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4 years ago

What is the slope of the line?

Mathematics

1 answer:

riadik2000 [5.3K]4 years ago

8 0

Answer:

The slope of the line must be 3

Step-by-step explanation:

The picture of the question in the attached figure

step 1

we know that

The volume of a rectangular prism is equal to

$V_r_p=Bh$ ----> equation A

where

B is the area of the base of the prism

h is the height of the rectangular prism

step 2

The volume of a square pyramid is equal to

$V_s_p=\frac{1}{3}Bh$ -----> equation B

where

B is the area of the square base of pyramid

h is the height of the pyramid

step 3

substitute equation A in equation B

$V_s_p=\frac{1}{3}V_r_p$

Find the relationship between the volume of a rectangular prism and the volume of a square pyramid

$\frac{V_r_p}{V_s_p}=3$

therefore

The slope of the line must be 3

let's check it

To solve for the slope of the line, you must choose two coordinates first and use the formula

$m=\frac{y2-y1}{x2-x1}$

Choosing the points (2,6) and (3,9)

substitute

$m=\frac{9-6}{3-2}=3$ ----> is correct

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igor_vitrenko [27]

Answer:

$7,000 at a rate of 7% and $21,000 at a rate of 14%.

Step-by-step explanation:

Let x be amount invested at 7% and y be amount invested at 14%.

We have been given that a women's professional organization made two small-business loans totaling $28,000. We can represent this information in an equation as:

$x+y=28,000...(1)$

The interest earned at 7% in one year would be $0.07x$ and interest earned at 14% in one year would be $0.14x$ .

We are also told that the organization received from these loans was $3,430. We can represent this information in an equation as:

$0.07x+0.14y=3,430...(2)$

Form equation (1), we will get:

$x=28,000-y$

Upon substituting this value in equation (2), we will get:

$0.07(28,000-y)+0.14y=3,430$

$1960-0.07y+0.14y=3,430$

$1960+0.07y=3,430$

$1960-1960+0.07y=3,430-1960$

$0.07y=1470$

$\frac{0.07y}{0.07}=\frac{1470}{0.07}$

$y=21,000$

Therefore, an amount of $21,000 was invested at a rate of 14%.

$x=28,000-y$

$x=28,000-21,000$

$x=7,000$

Therefore, an amount of $7,000 was invested at a rate of 14%.

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4 years ago

Zhao Xue wants to buy milk and yogurt. She wants to buy a total of at least 6.5 gallons of dairy products (condition A), and she

Marta_Voda [28]

Answer: The answer is (D). Zhao Xue doesn’t have enough money left to buy any yofurt

Step-by-step explanation: Given that Zhao Xue is buying buy milk and yogurt, a total of at least 6.5 gallons of dairy products and she has a budget of $20. The given graph represents the constraints on the number of gallons of milk 'M' and yogurt 'Y' Zhao Xue buys. Zhao Xue buys 4 gallons of milk. We need to calculate the number of gallons of yogurt she can buy to meet both her constraints.

From the graph, we can write

Condition A :

$M+Y\geq 6.5.$

Condition B :

$8M+5Y\leq40.$

Now, if she buys 4 gallons of milk, the the conditions become

$4+Y\geq 6.5~~\Rightarrow Y\geq 2.5,\\\\8\times 4+5Y\leq 40~~\Rightarrow Y\leq 1.6.$

Here, there will be no solution to these constraints.

Therefore, she does not have enough money left to buy any yogurt.

Thus, the correct option is (D).

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Answer:

Step-by-step explanation:

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