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3 years ago

In ΔFGH, ∠H \cong≅∠G, FG = 14 and GH = 13. Find the length of HF.

Mathematics

1 answer:

Taya2010 [7]3 years ago

6 0

Answer:

Step-by-step explanation:

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Primitive function for:<br><br> 1. f(x)=4e2x+e−x, sådan att F(0)=2

Free_Kalibri [48]

The primitive function for $f(x) = 4e^{2x} + e^{-x}$ is given by it's indefinite integral.

To calculate it, recall:

$\frac{d}{dx}e^{ax}=ae^{ax}$

$\int c f(x)dx = c\int f(x)dx$

Let's begin

$\int 4e^{2x}+e^{-x}dx \\4\int e^{2x}dx+ \int e^{-x}dx\\4\frac{e^{2x}}{2}+\frac{e^{-x}}{-1} + c\\$

$F(x) = 2e^{2x}-e^{-x} +c$

To find the costant, we just need to use the fact that $F(0)=2$

$F(0) = 2 \\4e^{0}+e^{0} + c =2\\5+c =2\\c=-3$

Therefore,

$\boxed{F(x) = 2e^{2x} - e^{-x} -3 }$

6 0

2 years ago

Y is equal to the additive inverse of 4x. Use this information to find the value of the expression 17x + 3y in terms of x.

nevsk [136]

Answer:

Step-by-step explanation:

The additive inverse of a function is that value added that will sum it up to zero

If y is the additive inverse of 4x, then y = -4x

Given the expression 17x+3y

Substitute y = -4x into the expression to have;

17x + 3(-4x)

17x -12x

Hence the value of the expression in terms of x is 5x

5 0

2 years ago

Based on the model, approximately how many customers will be on the restaurant when there are 10 cars parked in the restaurant’s

Zanzabum

Answer:

Step-by-step explanation:

From the graph, derive the best fit equation :

Using the points ;

(0,2.5) (100 ,35)

x1 = 0 ; y1 = 2.5 ; x2 = 100 ; y2 = 35

Slope formula, m = (y2-y1)/(x2-x1)

m = (35-2.5)/(100-0)

m= (32.5)/100

m = 0.325

The y intercept, value on the graph where best fit line crosses the y axis = 2.5

The equation :

y = mx + c

c = intercept ; m = slope

y = 0.325x + 2.5

y = Number of cars

x = number of customers

The number of customers if there are 10 cars parked :

10 = 0.325x + 2.5

10 - 2.5 = 0.325x

7.5 = 0.325x

x = 7.5 / 0.325

x = 23.076

x = 23

6 0

3 years ago

Greg spent 6.4 hours working with his dad one Saturday. If his dad paid him$45.76, how much did Greg make per hour?

nordsb [41]

Answer:

$7.15

Step-by-step explanation:

The best way to solve this is by crossing out the data you don't need so you're left looking at the key pieces to put the equation together. If his dad paid him $45.76 for 6.4 hours, then all you need to do is divide 45.76 by 6.4. (Hint: Use a calculator, it makes it ten times faster than trying to write it out!)

45.76 ÷ 6.4 = 7.15

So Greg made $7.15 an hour working with his dad.

6 0

2 years ago

Ms. Abrams receives a 4% commission plus a salary of $275.00 per week. If her total sales for one week are $2,880.00, how much d

Marta_Voda [28]

390.20 is the answer because 4%of 2880 is 115.20 plus 275.00 is 390.20

8 0

2 years ago