Illustrate it in standard form of quadratic equations. please ♥︎✍︎❤︎

1. 5x^2 + 32 - 12 x = 5x + 12

2. 7x^2 + 8x - 12 = 2x^2 + 8x + 12​

First, calculate the discount.

15% of 1250 is 187.5

Then, subtract 187.5 from 1250.

You get 1062.5

Next, to calculate the sales tax. I'm not 100% sure if you're supposed to do this before the discount or after, I'm just assuming after.

Anyway,  

6.5% of 1062.5 is approximately 69.06.

Add that to 1062.5 to get the final answer of $1131.56

Answer:

55

Step-by-step explanation:55-31=24

Answer:

Step-by-step explanation:

(x² + 2x - 3 ) *(4x² - 5x + 6) = x² *(4x² - 5x +6) +2x*(4x² - 5x + 6) -3*(4x² - 5x + 6)

 = x²*4x² + x²*(-5x) + x²*6 +2x*4x² + 2x*(-5x) +2x*6 + (-3)*4x² + (-3)*(-5x) + (-3)*6

= 4x⁴ - 5x³ + 6x² + 8x³ - 10x² + 12x - 12x² + 15x - 18

= 4x⁴ - 5x³ + 8x³  + 6x² -10x² - 12x² + 12x + 15x - 18

= 4x⁴ + 3x³ - 16x² + 27x - 18

Answer:

\(\large\boxed{\textsf{See Below.}}\)

Step-by-step explanation:

\(\textsf{We are asked to solve for the values of x, given values to select from.}\)

\(\textsf{Instead of using the FOIL Method, we can simply substitute in the given options}\)

\(\textsf{then identify if the two expressions are actually equal to each other. This is}\)

\(\textsf{the \underline{Substitution Property of Equality}.}\)

\(\large\underline{\textsf{What is the Substitution Property of Equality?}}\)

\(\textsf{The Substitution Property of Equality is a property that allows us to substitute in}\)

\(\textsf{a known value for a placeholder, or an unknown variables and the equation will}\)

\(\textsf{still remain equal. However for our problem we are given the value of x, but we're}\)

\(\textsf{not certain that the value will make the equation true. That's why we should}\)

\(\textsf{check every option provided.}\)

\(\large\underline{\textsf{Use the Substitution Property of Equality;}}\)

\(\textsf{Our first option given is -46. Substitute that value in for x.}\)

\(\tt (-46 - 3)^{2} = 49\)

\(\textsf{Follow Order of Operations (PEMDAS), and simplify inside the parentheses first.}\)

\(\tt (-46 -3)^{2}=(-49)^{2}=(-49 \times -49)=2401.\)

\(\tt 2401 \neq 49.\)

\(\textsf{-46 is not a value of x.}\)

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

\(\textsf{Our second option given is -4. Substitute that value in for x.}\)

\(\tt (-4 - 3)^{2} = 49\)

\(\textsf{Follow Order of Operations (PEMDAS), and simplify inside the parentheses first.}\)

\(\tt (-4 -3)^{2}=(-7)^{2}=(-7 \times -7)=49.\)

\(\tt 49 = 49. \large\checkmark\)

\(\large\boxed{\textsf{-46 is a value of x.}}\)

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

\(\textsf{Our third option given is 10. Substitute that value in for x.}\)

\(\tt (10 - 3)^{2} = 49\)

\(\textsf{Follow Order of Operations (PEMDAS), and simplify inside the parentheses first.}\)

\(\tt (10 -3)^{2}=(7)^{2}=(7 \times 7)=49.\)

\(\tt 49 = 49. \large\checkmark\)

\(\large\boxed{\textsf{10 is a value of x.}}\)

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

\(\textsf{Our last option given is 52. Substitute that value in for x.}\)

\(\tt (52 - 3)^{2} = 49\)

\(\textsf{Follow Order of Operations (PEMDAS), and simplify inside the parentheses first.}\)

\(\tt (52 -3)^{2}=(49)^{2}=(49 \times 49)=2401.\)

\(\tt 2401 \neq 49.\)

\(\textsf{52 is not a value of x.}\)

The inverse of the function (1/2)^x/3

Given function,

y = 3\(log_{1/2}\) x

Now,

y = 3\(log_{1/2}\) x

Let y = f(x)

then,

x = \(f^{-1} (y)\)

Now put \(f^{-1} (y)\) in the place of x,

y = 3\(log_{1/2}\) \(f^{-1} (y)\)

Simplifying,

y/3 = \(log_{1/2} f^{-1} (y)\)

\(f^{-1} (y) = 1/2^{y/3}\\\)

Replace y variable with x,

\(f^{-1} (x)\) = \((1/2)^{x/3}\)

Hence the inverse of function is \((1/2)^{x/3}\) .

Know more about inverse functions,

https://brainly.com/question/13135813

#SPJ1

Answer:

m∠JKM = 63°

m∠MKL = 27°

Step-by-step explanation:

Since ∠JKL is a right angle. This means that by summing up both m∠JKM and m∠MKL will result in the same as ∠JKL figure. Thus, m∠JKM + m∠MKL = m∠JKL which is 90° by a right angle definition.

\(\displaystyle{\left(12x+3\right)+\left(6x-3\right) = 90}\)

Solve the equation for x:

\(\displaystyle{12x+3+6x-3 = 90}\\\\\displaystyle{18x=90}\\\\\displaystyle{x=5}\)

We know that x = 5. Next, we are going to substitute x = 5 in m∠JKM and m∠MKL. Thus,

m∠JKM = 12(5) + 3 = 60 - 3 = 63°

m∠MKL = 6(5) - 3 = 30 - 3 = 27°

After calculating the partial derivatives and the cross product, we can find the double integral of the magnitude over the region (0 ≤ r ≤ √3, 0 ≤ θ ≤ 2π). This double integral gives the surface area of the part of the plane inside the cylinder.

To find the area of the surface of the part of the plane x + 2y + 3z = 1 that lies inside the cylinder x^2 + y^2 = 3, we can use a parametric representation for the plane and cylinder intersection.

Let x = r * cos(θ) and y = r * sin(θ), where r^2 = 3 (from the cylinder equation). Now, we can find z in terms of r and θ using the plane equation:

z = (1 - x - 2y) / 3
z = (1 - r * cos(θ) - 2r * sin(θ)) / 3

Now, we have the parametric representation of the intersection: (r * cos(θ), r * sin(θ), (1 - r * cos(θ) - 2r * sin(θ)) / 3). To find the surface area, we need to calculate the partial derivatives with respect to r and θ and then find the magnitude of the cross product.

After calculating the partial derivatives and the cross product, we can find the double integral of the magnitude over the region (0 ≤ r ≤ √3, 0 ≤ θ ≤ 2π). This double integral gives the surface area of the part of the plane inside the cylinder.

To know more about Derivatives  visit :

https://brainly.com/question/29144258

#SPJ11

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

For similar question on population proportion.

https://brainly.com/question/29516589  

#SPJ8

Answer:

89

Step-by-step explanation:

so you have an 10 pound object on earth then you put it on mars and it weighs 4 pounds.

Answer:B

Step-by-step explanation: had the question before

Answer:

21.1111 m/s

Step-by-step explanation:

Answer:

boi just use a claculator

Step-by-step explanation:

bye luve

Answer: A 21,369

Explanation I got it right on the test :)

Answer:

The equation of the line is y =  \(-\frac{4}{5}\) x + \(\frac{3}{5}\)

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

The rule of the slope is m = \(\frac{y2-y1}{x2-x1}\) , where

∵ A line passes through points (2, -1) and (-3, 3)

∴ x1 = 2 ad y1 = -1

∴ x2 = -3 and y2 = 3

→ Use the rule of the slope above to find the slope of the line

∵ m = \(\frac{3--1}{-3-2}\) = \(\frac{3+1}{-5}\) = \(\frac{4}{-5}\)

∴ m = \(-\frac{4}{5}\)

→ Substitute the value of m in the form of the equation above

∴ y =  \(-\frac{4}{5}\) x + b

→ To find b substitute x and y in the equation by the coordinates of one  

   point of the given points

∵ x = 2 and y = -1

∴ -1 = \(-\frac{4}{5}\) (2) + b

∴ -1 = \(-\frac{8}{5}\) + b

→ Add \(\frac{8}{5}\) t both sides

∵ -1 + \(\frac{8}{5}\) = b

∴ \(\frac{3}{5}\) = b

→ Substitute the value of b in the equation

∴ y = \(-\frac{4}{5}\) x + \(\frac{3}{5}\)

∴ The equation of the line is y =  \(-\frac{4}{5}\) x + \(\frac{3}{5}\)

Answer: 16 lbs.

Step-by-step explanation:

If there are 7 packages and all of the packages weigh the same, then you would divide the number of packages by the total weight of the packages.

112÷7=16. 16 would be the weight of each package individually.

So, the answer is C;16 lbs.

By applying angle relationships theory, it can be concluded that BCE and CED are Alternate Interior angles.

When a transversal intersects two parallel lines, there will be some angle relationships:

Now we take a look at the picture given and use the angle types above to name the relationship between angles.

As we are asked to determine the relationship between angles BCE and CED, we can take a look at the above explanation.

Thus, the angle relationship describes angles BCE and CED as Alternate Interior angles.

To learn more about angle relationships, click here: https://brainly.com/question/29180445

#SPJ4

Answer:

m∠ABC = m∠BED; Corresponding Angles Theorem

Step-by-step explanation:

I took the test on FLVS and got it right

Answer:

14/15

Step-by-step explanation:

3/5 + 1/3 = 9/15 + 5/15

9+5/15 = 9+5/15

14/15 = 14/15

Hope you got it.

srry for late..

a)The exact probability that there are at most 3 defectives in the sample is 0.4234. b) The exact probability that there are at most 3 defectives in the sample is 0.4234. c) the probability that between 4 and 7, inclusive, are defective by normal approximation is 0.2

a) To find the exact probability that there are at most 3 defectives in the sample, we can use the binomial distribution formula. The probability of getting at most 3 defectives is the sum of the probabilities of getting 0, 1, 2, or 3 defectives.

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Where X is the number of defective bolts in the sample.

Using the binomial distribution formula, we get:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

Where n is the sample size (100), p is the probability of a bolt being defective (0.06), and k is the number of defective bolts.

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
         = 0.4234

Therefore, the exact probability that there are at most 3 defectives in the sample is 0.4234.

b) To find the probability that there are at most 3 defectives by normal approximation, we need to calculate the mean and standard deviation of the binomial distribution.

Mean = np = 100 * 0.06 = 6
Standard deviation = sqrt(np(1-p)) = sqrt(100 * 0.06 * 0.94) = 2.424

We can then use the normal distribution to approximate the binomial distribution:

P(X ≤ 3) ≈ P(Z ≤ (3.5 - 6)/2.424)

Where Z is a standard normal random variable.

Using a standard normal table or calculator, we get:

P(Z ≤ -1.23) = 0.1093

Therefore, the probability that there are at most 3 defectives by normal approximation is 0.1093.

c) To find the probability that between 4 and 7, inclusive, are defective by normal approximation, we can use the same approach as in part b.

Mean = np = 100 * 0.06 = 6
Standard deviation = sqrt(np(1-p)) = sqrt(100 * 0.06 * 0.94) = 2.424

We can then use the normal distribution to approximate the binomial distribution:

P(4 ≤ X ≤ 7) ≈ P(3.5 ≤ X ≤ 7.5) ≈ P((3.5 - 6)/2.424 ≤ Z ≤ (7.5 - 6)/2.424)

Where Z is a standard normal random variable.

Using a standard normal table or calculator, we get:

P(-1.23 ≤ Z ≤ 0.62) = 0.2816

Therefore,  the probability that between 4 and 7, inclusive, are defective by normal approximation is 0.2

To learn more about probability  click here

brainly.com/question/30034780

#SPJ11

Answer: The mistake is improper use of distribution property.

Step-by-step explanation:

It is given that \(3\times (4+2)=12+2\).

We need to find the mistake.

The given expression is

\(3\times (4+2)\)

Using distribution property, we get

\(3\times (4)+3\times(2)\)

\(12+6\)

So, \(3\times (4+2)=12+6\).

In the given calculation the 3 is not distributed properly because 3 is not multiplied with 2.

Therefore, the mistake is improper use of distribution property.

Answer: The time taken for the mass to reduce from 50 g to 41 g is 6 years

Step-by-step explanation:

Expression for rate law for first order kinetics is given by

\(t=\frac{2.303}{k}\log\frac{a}{a-x}\)

where,

k = rate constant  

t = age of sample

a = let initial amount of the reactant  

a - x = amount left after decay process  

a) for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

\(t_{\frac{1}{2}}=22 years\)

\(k=\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{22}=0.0315years^{-1}\)  

b) for mass to reduce from 50 g to 41 g

\(t=\frac{2.303}{0.0315}\log\frac{50}{41}\)

\(t=6years\)  

The time taken for the mass to reduce from 50 g to 41 g is 6 years

Answer:

\(2\sqrt{14\\}\) = q

Step-by-step explanation:

use geometric mean method

4/s = s/10

s^2 = 40

s = 2\(\sqrt{10}\)

consider the triangle STR and using the Pythagorean theorem

\(s^{2} +16 = q^{2} \\\)

\((2\sqrt{10})^{2} +16 = q^{2}\)

40 + 16 = q^2

56 = q^2

\(2\sqrt{14\\}\) = q

(A) The probability of obtaining 5 individuals with brown eyes, 3 individuals with blue eyes, and 2 individuals with green eyes is approximately 0.246 * 0.190 * 0.282 ≈ 0.013.

(B) The probability of selecting exactly 1 individual with blue eyes and 1 individual with green eyes is given by (3 choose 1) * (1 choose 1) * (6 choose 8) / (10 choose 2) ≈ 0.429.

(C) The probability that at least 7 of the 10 people have brown eyes is 0.452.

(a) The probability of selecting 5 individuals with brown eyes, 3 individuals with blue eyes, and 2 individuals with green eyes out of a sample of 10 people can be calculated using the binomial probability formula. Here, the probability of success (i.e., an individual having brown eyes) is 0.51, and the probability of failure (i.e., an individual not having brown eyes) is 0.49. The probability of obtaining 5 individuals with brown eyes is given by (10 choose 5) * 0.51^5 * 0.49^5 ≈ 0.246. Similarly, the probability of obtaining 3 individuals with blue eyes is (10 choose 3) * 0.32^3 * 0.68^7 ≈ 0.190, and the probability of obtaining 2 individuals with green eyes is (10 choose 2) * 0.17^2 * 0.83^8 ≈ 0.282. Therefore, the probability of obtaining 5 individuals with brown eyes, 3 individuals with blue eyes, and 2 individuals with green eyes is approximately 0.246 * 0.190 * 0.282 ≈ 0.013.

(b) To calculate the probability of exactly one person in the sample having blue eyes and exactly one person having green eyes, we can use the hypergeometric distribution. Here, we have a population of N = 10 individuals, of which n1 = 3 have blue eyes and n2 = 1 have green eyes. We need to select 2 individuals from the population who have blue and green eyes, respectively, and the remaining 8 individuals can have any eye color. Therefore, the probability of selecting exactly 1 individual with blue eyes and 1 individual with green eyes is given by (3 choose 1) * (1 choose 1) * (6 choose 8) / (10 choose 2) ≈ 0.429.

(c) To calculate the probability that at least 7 of the 10 people have brown eyes, we can use the binomial probability formula again. Here, we need to calculate the sum of probabilities for selecting 7, 8, 9, or 10 individuals with brown eyes. Therefore, the probability of selecting at least 7 individuals with brown eyes is given by the sum of the probabilities for selecting 7, 8, 9, or 10 individuals with brown eyes. This is approximately equal to (10 choose 7) * 0.51^7 * 0.49^3 + (10 choose 8) * 0.51^8 * 0.49^2 + (10 choose 9) * 0.51^9 * 0.49^1 + (10 choose 10) * 0.51^10 * 0.49^0 ≈ 0.452.

Learn more about Probability:

brainly.com/question/32117953

#SPJ11

Answer:

Fred will have read 36 books in 12 months.

Step-by-step explanation:

We use ratios for this equation:

\(\frac{12}{4} =\frac{x}{12} \\\\4x=144\\x=36\)

This inequality represents that the weight of Duri's backpack is w < 45

Given that

Weight = Less than 45 pounds

We can use the inequality symbol to represent Duri's weight limit as follows:

w < 45

This inequality states that the weight of Duri's backpack, represented by w, must be less than 45 pounds.

Any weight value for w that satisfies this inequality is within Duri's weight limit and can be carried in their backpack.

For example, if Duri's backpack weighs 30 pounds, then w = 30 satisfies the inequality w < 45, so Duri can carry this weight.

However, if the backpack weighs 50 pounds, then w = 50 does not satisfy the inequality w < 45, so Duri cannot carry this weight.

Read more about inequality at

https://brainly.com/question/25275758

#SPJ1

The probability that the child will be color blind is 25%.

In this scenario, the father and mother are carriers of the color-blindness allele. They have one dominant normal vision allele and one recessive color-blindness allele, so they themselves do not have color blindness. Both of their fathers, however, had color blindness. This means that the fathers had two recessive color-blindness alleles, and so they had the condition.

The probability of the child being color-blind can be calculated by a Punnett square. Let's call the normal vision allele "N" and the color-blindness allele "n". The father's genotype is Nn, and the mother's genotype is also Nn. When these are crossed, there are four possible offspring genotypes:NN (normal vision)Nn (normal vision, but carrier of color-blindness allele)nn (color-blind)NN Nn Nn nnNN Nn Nn nnN N N N Nn Nn N n Nn Nn nn nnWhen we count up the possible offspring, we see that there is one chance of an nn genotype out of four possible genotypes, so the probability is 1/4 or 25%.

Learn more about  probability:https://brainly.com/question/24756209

#SPJ11

Answer:

2((6(14) + 6(5) + 14(5)) = 2(84 + 30 + 70) =

2(184) = 368 square centimeters

Answer:3

Step-by-step explanation:

Nor except

The correct option is (C) The graph of Function g is a transformation of the parent cosine function such that g(x) = 3 cos(x + 2) + 1 as it the graph of cosine function.

The ratio between the adjacent side and the hypotenuse is known as the cosine function (or cos function) in triangles. One of the three primary trigonometric functions, cosine is the complement of sine (co+sine) and one of the three main trigonometric functions.

A graph is a structure that resembles a set of objects in mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Option (C) gives a graph of the parent cosine function is transformed into function g such that g(x) = 3 cos(x + 2) + 1 on the cosine function graph.

To know more about graph:

brainly.com/question/17267403

#SPJ4

Answer:

see photo

be sure to look closely, the top curves go to 4 and the bottom goes to -2, there are 2 with this same shape but the other one does not go high enough.

Step-by-step explanation:

Plato/Edmentum

The approximation to a zero of the function f using the tangent line at x = 3 is 2.5 (option c).

When we have a differentiable function and we know the value of the function and its derivative at a specific point, we can use the tangent line at that point to approximate zeros of the function.

In this case, the function f has a tangent line at x = 3, and we know that the function value f(3) is 2 and the derivative f'(3) is 5.

The tangent line has the same slope as the derivative at that point, so its slope is 5. The equation of the tangent line can be written as: y - f(3) = f'(3)(x - 3)

Plugging in the values we know, we have: y - 2 = 5(x - 3)

Simplifying the equation, we get: y = 5x - 13

To find the zero of the function, we set y equal to zero and solve for x: 0 = 5x - 13

5x = 13

x = 13/5

So the approximation to a zero of the function f using the tangent line at x = 3 is 2.6, which is closest to 2.5 (option c).

To know more about derivative click here

brainly.com/question/29096174

#SPJ11