All categories

2 years ago

Which best describes the effect on the x-intercept of the graph of y=34x−3 if the slope is changed to −34

Mathematics

2 answers:

inysia [295]2 years ago

8 0

Answer:

Step-by-step explanation:

⊕ The x-intercept becomes negative and the new line intersects the original line { at (0, - 3) }

lesantik [10]2 years ago

3 0

Answer:

The last option: The x-intercept becomes negative and the new line intersects the original line.

Step-by-step explanation:

Remember that when finding the x-intercept you set y to 0.

Let's compare the two equations when we solve for x:

0=34x-3 0=-34x-3

1. Add 3 to both sides of the equations

3=34x 3=-34x

2. Divide the coefficients

$\frac{3}{34}$ =x $\frac{3}{-34}$ =x

We know that the new slope does not remain the same as stated in the first and third options. In order for two lines to be parallel, the slopes must be exactly the same, so the second option is incorrect. Therefore, the last option is correct.

You might be interested in

Greta bought 3 lb and 4 oz of peanuts and shared 1 lb 12 oz with the class. what is the weight of the remaining peanuts ?

makkiz [27]

Answer:

1lb 8 oz

Step-by-step explanation:

Take 3 lbs and separate it into 48oz + 4 oz = 52 oz.

Same with the 1 lb 12 oz. 16 oz + 12 oz = 28.

Subtract 28 from 52 = 24 oz = 1 lb 8 oz.

Hope this helps.

5 0

3 years ago

Find a cubic function f(x) = ax^3 + bx^2 + cx + d that has a local maximum value of 3 at x = −3 and a local minimum value of 0 a

Ahat [919]

Answer:

f(x) = (3x³ + 9x² - 27x + 15)/32

Step-by-step explanation:

f'(x) = 3ax² + 2bx + c

Maximum or minimum: f'(x) = 0

Maximum: f'(-3) = 0 and f(-3) = 3

Minimum: f'(1) = 0 and f(1) = 0

f'(-3) = 0 leads 27a - 6b + c = 0 (1)

f'(1) = 0 leads 3a + 2b + c = 0 (2)

f(-3) = 3 leads -27a + 9b -3c + d = 3 (3)

f(1) = 0 leads a + b + c + d = 0 (4)

(1) - (2): 24a - 8b = 0, or 3a - b = 0, b = 3a

(3) - (4) -28a + 8b - 4c = 3 (5)

(1) * 4 + (5): 80a - 16b = 3,

use b = 3a, get 80a - 16*3a = 3, 32a = 3, a = 3/32, b = 3a = 9/32

From (2): c = -3a - 2b = -9/32 - 18/32 = -27/32

From (4): d = -a - b - c = -3/32 - 9/32 + 27/32 = 15/32

f(x) = (3x³ + 9x² - 27x + 15)/32

3 0

2 years ago

Using the Principle of Mathematical Induction, prove that . n ^2 − n is even for n ≥ 1

Tamiku [17]

Base case: if n = 1, then

1² - 1 = 0

which is even.

Induction hypothesis: assume the statement is true for n = k, namely that k ² - k is even. This means that k ² - k = 2m for some integer m.

Induction step: show that the assumption implies (k + 1)² - (k + 1) is also even. We have

(k + 1)² - (k + 1) = k ² + 2k + 1 - k - 1

… = (k ² - k) + 2k

… = 2m + 2k

… = 2 (m + k)

which is clearly even. QED

8 0

3 years ago

How many 3 digit palindromes are divisible by 9?

ludmilkaskok [199]

Interesting problem.

A palindrome is a number which is identical when read/interpreted left-to-right or right-to-left. For example, 14241 is a palindrome, so is 444444.

A three digit palindrome must be made up of two distinct digits only, one for the first and last digits, and one for the middle, for example, 424, or 515, etc.

For a number to be divisible by 9, the sum of the digits must add up to a multiple of 9, such as 0, 9, 18, 27, etc.

We can now form a table of the possible 3-digit palindromes divisible by 9, starting with the first/last digits (=A), and finding the middle digit (=B). The number is therefore represented by the pattern ABA.

For example, when A=1, we have the number 1B1. For the number to be divisible by 9, B=7 so that sum=1+7+1=9, which is divisible by 9.

For each value of A (from 1 to 9) we can only find one value of B that makes the number divisible by 9. Thus we can only find nine such numbers, with A equal to 1 to 9.

Here's a list of the numbers

A B number

1 7 171

2 5 252

3 3 333

4 1 414

5 8 585

6 6 666

7 4 747

8 2 828

9 0 909

3 0

3 years ago

√5 percent of 5√5 = a. 0.05 b. 0.25 c. 0.5 d. 2.5 e. 25

Stels [109]

$\sqrt{5} \% \times 5\sqrt{5}=\frac{\sqrt{5}}{100} \times 5\sqrt{5}=\frac{5 \times \sqrt{25}}{100}=\frac{5 \times 5}{100}=\frac{25}{100}=0.25$

The answer is B. 0.25.

8 0

3 years ago