 x 12 = 24)

[tex]\frac{24}{40}[/tex] = [tex]\frac{3}{5}[/tex]  Divide the top (numerator) and the bottom (denominator) by 8 to simplify.

The slowest rate of change that is the slowest for the training program is: 3 minutes per day.

In a given function that is expressed in slope-intercept form as .f(x) = mx + b, the rate of change of the function is represented as "m", while the starting or initial value is represented as "b" in the equation.

Given that Rachel increases the time she runs by 3 minutes for each day, then, the rate of change per day for the training program or Rachel is 3.

Given that the function .f(x) = 5x + 30 represents the minutes Nicole runs per day in the training program, then the rate of change is represented as "5" in the equation. This means that each day, Nicole increases her time of running by 5 minutes as compared to 3 minutes per day that Rachel increases her daily runs.

3 minutes per day is slower than 5 minutes per day, in order words, the slowest rate of change is therefore: 3 minutes per day.

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Amon the choices given, letter D is equivalent to - 3x - 15.

-3 ( x + 5 )

if we distribute -3 , we will have

-3 (x ) = -3x , and

-3 ( +5) = -15

-3 ( x + 5) = -3x - 15

Answer: D. -3 (X + 5)

Rationalization of the surd [tex]\frac{(3+\sqrt{2} )}{(\sqrt{5} )+\sqrt{3} }[/tex] gives [tex]\frac{3\sqrt{5} -3\sqrt{3}+\sqrt{10} -\sqrt{6} }{2}[/tex]

In mathematics surd refers to the root of numbers that do not have a perfect root. Surds are used to represent irrational numbers in square root, cube root and so on.

The data given the question is

[tex]\frac{(3+\sqrt{2} )}{(\sqrt{5} )+\sqrt{3} }[/tex]

This is solved as follows;

[tex]\frac{(3+\sqrt{2} )}{(\sqrt{5} )+\sqrt{3} }[/tex]

Rationalizing the denominator

[tex]\frac{(3+\sqrt{2} )}{(\sqrt{5} +\sqrt{3} }*\frac{\sqrt{5} -\sqrt{3} }{\sqrt{5} -\sqrt{3} }[/tex]

multiplying out

[tex]\frac{3\sqrt{5}-3\sqrt{3} +\sqrt{10}-\sqrt{6} }{5-\sqrt{15} +\sqrt{15} -3}[/tex]

adding and subtraction when required

[tex]\frac{3\sqrt{5}-3\sqrt{3} +\sqrt{10}-\sqrt{6} }{5-3}[/tex]

[tex]\frac{3\sqrt{5}-3\sqrt{3} +\sqrt{10}-\sqrt{6} }{2}[/tex]

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Here, we want to check for the relationship between the image and its pre-image

The pre-image is (x,y)

The image is (3x,3y+5)

As we can see, the pre-image is not similar

This is because the transformation applied to the two values are not same

Thus, we have that;

No, the image is not similar to the pre-image as the translations applied to both coordinates are not same

The pre-image was transformed by dilating the x-coordinate of the pre-image by 3 units while the y-coordinate was transformed by dilating the y-coordinate of the pre-image by 3 and translating it upward by 5 units

Then, to solve the exercise, we need to know the slope of each line. The slope of a line is the measure of the steepness of a line.

The graph shows that the red line has a greater steepness than the blue line. Thus, the lines have different slopes. Also, two lines are parallel if they have the same slope. Since these lines have different slopes, they are not parallel.

Therefore, student B is correct because the lines are not parallel, so they will intersect.

Answer:

g(-5)=46

Step-by-step explanation:

given that function is,

g(k) = 2k² - 4,

and we find the value of g(-5)

so,

g(-5)=2(5)^2-4

simpley put -5 in place of k

g(-5)=2×25-4

g(-5)=46

Answer:

g(-5) = 46

Step-by-step explanation:

Given function:

[tex]g(k)=2k^2-4[/tex]

To find g(-5), substitute k = -5 into the given function:

[tex]\begin{aligned}\implies g(-5)&=2(-5)^2-4\\&=2(25)-4\\&=50-4\\&=46\end{aligned}[/tex]

An order relationship with greater than, greater than or equal to, less than, or less than or equal to between two algebraic expressions. The solution of inequality -3x+4≥10 is x≤-2

An order relationship with greater than, greater than or equal to, less than, or less than or equal to between two algebraic expressions.

The given inequality is

-3x+4≥10.

To solve the above inequality  

Subtract -4 from both sides.

-3x+4-4≥10-4

+4 and -4 we get zero.

-3x≥6

Divide by 3 on both sides

-x≥2

When negative sign is multiplied on both sides, the greater than or equal to symbol changes to lesser than or equal to.

x≤-2

Hence x≤-2 is solution for -3x+4≥10.

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Step by step explanation:

Assuming x as the number of books, the function of production cost is:

And the selling price function would be:

For rhe production cost to be equal to the money from sales we have:

Answer:

The publisher must produce 2784 books

Given:

Answer:

Step-by-step explanation:

Solve:

12/40 = 30/×

12 : 40 = 30 : x

x = 30 * 40 : 12

x = 1200 : 12

x = 100

In order prove that the triangles are similar by the SAS similarity theorem, it needs to be proven that A. J measures 60°.

The SAS Similarity Theorem states that two triangles are similar if their included angles are congruent and their two sides are proportionate to one other. Triangle congruence and resemblance are both criteria for SAS.

The triangles are congruent if two sides and the included angle of one triangle are equivalent to two sides and the included angle of another triangle.

In this case, the length of side FE is 40 and the length of side IH is 20. This gives a value of 60. Therefore, J should measure 60°.

In conclusion, the correct option is A.

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Triangles G E F and J H I are shown. The length of side G F is 20 and the length of side I J is 10. Th elength of side F E is 40 and the length of side I H is 20. To prove that the triangles are similar by the SAS similarity theorem, it needs to be proven that

J measures 60°.

J measures 30°.

I measures 60°.

I measures 30°.

OB. The statement makes sense. The value of 10^5 is 100,000 is the correct answer.

10^5 = 10*10*10*10*10 = 100,000

Repeated multiplication is expressed using exponential notation.

For instance, 10*10*10 can be expressed more briefly as 10^3.

The base is the number 10 in 10^3.

Exponent refers to the 3 in 10^3.

The exponential expression is known as the number 10^3.

You can learn how to conduct mathematical operations on an exponential expression or term by being familiar with its constituent parts' names.

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1) Let's proceed the steps

To convert a decimal to do a fraction for the decimal over one

Ex

0.5/1

And multiply the numerator and denominator by ten

Ex

5/10

(..) *until there is no longer a decimal in the numerator then simplify your fraction

Ex

1/2

Answer:

60 seconds

Step-by-step explanation:

The LCM of 10 and 12 is

10 = 2 × 5

12 = 2² × 3

LCM = 2² × 3 × 5 = 60

Answer: 60 seconds

the anwser is 60 seconds

The  smallest 3 digit number that is divisible by 2, 3, 4 , 5 and 6 is 720.

Let us find the factors of the given numbers which are Factors of 2 are 1 and 2. then the factors of  3 are 1 and 3, the Factors of 4 are 1, 2 and 2, then the Factors of 5 are 12 and 5, then the Factors of 6 are 12, 2 and 3.

Then we can find the Lowest Common Factor of them as (1*2*3*2*2*5*2*3) which will give us 720.

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Let the number be r then

2r is the product of 2 and the number

2r + 7 is when the product is increased by 7

2r + 7 = -36

2r = -36 - 7

2r = -41

r = -41/2

= -20 1/2

Answer:

$5507.98

Explanation:

To find the value of the account, we use the compound interest formula below:

From the given information:

• Principal,P=$4500

• Interest Rate, r=4.5%=0.045

• Number of compounding periods, n=12 (Monthly)

• Time, t=4.5 years

Substituting the given values, we have:

The value of the account when the customer takes the money at the end of the 4.5 years is $5507.98.