The image shows a geometric representation of the function f(x) = x2 + 2x + 3 written in standard form. An algebra tile configuration. Only the Product spot is shown. 6 tiles are in the Product spot in 4 columns with 2 rows. First row: 1 + x squared, 1 + x. Second row: 1 + x, 3 +. What is this function written in vertex form? f(x) = (x + 2)2 + 3 f(x) = (x2 + 2x)2 + 3 f(x) = (x + 1)2 + 2 f(x) = (x + 3)2 + 2x

Answers

Answer 1
Answer:

The function written in vertex form; f(x) = (x + 3)^2 + 2x. Hence, correct option is D.

What is a quadratic equation?

A quadratic equation is the second-order degree algebraic expression in a variable.

The standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

x² + 2x + 3 = 0 is a quadratic equation.

An algebra tile configuration showing Only the Product spot is shown. 6 tiles are in the Product spot in 4 columns with 2 rows.

First row: 1 + x squared, 1 + x.

Second row: 1 + x, 3 +.

Then,

The factors of the polynomial are;

(2x + 3) (x + 1)

Thus, the function written in vertex form;

f(x) = (x + 3)^2 + 2x

Hence, correct option is D.

More about the quadratic equation link is given below;

brainly.com/question/2263981

#SPJ5

Answer 2
Answer:

Answer:

The factors of the polynomial are (2x + 3) (x + 1)

Step-by-step explanation:


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A quadrilateral has angles that measure 60°, 95°, and 150°. What is the measure of the fourth angle? A. 25° B. 55° C. 85° D. 125°

Solve the inequality.
x/3-x-1/2≥1 a. x≤-3 b. x≥-3 c. x≤3 d. x≥3​

Answers

Answer:

x ≤-9/4

Step-by-step explanation:

x/3-x-1/2≥1

Multiply each side by 6 to get rid of the fractions

6(x/3-x-1/2)≥1*6

2x -6x -3≥6

Combine like terms

-4x-3≥6

Add 3 to each side

-4x-3+3≥6+3

-4x ≥9

Divide each side by -4, remembering to flip the inequality

-4x/-4 ≤9/-4

x ≤-9/4

What is the length of the hypotenuse of the right angle defined by the points (-3,-1),(1,-1),and (1,2)?A)square root of 3
B)square root of 3
C) 2 timessquare root of 3
D)5

Answers

To find the length of the triangle first find the two coordinates with a common x coordinate, (1,-1) and (1,2). Now find the difference between their y coordinates, -1 and 2. This means that the length of the triangle is 3.
To find the width of the triangle first find the two coordinates with a common y coordinate, (-3,-1) and (1,-1). Now find the difference between their x coordinates, -3 and 1. This means that the width of the triangle is 4. 
By Pythagoras' theorem, we know that hypotenuse = \sqrt{ width^(2) + length^(2) }. Inserting our newfound values into this equation, we an find thelength of the hypotenuse:
hypotenuse = \sqrt{ 4^(2) +3^(2)} hypotenuse = √(16+9) hypotenuse =  √(x) 25hypotenuse = 5
Therefore, your answer is D0 5. To visualise this question better, you can plot the points on a graph. 

90 units needed 8units per case

Answers

Answer: 90/8=11.25

Step-by-step explanation:

The popular candy Skittles comes in 5 colors. According to the Skittles website, the 5 colors are evenly distributed in the population of Skittle candies. So each color makes up 20% of the population. Suppose that we purchase a small bag of Skittles. Assume this size bag always has 40 candies. In this particular bag 10 are green. What is the probability that a randomly selected bag of this size has 10 or more green candies

Answers

Answer:

27.76% probability that a randomly selected bag of this size has 10 or more green candies

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

√(V(X)) = √(np(1-p))

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = (X - \mu)/(\sigma)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = √(V(X)).

In this problem, we have that:

n = 40, p = 0.2

So

\mu = E(X) = np = 40*0.2 = 8

\sigma = √(V(X)) = √(np(1-p)) = √(40*0.2*0.8) = 2.53

What is the probability that a randomly selected bag of this size has 10 or more green candies

Using continuity correction, this is P(X \geq 10 - 0.5) = P(X \geq 9.5), which is 1 subtracted by the pvalue of Z when X = 9.5. So

Z = (X - \mu)/(\sigma)

Z = (9.5 - 8)/(2.53)

Z = 0.59

Z = 0.59 has a pvalue of 0.7224

1 - 0.7224 = 0.2776

27.76% probability that a randomly selected bag of this size has 10 or more green candies

Answer:

P(x\geq 10)=0.2682

Step-by-step explanation:

The number x of green candies in a bag of 40 candies follows a binomial distribution, because we have:

  • n identical and independent events: 40 candies
  • a probability p of success and (1-p) of fail: a probability of 0.2 to get a green candie and 0.8 to doesn't get a green candie.

So, the probability that in a bag of 40 candies, x are green is calculated as:

P(x)=(n!)/(x!(n-x)!)*p^(x)*(1-p)^(n-x)

Replacing, n by 40 and p by 0.2, we get:

P(x)=(40!)/(x!(40-x)!)*0.2^(x)*(1-0.2)^(40-x)

So, the probability that a randomly selected bag of this size has 10 or more green candies is equal to:

P(x\geq 10)=P(10)+P(11)+...+P(40)\nP(x\geq 10)=1-P(x<10)

Where P(x<10)=P(0)+P(1)+P(2)+P(3)+P(4)+P(5)+P(6)+P(7)+P(8)+P(9)

So, we can calculated P(0) and P(1) as:

P(0)=(40!)/(0!(40-0)!)*0.2^(0)*(1-0.2)^(40-0)=0.00013\nP(1)=(40!)/(1!(40-1)!)*0.2^(1)*(1-0.2)^(40-1)=0.00133

At the same way, we can calculated P(2), P(3), P(4), P(5), P(6), P(7), P(8) and P(9) and get that P(x<10) is equal to:

P(x<10)=0.7318

Finally, the probability P(x\geq 10) that a randomly selected bag of this size has 10 or more green candies is:

P(x\geq 10)=1-P(x<10)\nP(x\geq 10)=1-0.7318\nP(x\geq 10)=0.2682

Which of the following statements is not​ true? A. If the probability of an event occurring is​ 1.5, then it is certain that event will occur. B. If the probability of an event occurring is​ 0, then it is impossible for that event to occur.

Answers

Answer:

Therefore, we conclude that the statement in (A) is incorrect.

Step-by-step explanation:

We have the following sentences:

A) If the probability of an event occurring is​ 1.5, then it is certain that event will occur.  

B) If the probability of an event occurring is​ 0, then it is impossible for that event to occur.

We know that the range of probability of an event occurring is in the segment [0, 1]. In statement under (A), we have the probability that  is equal to 1.5.

Therefore, we conclude that the statement in (A) is incorrect.

A floor plan is drawn using a scale of (3 cm)/(15ft) What length is represented by 1 centimeter ?

Answers

Answer:

5 feet per 1 cm

Step-by-step explanation:

Answer:

The answer is 5 feet.

Step-by-step explanation:

Set up a proportion.

3/15 = 1/x (x being the number of feet)

Cross multiply.

3x = 15

Solve for x. (divide both sides by 3)

x = 5

I hope this helps! :)