Find the product: (5x + 5y) (x + 4y)

What is the value of x?<br> a. 2 /29<br> b. 3 /61<br> c. 2/ 101<br> d. 2/333

stiv31 [10]

Answer:

2√133

Step-by-step explanation:

a²+b²=c²

8²+12²=c²

c²=208

208+18²=532

√532=23

3 0

3 years ago

plz help me suzy spent 6 7/8 days working on her English paper 3 1/6 days on her science project and 1 1/2 days studying for her

malfutka [58]

Answer:

English time + Math Time = 6 7/8 + 1 4/8 = 7 7/8+4/8 = 8 3/8

8 3/8 - Science time = difference = 8 3/8- 3 1/6 = 5 5/24

She spent 5 5/24 days more on her English and Math test than Science

Step-by-step explanation:

5 0

3 years ago

In 1950 the number of retirees was approximately 150 per thousand people aged 20-64. In 1990 this number rose to approximately 2

serg [7]

Answer: 233 people per thousand

Step-by-step explanation:

Using extrapolation method,

if 150/k in 1950,

200/k in 1990,

275/k in 2020,

2003 lies in between 1990 and 2020. So, you extrapolate the values of 200/k and 275/k for the years respectively.

Therefore,

(2003 - 1990)/(2020 - 2003) = (x - 200)/(275 - x)

Where x is the number of retirees per thousand for 2003

Making x the subject of relation in the above equation.

Cross multiply the equation above;

(2003 - 1990)(275-x) = (2020 - 2003)(x - 200)

13(275 - x) = 17(x-200)

3575 - 13x = 17x - 3400

Collect the like terms

3575+3400 = 17x + 13x

30x = 6975

x = 6975/30

x = 232.5

x = 233 people per thousand to the nearest integer

6 0

3 years ago

The horizontal line segment at the top of the polygon on the grid below is how many units long?

Ymorist [56]

Answer:

6 units long.

Step-by-step explanation:

Given:

A polygon drawn on a graph.

In order to determine the distance of the horizontal line at the top, we find the coordinates of the end points and then use distance formula to find the exact distance.

Let us label the polygon as ABCD as shown below. AB is the length of the horizontal line.

Coordinates of A are $(x_1,y_1)=(-3, 4)$ as seen in the graph.

Coordinates of B are $(x_2,y_2)=( 3, 4)$ as seen in the graph.

Now, distance formula for two points $(x_1,y_1)\ and\ (x_2,y_2)$ is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d_{AB}=\sqrt{(3-(-3))^2+(4-4)^2}\\d_{AB}=\sqrt{(3+3)^2+0}\\d_{AB}=\sqrt{36}=6\ units$

Therefore, the horizontal line at the top is 6 units long.

4 0

3 years ago

Given f(x) = x^2 + 14x + 40 . Enter the quadratic function in vertex form in the box. f(x)=

finlep [7]

Recall that the vertex form of a quadratic function (or parabolic function) is equal to

$f(x) = a(x - h)^{2} + k$

Now, given that we have f(x) = x² + 14x + 40, to express f into its vertex form, we must first fill in the expression to form a perfect square.

One concept that we must remember when completing the square is that

(a + b)² = a² + 2ab + b²

So, to complete the square for (x² + 14x + ____), we have 2ab = 14 where a = 1. Thus, b = 14/2 = 7. Hence, the last term of the perfect square must equal to 7² = 49.

So, going back to the function, we have

$f(x) = (x^{2} + 14x + 40 + 0)$
$f(x) = (x^{2} + 14x + 40 + 49 - 49)$
$f(x) = (x^{2} + 14x + 49) + 40 - 49$
$f(x) = (x + 7)^{2} - 9$

Thus, we have derived the vertex form of the function.

Answer: f(x) = (x + 7)² - 9

6 0

3 years ago

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