All categories

2 years ago

The function f is defined by f(x) = x^2 + 3x -10 , if f(x + 5) = x^2 + kx + 30, k=

Mathematics

1 answer:

boyakko [2]2 years ago

6 0

Answer:

k = 13

Step-by-step explanation:

substitute x = x + 5 into f(x) , that is

f(x + 5) = (x + 5)² + 3(x + 5) - 10 ← expand squared factor using FOIL

= x² + 10x + 25 + 3x + 15 - 10

= x² + 13x + 30

compare this with f(x + 5) = x² + kx + 30

for the 2 expressions to be equal , then k = 13

You might be interested in

Quadratic equations are never used to solve word problems. True or false?

mel-nik [20]

Quadratic equations CAN be used to solve word problems so the answer to your question is false

7 0

3 years ago

Emir is standing in a treehouse and looking down at a swingset in the yard next door. The angle of depression from Emir's eyelin

boyakko [2]

<h3>Answer: 24 feet (Choice D)</h3>

=============================================

Explanation:

Refer to the diagram below. The goal is to find x, which is the horizontal distance from the base of the tree to the swing set.

Focus on triangle BCD.

The angle B is roughly 30.26 degrees, and this is the angle of depression. This is the amount of degrees Emir must look down (when starting at the horizontal) to spot the swing set.

We know that he's 14 ft off the ground, which explains why AB = CD = 14.

The goal is to find BC = AD = x.

---------------------------

Again, keep your focus on triangle BCD.

We'll use the tangent ratio to say

tan(angle) = opposite/adjacent

tan(B) = CD/BC

tan(30.26) = 14/x

x*tan(30.26) = 14

x = 14/tan(30.26)

x = 23.9965714046732

That value is approximate. Make sure your calculator is in degree mode.

That value rounds to 24 feet when rounding to the nearest whole foot.

6 0

3 years ago

PLZ HELP FAST <br><br> If you spend $3 on 6b apples, what is the unit rate (in dollars) per apple?

Ierofanga [76]

Answer:.

.50

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Enos took out a 25-year loan for $135,000 at an APR of 6.0%, compounded monthly, and he is making monthly payments of $869.81. W

Alborosie

Present value = 135000
Monthly interest, i = 0.06/12 = 0.005
Monthly payment, A= 869.81

Future value of loan after 16 years
$F=P(1+i)^n$ [compound interest formula]
$=135000(1+.005)^{16*12}$
$=351736.652$

Future value of payments after 16 years
$\frac{A((1+i)^n-1)}{i}$
$=\frac{869.81((1+0.005)^{16*12}-1)}{0.005}$
$=279287.456$

Balance = future value of loan - future value of payments
=351736.652-279288.456
= $ 72448.20

Note: the exact monthly payment for a 25-year mortgage is
$A=\frac{P(i*(1+i)^n)}{(1+i)^n-1}$
$=\frac{135000(0.005*(1+0.005)^{25*12}}{(1+0.005)^{25*12}-1}$
$=869.806892$

Repeating the previous calculation with this "exact" monthly payment gives
Balance = 72448.197, very close to one of the choices.

So we conclude that the exact value obtained above differs from the answer choices is due to the precision (or lack of it) of the provided data.

The closest choice is therefore <span>$72,449.19</span>

6 0

3 years ago

Read 2 more answers

Pls help I’ll brainlest

Natali [406]

Answer:

C. 5.8 × $10^{-5}$

Step-by-step explanation:

0.000058

4 zeros

4 + 1 = 5

5.8 × 10⁻5

8 0

3 years ago