n the figure, 2004-02-04-06-00_files/i0250000.jpg. If the ratio of the perimeter of to that of is 3:2 and the sum of the perimeters of the two triangles is 110, find the perimeter of each triangle.
A.
perimeter of = 66
perimeter of = 44
B.
perimeter of = 73
perimeter of = 37
C.
perimeter of = 37
perimeter of = 73
D.
perimeter of = 44
perimeter of = 66

Answer    7j = 91

Step-by-step explanation: Whenever it says "the product of", that's when you know you need to multiply.  Since we already have the solution we need to divide 91 and 7 to get j. 91 divided by 7 is 13. So j=13

Final answer:

The product of 7/8 and 8 is the multiplication of a fraction by a whole number, leading to the simplified result of 7. This is because multiplying by 8/8 (which equals 1) does not change the original numerator of the fraction.

Explanation:

When we talk about the product of 7/8 and 8, we are performing a multiplication between a fraction and a whole number. To do this, you can multiply the numerator of the fraction by the whole number and leave the denominator unchanged. Since 7/8 multiplied by 8/1 is the same as 7/8 times 8, you can simplify the equation by multiplying 7 by 8, which gives you 56, and then divide that by the denominator, which is 8. So, the product is 56/8, which simplifies to 7. This is because 8/8 is essentially 1, and multiplying by 1 doesn't change the value of the number, thus the product of 7/8 and 8 is the same as the numerator 7.

You have to multiply the price by the quantity and you will find the total cost.

1.43 * 22 = 31.46

Answer:

Step-by-step explanation:

Alright, lets get started.

Since we know,

[tex]3.28084 feet = 1 meter[/tex]

So,

[tex]1 feet = \frac{1}{3.28084} meter[/tex]

[tex]1 cubic feet= \frac{1}{3.28084} *\frac{1}{3.28084}* \frac{1}{3.28084}cubic meters[/tex]

Hence

[tex]1 cubic feet = 0.0283168 cubic meters[/tex]

So, 30000 cubic feet = [tex]30000*0.0283168 = 849.5[/tex] cubic meters

hence the answer is 849 cubic meters. :   Answer

Hope it will help :)

The line will shift vertically down by 4 tons.

Final answer:

To calculate the time it takes for a race car to complete 35 laps at 182 miles per hour, multiply the number of laps by the lap distance to get the total distance, then divide by rate to get time, resulting in 0.5 hours or 30 minutes.

Explanation:

To find the time it takes to complete 35 laps in a high-speed automobile race using the equation d = rt, where d is distance, r is rate, and t is time, follow these steps:

Performing the calculation, the time to complete the laps is 0.5 hours or 30 minutes.

The average rate of change in the cost of the pizza from an 8-inch to a 16-inch pizza is 0.9425.

Given that:

There are five sizes of pizza.

Personal of size 8 inches, small size of 10 inches, medium size of 12 inches, large size of 14 inches, and extra large size of 16 inches.

The cost of the pizza is a function of the diameter.

Also, a table is given that shows the diameter of the pizza and the cost of the pizza based on the diameter.

From the table:

Cost of 8-inch pizza = 2.51

Cost of 16-inch pizza = 10.05

The average rate of change of a function f(x) from points a to b can be found as:

[tex]\text AroC=\frac{f(b)-f(a)}{b-a}[/tex]

The average rate of change in cost is:

[tex]\text AroC=\frac {10.05-2.51}{16-8} \\\text AroC=\frac{7.54}{8} \\\text AroC=0.9425[/tex]

Hence, the average rate of change in cost is 0.9425.

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The table showing the cost as a function of diameter is given below.

The average rate of change in cost from an 8-inch to a 16-inch pizza is 0.9425 dollars per inch.

To find the average rate of change in cost from an 8-inch to a 16-inch pizza, we need to calculate the average rate of change of the cost function [tex]\( C(d) \)[/tex] with respect to the diameter [tex]\( d \).[/tex]

Given data:

[tex]- \( C(8) = 2.51 \)\\- \( C(10) = 3.93 \)\\- \( C(12) = 5.65 \)\\- \( C(14) = 7.70 \)\\- \( C(16) = 10.05 \)[/tex]

The average rate of change of [tex]\( C(d) \)[/tex] from 8 inches to 16 inches is given by:

[tex]\[\text{Average rate of change} = \frac{C(16) - C(8)}{16 - 8}\][/tex]

First, calculate [tex]\( C(16) - C(8) \):[/tex]

[tex]\[C(16) - C(8) = 10.05 - 2.51 = 7.54\][/tex]

Then, calculate [tex]\( 16 - 8 \):[/tex]

[tex]\[16 - 8 = 8\][/tex]

Now, divide to find the average rate of change:

[tex]\[\text{Average rate of change} = \frac{7.54}{8} = 0.9425\][/tex]

Therefore, the average rate of change in cost from an 8-inch to a 16-inch pizza is 0.9425 dollars per inch.

The complete question is:

Pizza palace offers five sizes personal: (8 inches) small:(10 inches) medium:(12 inches) large:(14 inches) and extra large:(16 inches) the cost c(d) of making a pepperoni pizza can be expressed as a function of the diameter D of the pizza. What is the average rate of change in cost from an eight inch to a sixteen inch pizza?

The distance function for Aubrey and Charlie's trip is d(t) = 20 + 50t, accounting for an initial 20 miles already traveled. The reasonable domain for time t in this situation is from 0 to 2 hours since they are traveling at 50 miles per hour and have 100 miles remaining.

Aubrey and Charlie have already traveled 20 miles and are continuing to travel towards a city that is 120 miles away from their start at a constant rate of 50 miles per hour. To complete the function that models the distance they drive as a function of time, we use the formula distance traveled is velocity  imes time. With a start of 20 miles, the function can be written as:

d(t) = 20 + 50t

Where d(t) represents the distance traveled at time t in hours. For the domain, since they have already traveled 20 miles, the remaining distance is 100 miles. At a rate of 50 miles/hour, the maximum time needed to cover the remaining distance is 2 hours. Hence, the reasonable domain for time t is 0 ≤ t ≤ 2.

Let

x------> represents the number of AA batteries

y------> represents the number of 9V batteries

we know that

The constraints are

[tex]x\geq 6[/tex]

[tex]x\leq 12[/tex]

so

[tex]6\leq x\leq 12[/tex] --------> inequality A    

[tex]y\leq 15[/tex] --------> inequality B

[tex](x+y)\geq 20[/tex]        

[tex](x+y)\leq 27[/tex]

so

[tex]20\leq (x+y) \leq 27[/tex]-----> inequality C

The solution of the system of inequalities is the shaded area in the attached figure

If a ordered pair meet all the constraints and make sense in the context of the situation, then the ordered pair is a solution of the system of inequalities

let's check each of the ordered pairs

case A) point [tex](7,13)[/tex]      

[tex]x=7\ y=13[/tex]

Verify inequality A

[tex]6\leq 7\leq 12[/tex]--------> is true

Verify inequality B

[tex]13\leq 15[/tex] -------> is true

Verify inequality C

[tex]20\leq (7+13) \leq 27[/tex]

[tex]20\leq (20) \leq 27[/tex]------> is true

The ordered pair  [tex](7,13)[/tex] meets all restrictions, therefore the ordered pair is a solution of the system of inequalities

case B) point [tex](8,11)[/tex]      

[tex]x=8\ y=11[/tex]

Verify inequality A

[tex]6\leq 8\leq 12[/tex]--------> is true

Verify inequality B

[tex]11\leq 15[/tex] -------> is true

Verify inequality C

[tex]20\leq (8+11) \leq 27[/tex]

[tex]20\leq (19) \leq 27[/tex]------> is not true

The ordered pair  [tex](8,11)[/tex]   does not meet all the restrictions, therefore the ordered pair is not a solution of the system of inequalities.

case C) point [tex](10,16)[/tex]      

[tex]x=10\ y=16[/tex]

Verify inequality A

[tex]6\leq 10\leq 12[/tex]--------> is true

Verify inequality B

[tex]16\leq 15[/tex] -------> is not true

Verify inequality C

[tex]20\leq (10+16) \leq 27[/tex]

[tex]20\leq (26) \leq 27[/tex]------> is not true

The ordered pair  [tex](10,16)[/tex]   does not meet all the restrictions, therefore the ordered pair is not a solution of the system of inequalities.

case D) point [tex](12,12)[/tex]      

[tex]x=12\ y=12[/tex]

Verify inequality A

[tex]6\leq 12\leq 12[/tex]--------> is true

Verify inequality B

[tex]12\leq 15[/tex] -------> is true

Verify inequality C

[tex]20\leq (12+12) \leq 27[/tex]

[tex]20\leq (24) \leq 27[/tex]------> is true

The ordered pair   [tex](12,12)[/tex]  meets all restrictions, therefore the ordered pair is a solution of the system of inequalities

the answer is

[tex](7,13)[/tex]

[tex](12,12)[/tex]

The edge length of a Rubik's cube, given a face perimeter of 22.2 cm is 5.55 cm.

The question asks for the length of an edge of a Rubik's cube, given that the perimeter of each face of the cube is 22.2 cm. A Rubik's cube is a square based cube, meaning each face of the cube is a square.

In a square, all sides have equal length and the perimeter is four times the length of one edge. Therefore, to find the length of one edge, you divide the perimeter of the square by four. Using the provided perimeter of 22.2 cm, the length of an edge would be 22.2 ÷ 4 = 5.55 cm

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0.072. is 0.468 divided by 6.5.

divide in math is the operation of breaking a number up into equal parts, and finding out how many equal parts can be made.

To determine 0.468 / 6.5

first we change into fraction from

0.468 = 468 * 1/1000

6.5  = 65 * 1/10

468 /1000  * 65 /10

= 0.072.

Therefore, the final answer is 0.072.

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To solve problems with integers and rational numbers, one should apply operations' properties such as commutativity, associativity, and distributivity, which streamline calculations and assist in combining numbers in an order that simplifies the process.

Integers and rational numbers are essential elements of algebra that allow for diverse mathematical operations. Integers are the set of whole numbers including zero, and their negative counterparts (e.g., -1, 0, 1), while rational numbers are ratios of integers (e.g., 2/1, 3/4) that can represent fractions and decimals that terminate or repeat. When solving problems, it is crucial to remember the properties of operations, which include commutativity associativity , distributivity, the additive inverse and the multiplicative inverse.

For example, when adding fractions with different denominators, you find a common denominator and use commutativity and associativity to combine these fractions. A problem involving multiplication of a negative integer and a fraction may require both the distributive property and understanding of the multiplicative inverse. Mastering these properties provides a foundation for solving algebraic expressions and equations, ensuring accuracy whether the numbers are complex, real, rational, or integers.

Answer:

Jay has 8 computer games

Step-by-step explanation:

Let

x -----> the number of computer games Sherry has

y -----> the number of computer games Jay has

z -----> the number of computer games  Nairan has

we know that

[tex]x=5y[/tex] ----> equation A

[tex]z=3y[/tex] ----> equation B

[tex]x=z+16[/tex] ----> equation C

Substitute equation A and equation B in equation C and solve for y

[tex]5y=3y+16[/tex]

[tex]5y-3y=16[/tex]

[tex]2y=16[/tex]

[tex]y=8[/tex]

therefore

Jay has 8 computer games

Use 1.75 cups of blue and 1 cup of yellow

The given problem can be placed in the category of ratios and proportions. There is a ratio of color mixing which contains the proportion of two colors i.e blue and yellow. When we use 2 cups of yellow with 3.5 cups of yellow then we get green color so if we mix half of their amounts then we can get less or simply half amount of color too. Hence adding 1 cup of yellow and 1.75 cup of blue will give us small amount in result.

Final answer:

To spot Sienna's error in using base-ten blocks for dividing 45 by 3, we need to verify the even distribution of tens and ones among three groups. The correct result should be 15, with each group receiving 1 ten block and 5 ones blocks.

Explanation:

To find the error made by Sienna in dividing 45 by 3 using base-ten blocks, we need to visualize the process. The number 45 consists of 4 tens (which are blocks representing the number 10) and 5 ones (single blocks representing the number 1). Since she is dividing by 3, Sienna should group the blocks into 3 equal groups to find the quotient, which should be the same number in each group when the blocks are divided evenly.

If Sienna were to correctly divide the blocks to find 45 ÷ 3, she would need to distribute the 4 tens blocks evenly among 3 groups, which would give each group one ten blocks, with one ten blocks remaining. These remaining ten blocks should then be exchanged for ten one's blocks, which, added to the existing five one's blocks, makes a total of fifteen one's blocks. These fifteen blocks can then be evenly distributed, giving each group five blocks. In the end, each group will have one ten-block and five blocks, meaning the quotient is 15.

Therefore, the error that Sienna could have made could include not exchanging a remaining tens block for ones blocks, or not distributing the ones blocks correctly after exchanging. It’s important to keep track of remainders and ensure even distribution among the groups to find the correct quotient in division with base-ten blocks.

Answer:

25%

Step-by-step explanation:

Answer:

Option 3 - (-0.7,1)  

Step-by-step explanation:

Given : Function  [tex]y=2x^3-x^2-4x+5[/tex]

To find : Over which interval is the function decreasing?

Solution :

First we plot the graph using graphing calculator.

Refer the attached figure below.

Now, Examining the graph

From [tex]-\infty[/tex] to (-0.667,6.63) the graph is increasing as the curve is increasing.

From (-0.667,6.63) to (1,2) the graph decreasing as the curve is decreasing.

From  (1,2) to [tex]\infty[/tex] the graph is increasing as the curve is increasing.

So, The interval in which the function is decreasing is given by (-0.667,1)

Round to nearest tenth,  (-0.7,1)

Therefore, Option 3 is correct.