The diagram shows an equilateral triangle, a square, and one diagonal of the square. what is the value of x

satela [25.4K]

the slope is -2

have a nice day :D

8 0

2 years ago

harlie invests $325 in an account that pays 8% simple interest for 15 years. Use the simple interest formula, I = P ∙ r ∙ t, to

Alina [70]

$390 is the interest will Charlie’s initial investment earn over the 15-year period. The money does Charlie have after the 15 years is $715.

Step-by-step explanation:

Harlie invests $325 in an account.

Principal, P = $325
Interest rate, r = 8% ⇒ 0.08
Number of years, t = 15

The formula to find the interest will Charlie’s initial investment earn over the 15-year period :

⇒ $I = Prt$

⇒ $325\times 0.08\times15$

⇒ $390$

Therefore, $390 is the interest will Charlie’s initial investment earn over the 15-year period.

Money Charlie has after 15 years :

It is given by the formula,

⇒ Amount = Principal + Interest.

⇒ 325 + 390

⇒ 715 dollars.

∴ The money does Charlie have after the 15 years is $715.

3 0

3 years ago

Read 2 more answers

Suppose Upper F Superscript prime Baseline left-parenthesis x right-parenthesis equals 3 x Superscript 2 Baseline plus 7 and Upp

Sedaia [141]

It looks like you're given

F'(x) = 3x² + 7

and

F (0) = 5

and you're asked to find F(b) for the values of b in the list {0, 0.1, 0.2, 0.5, 2.0}.

The first is done for you, F (0) = 5.

For the remaining b, you can solve for F(x) exactly by using the fundamental theorem of calculus:

$F(x)=F(0)+\displaystyle\int_0^x F'(t)\,\mathrm dt$

$F(x)=5+\displaystyle\int_0^x(3t^2+7)\,\mathrm dt$

$F(x)=5+(t^3+7t)\bigg|_0^x$

$F(x)=5+x^3+7x$

Then F (0.1) = 5.701, F (0.2) = 6.408, F (0.5) = 8.625, and F (2.0) = 27.

On the other hand, if you're expected to approximate F at the given b, you can use the linear approximation to F(x) around x = 0, which is

F(x) ≈ L(x) = F (0) + F' (0) (x - 0) = 5 + 7x

Then F (0) = 5, F (0.1) ≈ 5.7, F (0.2) ≈ 6.4, F (0.5) ≈ 8.5, and F (2.0) ≈ 19. Notice how the error gets larger the further away b gets from 0.

A better numerical method would be Euler's method. Given F'(x), we iteratively use the linear approximation at successive points to get closer approximations to the actual values of F(x).

Let y(x) = F(x). Starting with x₀ = 0 and y₀ = F(x₀) = 5, we have

x₁ = x₀ + 0.1 = 0.1

y₁ = y₀ + F'(x₀) (x₁ - x₀) = 5 + 7 (0.1 - 0) → F (0.1) ≈ 5.7

x₂ = x₁ + 0.1 = 0.2

y₂ = y₁ + F'(x₁) (x₂ - x₁) = 5.7 + 7.03 (0.2 - 0.1) → F (0.2) ≈ 6.403

x₃ = x₂ + 0.3 = 0.5

y₃ = y₂ + F'(x₂) (x₃ - x₂) = 6.403 + 7.12 (0.5 - 0.2) → F (0.5) ≈ 8.539

x₄ = x₃ + 1.5 = 2.0

y₄ = y₃ + F'(x₃) (x₄ - x₃) = 8.539 + 7.75 (2.0 - 0.5) → F (2.0) ≈ 20.164

4 0

2 years ago

Suppose a 5x8 coefficient matrix for a system has pivot columns. Is the system consistent? Why and Why not?

Lyrx [107]

Step-by-step explanation:

All the 5 rows of the coefficient matrix (since it is of order 5×8) will have a pivot position. The augmented matrix obtained by adding a last column of constant terms to the 8 columns of the coefficient matrix will have nine columns and will not have a row of the form [0 0 0 0 0 0 0 0 1]. So the system is consistent.

7 0

3 years ago

Best explained and correct answer gets brainliest.

Ahat [919]

The answer is C
short explanation: the two triangles are congruent so that would make BD equal to AC and if AC is 6 then BD is 6
hope this helps

5 0

3 years ago

Read 2 more answers