Rank and alice are penguins. at birth, frank's beak was 1.95 inches long, while alice's was 1.50 inches long. homework help ✎ frank's beak grows by 0.25 inches per year and alice's grows by 0.40 inches per year. write an equation to represent the length of each penguin's beak in x years. how old will they be when their beaks are the same length?

Answer:

Step-by-step explanation:

B

Final answer:

To solve the equation 2y+7x=4 for x=5, x=10, and x=15, substitute each value into the equation and solve for y to get y=-15.5, y=-33, and y=-50.5 respectively. It’s important to check the solutions by substituting them back into the original equation.

Explanation:

To solve the given linear equation 2y+7x=4 for different values of x (x=5, x=10, x=15), we need to substitute these values of x into the equation and solve for y. Here’s how it can be done:

Answer:

(15, 11) and (12, 10.5).

Step-by-step explanation:

Let x represents the poodle’s body length and y represents the shoulder height.

A miniature poodle must be between 10 in. and 15 in. at the shoulder.

[tex]10\leq y\leq 15[/tex]

The body length must be no more than 16 in.

[tex]0\leq x\leq 16[/tex]

The poodle’s shoulder height must be no more than 1 in. longer than its body length.

[tex]y\le1+x[/tex]

From the below figure it is clear that only two points (15, 11) and (12, 10.5) lie in the feasible region.

Therefore, ordered pairs (15, 11) and (12, 10.5) meet all the constraints for a successful poodle measurement and make sense in context of the situation.

The oil tank in your car is leaking at a rate of 1.2 oz per mile driven. You drove 15 miles over to your grandma's house. Therefore, it would be 2 cups and 4 oz leaked out.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

The oil tank in your car is leaking at a rate of 1.2 oz per mile driven. You drove 15 miles over to your grandma's house.

There are 8 oz in a cup

So,

8 x 3 = 24 which is too high

So,

8 x 2 = 16 leaving about 4 oz left

Therefore, it would be 2 cups and 4 oz leaked out.

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Answer:

x=55 acute

Step-by-step explanation:

Because of the 3-6 theorum of triangles

The cost for someone who went on 9 rides is $23.

An equation is a mathematical sentence that has two equal sides separated by an equal sign.

Given that, The cost of admission to an amusement park is $9.50 plus $1.50 per ride.

The equation can be made,

C = 9.50 + 1.50n, where n is the number of rides.

For n = 9

C = 9.50 + 1.50*9 = $23

Hence, The cost for someone who went on 9 rides is $23.

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put 7.6*10^-4 into the equation:

10log(1/7.6*10^-4)

this equals 31.19 db

The probability that a person is color-blind given they are male is 69/133. Calculating the probability of being both male and color-blind requires additional information about the total and male population. This showcases the importance of context in probability calculations.

The question involves calculating the probability of specific conditions related to color-blindness and gender. To address both parts of the question:

Understanding probabilities in genetics, like color-blindness, often involves considering various factors including the overall population and specific subgroups within that population (such as males in this case).

To find the distance Marcos's car was towed, subtract the service fee from the total bill amount. Then divide the remaining bill amount by the additional fee charged per mile. The distance towed is 12 miles.

To find the distance Marcos's car was towed, we need to subtract the service fee from the total bill amount. The additional fee charged per mile is $1.75, so we can calculate the number of miles towed by dividing the remaining bill amount by $1.75.

Let's assume the distance towed is 'x' miles.

The total bill amount is $71, and the service fee is $50. Therefore, the additional fee charged for the distance towed is $71 - $50 = $21.

So we can write the equation:

$21 = $1.75 * x

To solve for 'x', we divide both sides of the equation by $1.75:

x = $21 / $1.75

x = 12 miles

Therefore, Marcos's car was towed for a distance of 12 miles.

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// Solve equation [2] for the variable  y  
 

// Plug this in for variable  y  in equation [1]

// Solve equation [1] for the variable  x  

// By now we know this much :

// Use the  x  value to solve for  y  

The machine will deposit 622 feet of lime powder to mark both foul lines on the playing field.

To solve this problem, we need to consider that the line-marking machine is laying down lime powder to mark two equal foul lines on a playing field. Each foul line measures 311 feet.

Since there are two lines of equal length, we simply need to add the lengths of these two lines together to find the total amount of lime powder deposited.

Here is the calculation:

Length of one foul line = 311 feet

Number of foul lines = 2

Total length of lime powder deposited = Length of one foul line [tex]\times[/tex] Number of foul lines

Total length of lime powder deposited = 311 feet [tex]\times[/tex] 2

Total length of lime powder deposited = 622 feet.

The correct answer is:

C. (1, 1/2) (2, 1/4) (3, 1/8) (4, 1/16)

Explanation:

In order to be an exponential function, the y-coordinates of each point should be multiplied by a constant to get the next y-coordinate.  For C, we multiply by 1/2:

1/2(1/2) = 1/4; 1/4(1/2) = 1/8; 1/8(1/2) = 1/16

This means it is an exponential function.

The answer for this question is parallel lines

Answer:

24r^2*s*t

Step-by-step explanation:

We can simply the following expression by looking at the which terms are common:

[tex]6*r*s*4*r*t[/tex]

We have two of r and according to the product rule we can add there exponents:

[tex]r*r=r^(1+1)=r^2[/tex]

Therefore the expression can be simplified as:

[tex]=6*4*s*t*r^2=24*s*t*r^2[/tex]

The statement " If two lines are intersected by a transversal so that the alternate interior angles are congruent, then the lines are paralle " is true.

Given:

If two lines are intersected by a transversal so that the alternate interior angles are congruent, then the lines are parallel.

We know whenever we have parallel line intersected by transversal line then we Alternate Interior Angle, Corresponding Angle, Alternate Exterior Angle, are congruent.

Thus, the statement showing when we have Alternate Interior Angle congruent then the lines were be parallel lines.

Hence, the statement is True.

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Answer:

Length

Step-by-step explanation:

mhm

1) The dimensions of the rectangular prism or box which I found are:

2) The shape of the cross-section when the box is cut parallel to the base will be a rectangle.

3) Surface Area of the box is234  in²

4) Surface Area of the box if scaled up by a factor of 10 is  23,400 in²

5) Volume of the box: 180 in³

6) Volume of the box if scaled down by a factor of 1/10 is  0.18 in³

Given:

Dimensions of the box to be:

Length: 6 inches

Width: 2.5 inches

Height: 12 inches (1 foot)

1) The shape of the cross-section when the box is cut parallel to the base will be a rectangle.

2) To calculate the surface area of the box:

Surface Area = 2*(Length*Width + Length*Height + Width*Height)

Surface Area = 2*(6*2.5 + 6*12 + 2.5*12)

Surface Area = 2*(15 + 72 + 30)

Surface Area = 2*(117)

Surface Area = 234 in²

3) If the box is scaled up by a factor of 10, the new dimensions would be:

Length: 6 inches * 10 = 60 inches

Width: 2.5 inches * 10 = 25 inches

Height: 12 inches * 10 = 120 inches

To find the new surface area:

New Surface Area = 2*(60*25 + 60*120 + 25*120)

New Surface Area = 2*(1500 + 7200 + 3000)

New Surface Area = 2*(11700)

New Surface Area = 23,400 in²

4) The volume of the box:

Volume = Length * Width * Height

Volume = 6 * 2.5 * 12

Volume = 180 in³

5) If the box is scaled down by a factor of 1/10, the new dimensions would be:

Length: 6 inches * 0.1 = 0.6 inches

Width: 2.5 inches * 0.1 = 0.25 inches

Height: 12 inches * 0.1 = 1.2 inches

To find the new volume:

New Volume = Length * Width * Height

New Volume = 0.6 * 0.25 * 1.2

New Volume = 0.18 in³

Full Question:

Although part of your question is missing, you might be referring to this full question:

Search your home for a rectangular prism. Some examples are a cereal box, a CD case, or a coffee table. Measure your prism using appropriate units, such as inches, centimeters, or feet.

Complete the following. Show all work for calculations.

List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).

Length:

Width:

Height:


Describe the shape of the cross section when the box is cut parallel to the base.
What is the surface area of the box?

What is the surface area of the box if it is scaled up by a factor of 10?

What is the volume of the box?

What is the volume of the box if it is scaled down by a factor of 1/10?

Answer:

Weight of full steel bead tire=1.76 pounds

weight of lighter wheel=1.54 pounds.

Step-by-step explanation:

it is given that:

The weight of a full steel bead tire is approximately 800 grams.

lighter wheel weighs only 700 grams.

Now we are given conversion that:

There are 453.592 grams in one pound.

Hence, 1 gram=1/453.592 pounds.

Hence, weight of a full steel bead tire is:

[tex]\dfrac{800}{453.592}pounds=1.76pounds[/tex]

Also weight of lighter wheel in pounds is:

[tex]\dfrac{700}{453.592}pounds\\\\=1.54 pounds[/tex]

Part A)

y = total houses, x = number of years

Neighborhood A  y = 30*(1.20)^x

Neighborhood B : y = 45 +3x

Part B) neighborhood A has : 30 *1.2^5 = 74.65 = 75 houses

             neighborhood B has: 45 +3(5) = 45 +15 = 60 houses

Part C)

30* 1.2^x = 45 +3x =

x = 3.3

check:

30 *1.2^3.3 = 54.75 = 55

45 + 3(3.3) = 45+9.9 = 54.9 =55

 so 3.3 years round to 3 years

Answer:

Part A)

y = total houses, x = number of years

Neighborhood A  y = 30*(1.20)^x

Neighborhood B : y = 45 +3x

Part B) neighborhood A has : 30 *1.2^5 = 74.65 = 75 houses

            neighborhood B has: 45 +3(5) = 45 +15 = 60 houses

Part C)

30* 1.2^x = 45 +3x =

x = 3.3

check:

30 *1.2^3.3 = 54.75 = 55

45 + 3(3.3) = 45+9.9 = 54.9 =55

so 3.3 years round to 3 years

Step-by-step explanation:

Answer: 212.54 in3

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Volume of a cylinder: π r² h

Where:

Replacing with the values given:

r = 4.75/2 = 2.375 in

h = 12in

V = π r² h

V= π (2.375)² (12) = 3.14 (5.640625) 12 =212.54 in3

So, the correct option is 212.54in3

Feel free to ask for more if needed or if you did not understand something.