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3 years ago

Assume a = b and c ≠ 0 . Which of the following sentences is not true?

Mathematics

1 answer:

Debora [2.8K]3 years ago

3 0

Answer:

Step-by-step explanation:

ac=0+0 which is 0 so 0 is 0

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X2 - 6x + 12 and y = 2x - 4, algebraically are

olga_2 [115]

The solution is (4, 4)

Solution:

Given system of equations are:

$y = x^2 - 6x + 12 ------ eqn\ 1\\\\y = 2x - 4 ---------- eqn\ 2$

Substitute eqn 2 in eqn 1

$x^2 - 6x + 12 = 2x - 4$

Make the right side of equation 0

$x^2 - 6x + 12 - 2x + 4 = 0\\\\x^2 -8x + 16 = 0$

Solve by quadratic equation

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=-8,\:c=16:\\\\x=\frac{-\left(-8\right)\pm \sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:16}}{2\cdot \:1}\\\\x=\frac{-\left(-8\right)\pm \sqrt{0}}{2\cdot \:1}\\\\x = \frac{8}{2}\\\\x = 4$

Substitute x = 4 in eqn 2

y = 2(4) - 4

y = 8 - 4

y = 4

Thus solution is (4, 4)

5 0

2 years ago

The ratio of x to y is 1/2 . If the ratio of x + 2 to y + 1 is 2/3 , then what is the value of x?

Natali5045456 [20]

Answer:

x =4

Step-by-step explanation:

x/y = 1/2

(x + 2) / (y + 1) = 2/3

Cross multiply the first equation

2x = y

Put that value for y into the second equation.

(x + 2) / (2x + 1) = 2/3 Cross multiply

3(x + 2) = 2(2x + 1) Remove the brackets.

3x + 6 = 4x + 2 Subtract 3x from both sides

6 = 4x - 3x + 2

6 = x + 2 Subtract 2 from both sides

6-2 = x

x = 4

5 0

2 years ago

6. (5 points) What is 3loga + logb − logc written as a single logarithm?

Jobisdone [24]

Answer: $log(\frac{a^3b}{c})$

Step-by-step explanation:

You need to use the following Properties of Logarithms:

$1)m*log(a)=log(a)^m\\\\2)log(a)+log(b)=log(ab)\\\\3)log(a)-log(b)=log(\frac{a}{b})$

Given the following expression:

$3log(a) + log(b) - log(c)$

You can follow these steps in order to write it as a single logarightm:

- Apply the first property shown above:

$=log(a)^3 + log(b) - log(c)$

- Apply the second property:

$=log(a^3b)- log(c)$

- Finally, apply the third property:

$=log(\frac{a^3b}{c})$

4 0

3 years ago

Find the area of a regular decagon with a side length of 14 and an apothem of 25.

andriy [413]

Area = 10 * 1/2* * 14 * 25 (note decagon has 10 sides)

= 1750

4 0

3 years ago

Consider the rates 45 mile in 8 minutes and 4 minutes to travel 25 mile. Select the statement(s) that are true. Multiple select

icang [17]

Answer:

F) The rates are not equivalent.

Step-by-step explanation:

Consider the rates 45 mile in 8 minutes and 4 minutes to travel 25 mile. Select the statement(s) that are true. Multiple select question.

We find the unit rates

a) 45 mile in 8 minutes , we find the unit rate in miles per minute

8 minutes = 45 miles

1 minute = x

8 × x = 45 miles × 1 minute

x = 45 miles/8 minutes

x = 5.625 miles/ minute

b) 4 minutes to travel 25 miles. Find the unit rate is minutes per mile

25 miles = 4 minutes

1 mile = x

25miles × x = 4 minutes × 1

x = 4 minutes/25 miles

x = 0.16 minutes/mile

Hence, the correct option is

F) The rates are not equivalent.

7 0

2 years ago