Jeff's club had $370 to divide equally among 2 people. About how much did each person receive? First, round the amount to the nearest hundred dollars. Each person received approximately $______.

Answers

Answer 1

Answer:

Answer:

$185.

Step-by-step explanation:

To find out how much each person received, we can divide the total amount of money, which is $370, by the number of people, which is 2.

370 ÷ 2 = 185

Therefore, each person received approximately $185.

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The length of a rectangle is 4 inches greater than the width. The perimeter of the rectangle is 24 inches. What are the dimensions of the rectangle

Answers

Answer:

L=8, W=4

Step-by-step explanation:

2L+2W=p

2(4)+2(8)=p

8+16=24

Answer:

length = 8 in.; width = 4 in

Step-by-step explanation:

WILL MARK BRAINLIEST Harry had $32. He spent all the money on buying 3 notebooks for $x each and 4 packs of index cards for $y each. If Harry had bought 5 notebooks and 5 packs of index cards, he would have run short of $18. A student concluded that the price of each notebook is $5 and the price of each pack of index cards is $1. Which statement best justifies whether the student's conclusion is correct or incorrect? The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 50 is (8, 2). The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 18 is (8, 2). The student's conclusion is correct because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 18 is (5, 1). The student's conclusion is correct because the solution to the system of equations 3x − 4y = 32 and 5x − 5y = 50 is (5, 1).

Answers

Let x be cost notebook and y be cost of index card
According to first condition
3x+4y=32

According to second comdition
5x+5y=32+15

Solve the two equations

Find the vertex, focus, directrix, and focal width of the parabola. x = 4y2.

Answers

- Vertex : ( 0, 0 ).
- Focus: ( p/2, 0 );
y² = 1/4 x
y² = 2 p x ⇒ 2 p = 1/4
p = 1/8
p/2 = 1/16
F ( 1/16, 0)
- Directrix:
x = - p/2 x
x = - 1/16 x
- The focal length:
2 p = 2 · 1/8 = 1/4

Answer:

The vertex is (0,0), focus of the parabola is $((1)/(16),0)$ , directrix of the parabola is $y=-(1)/(16)$ , focal width is $(1)/(4)$ .

Step-by-step explanation:

The given equation of parabola is

$x=4y^2$

It can be written as

$y^2=(1)/(4)x$ ....(1)

The general equation of parabola is

$(y-k)^2=4p(x-h)$ ... (2)

Where, (h,k) is vertex, (h+p,k) is focus, y=h-p is directrix and |4p| is focal width.

On comparing (1) and (2), we get

$h=0,k=0$

The vertex is (0,0).

$4p=(1)/(4)$

$p=(1)/(16)$

Focus of the parabola is

$(h+p,k)=(0+(1)/(16),0)=((1)/(16),0)$

Therefore focus of the parabola is $((1)/(16),0)$ .

Directrix of the parabola is

$y=h-p=0-(1)/(16)=-(1)/(16)$

Directrix of the parabola is $y=-(1)/(16)$ .

Focal width is

$|4p|=|4* (1)/(16)|=(1)/(4)$

Focal width is $(1)/(4)$ .

A deer population is estimated to be 4,350. The growth rate of the population is given by the equation y=4350(1.07) . What is the percent rate of growth of the deer population?43.5%

107%

7%

0.07%

Algebra 2

Answers

Answer:

Step-by-step explanation:

Analyzing the growth rate of 1.07:

If the growth rate is a number greater than 1, we have exponential growth; if the growth rate is a number greater than 0 but less than 1, we have exponential decay.

Our growth rate is actually growth. But the rate of growth is not 107%. The rate of growth means that we already had 100% of the population and that it is growing by 7% each year. 100% + 7% = 107%; as a decimal, 1.07

So the rate of growth is 7%

Cara has $25 to buy dry pet food and treats for the animal shelter. A pound of dog food cost $2 and treats are $1 apiece. If she buys 9 pounds of food, what is the greatest number of treats she can buy?

Answers

If dog food costs $2 a pound and Cara buys 9 pounds, her expenditure on dog food is 9 x 2. This makes $18. If she has a total budget of $25 and spends $18 on dog food, she has $7 left over for treats (25 - 18 = 7). At $1 each, she can buy up to 7 treats.

How many roots of the polynomial 30x^4 + 7x^3-125x^2-54x+72 have absolute value greater than 1?

Answers

Answer:

There are 3 roots of the given polynomial that have absolute value greater than 1.

Step-by-step explanation:

We are given the polynomial:

$p(x) = 30x^4 + 7x^3-125x^2-54x+72$

We can factorize the given polynomial as:

$p(x) = 30x^4 + 7x^3-125x^2-54x+72\n=(x-2)(2x+3)(5x-3)(3x+4)=0$

$\text{Solving for}\n(x-2) = 0\nx = 2\n|x| = 2 > 1$

$\text{Solving for}\n(2x+3) = 0\nx = (-3)/(2)\n\bigg|(-3)/(2)\bigg| = (3)/(2) > 1$

$\text{Solving for}\n(5x-3) = 0\nx = (3)/(5)\n\bigg|(3)/(5)\bigg| = (3)/(5) < 1$

$\text{Solving for}\n(3x+4) = 0\nx = (-4)/(3)\n\bigg|(-4)/(3)\bigg| = (4)/(3) > 1$

Thus, there are 3 roots of the given polynomial that have absolute value greater than 1.

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