Factorise it step by step
4r²-7r+3

Answers

Answer 1

Answer: To factor the quadratic expression 4r² - 7r + 3, we can use the factoring method. We're looking for two binomials in the form (ar + b)(cr + d) where ac = 4, ad + bc = -7, and bd = 3. Here's how to factor it step by step:

Step 1: Multiply the leading coefficient (4) by the constant term (3). This gives us 4 * 3 = 12.

Step 2: Find two numbers that multiply to 12 (the result from step 1) and add up to the middle coefficient (-7). These numbers are -4 and -3 because (-4) * (-3) = 12, and (-4) + (-3) = -7.

Step 3: Rewrite the middle term (-7r) using the numbers from step 2 (-4 and -3). We split the middle term like this:
4r² - 4r - 3r + 3

Step 4: Group the terms and factor by grouping:
(4r² - 4r) - (3r - 3)

Step 5: Factor out the greatest common factor from each group:
4r(r - 1) - 3(r - 1)

Step 6: Now you can see that (r - 1) is a common factor in both terms. Factor it out:
(r - 1)(4r - 3)

So, the factored form of the quadratic expression 4r² - 7r + 3 is (r - 1)(4r - 3).

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what is the equation in point-slope form of the line passing through (4, 0) and (2, 6)? y = 4x − 2 y = 2x − 4 y = −3(x − 4) y = 3(x 4)

Answers

Equation in point slope form is given by y - y1 = m(x - x1); where m = (y2 - y1)/(x2 - x1).

y - 0 = (6 - 0)/(2 - 4) (x - 4)
y = 6/-2 (x - 4)
y = -3(x - 4)

Answer:b

Step-by-step explanation:

If a hospital patient is given 50 milligrams of medicine which leaves the bloodstream at 10% per hour, how many milligrams of medicine will remain in the system after 6 hours? Use the function A(t) = Iert. A) 12.39 mg
B) 27.44 mg
C) 45.24 mg
D) 91.11 mg

Answers

A(t) = 50 e^-(0.1 x 6) = 50 e^-0.6 = 50 x 0.5488 = 27.44 mg

I think the answer is B.

Find the leg of each isosceles right triangle when the hypotenuse is of the given measure.Given = 6 square root two cm

Answers

we have given
hypotenuse=6√2
let us suppose leg =a
using Pythagorean theorem
a^2+a^2=(6√2)^2
2a^2=36*2
diving by 2 on both sides
a^2=36
taking square root on both sides
√a^2 =√36
a=6
therefore
the leg of each isosceles right triangle is 6

Express the decimal 2.39 as a percent

Answers

To express a decimal number as a percent transform the number to the equivalent fraction with 100 as denominator. The mathematical methodstep by step is: (1) place the decimal number as a fraction withdenominator 1, (2) multiply numerator and denominator times 100, 3)simplify to the minimum denominator, 4) the numerator is the numberexpressed as percent In this case,2.39 = 2.39/1 = (2.39*100) / (1*100)= 239/100 which means that 2.39 is equal to 239%

The decimal expression $2.39$ as a percentage is $\boxed{239\% }.$

Further Explanation:

After decimal the first place is the tenth place, the second place is the hundredth and the third place is the thousandth.

The first digit from the right is the ones place, the second digit from the right is the tens place, the third digit from the right is the hundreds place, the fourth digit from the right is the thousands.

Given:

The decimal expression is $2.39$

Explanation:

The given decimal expression is $2.39.$

The decimal expression can also be expressed as follows,

$\begin{aligned}A&= 2.39\n&= 2 + 0.39\n&= 2 + \frac{{39}}{{100}}\n\end{gathered}$

1 can be expressed in percentage as $100\%$ .

2 can be expressed in percentage as $200\%$ .

$0.39$ can be expressed as a percentage as $39\%.$

The decimal expression as a percentage can be expressed as follows,

$\begin{aligned}A&= 200\% + 39\% \n&= 239\%\n\end{aligned}$

The decimal expression $2.39$ as a percentage is $\boxed{239\% }.$

Learn more:

Learn more about inverse of the functionbrainly.com/question/1632445.
Learn more about equation of circle brainly.com/question/1506955.
Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Decimal and Percentage

Keywords: decimal, expression, 2.39, percent, place value, base value, decimal expression, as a percentage, percentage.

Given a = {1, 3, 5}, b = {2, 4, 6} and c={1, 2, 3, 4, 5, 6}, then a ∪ (b ∩
c. =

Answers

Match the following. Given A = {1, 2, 3, 4, 5} B = {2, 4, 6} C = {1, 3, 5}?1. A ∪ B __ {1, 2, 3, 4, 5}
2. A ∪ C __ null, or empty set
3. A ∩ B __ {1, 3, 5}
4. A ∩ C __ {1, 2, 3, 4, 5, 6}
5. B ∩ C __ {2, 4}

Final answer:

The result of a ∪ (b ∩ c) equals the union of set a with set b, since set b is completely contained within set c. The final answer is {1, 2, 3, 4, 5, 6}.

Explanation:

The question involves concepts of set theory and specifically deals with the union and intersection of sets. The sets given are a = {1, 3, 5}, b = {2, 4, 6}, and c = {1, 2, 3, 4, 5, 6}. We're asked to find the result of a ∪ (b ∩ c), which means we want to determine the union of set a with the intersection of sets b and c. First, we need to find b ∩ c, which are the elements common to both b and c. Since c contains all the elements of b, the intersection b ∩ c is simply b, which is {2, 4, 6}. Now, we take the union of set a with this result, so a ∪ (b ∩ c) = a ∪ b = {1, 2, 3, 4, 5, 6}. Hence, a ∪ (b ∩ c) contains all elements from both set a and set b, as there were no common elements in set a and set b originally.