What rule did samantha apply to make the new triangle

help please~!!! how many solutions does the equation 4y − 4y − 12 = 14 − 2 have? thanks! <3 first question will be marked as

luda_lava [24]

Answer:

No solutions

Step-by-step explanation:

The 4y and the -4y will always cancel each other out. This leaves us with

-12 = 14-2

or

-12 = 12

which is never true

8 0

4 years ago

The cake store is having a 30% off sale on all of its cakes. If the cake you want regularly costs $10, how much would you save w

Studentka2010 [4]

3 dollars. since 30% of 10 is 3

4 0

3 years ago

What is the slope of the line that passes through the points (10,8) and (-15,18) wrote the answer in simplest form

cupoosta [38]

Answer:

-2/5

Step-by-step explanation:

3 0

3 years ago

Kremena's bank account earns 4.5% simple interest. How much must she deposit in the account today if she wants it to be worth $1

anastassius [24]

Answer: Kremena needs to deposit $1,101 today to earn a total of $1,250 in 3 years at 4.5% simple interest rate

Step-by-step explanation:

Interest = Principal (P) × Rate (R) × Time (T)

Amount = Principal (P) + Interest

Amount = P + PRT

Amount = P (1 + RT)

1250 = P (1 + (0.045 × 3))

1250 = P (1 + 0.135)

1250 = P (1.135)

Principal = 1250 ÷ 1.135

Principal = approx. 1101

5 0

3 years ago

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

3 years ago