Evaluate x2 + 4x + 1 when x = -3

Step-by-step explanation:

I think substitution would be the easiest since you already have one of the variables solved for.

[tex]y=-x^2+4x+5\\y=x+1\\x+1=-x^2+4x+5\\x^2-3x-4=0\\(x-4)(x+1)=0\\x-4=0\\x=4\\x+1=0\\x=-1[/tex]

(You can just set the equations equal to each other since they both equal y).

Now, to get the points, plug in x = 4 and x = -1 into one of the equations (I'm going to plug them into y = x+1 because that one is much simpler)

[tex]y(4)=4+1\\y(4)=5\\y(-1)=-1+1\\y(-1)=0[/tex]

So, your final points are:

(4,5) and (-1,0)

Answer: A

Step-by-step explanation:

We can use substitution to solve this problem. Since we are given y=-x²+4x+5 and y=x+1, we can set them equal to each other.

-x²+4x+5=x+1        [subtract both sides by x]

-x²+3x+5=1            [subtract both sides by 1]

-x²+3x+4=0

Now that we have the equation above, we can factor it to find the roots.

-x²+3x+4=0           [factor out -1]

-1(x²-3x-4)=0         [factor x²-3x-4]

-1(x+1)(x-4)=0

This tells us that x=-1 and x=4.

We can narrow down our answer to A, but let's plug in those values to be sure it is correct.

-(-1)²+4(-1)+5=(-1)+1      [exponent]

-1+4(-1)+5=-1+1              [multiply]

-1-4+5=-1+1                    [add and subtract from left to right]

0=0  

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

-(4)²+4(4)+5=(4)+1      [exponent]

-16+4(4)+5=4+1           [multiply]

-16+16+5=4+1              [add and subtract from left to right]

5=5

Therefore, we can conclude that A is the correct answer.

Some symbols and numbers are missing. I assume the system is supposed to read

2x - y + 2z + w = -3

x + 2y - 3z + w = 12

3x - y - z + 2w = 3

-2x + 3y + 2z - 3w = -3

In matrix form, this is

[tex]\begin{bmatrix}2&-1&2&1\\1&2&-3&1\\3&-1&-1&2\\-2&3&2&-3\end{bmatrix}\begin{bmatrix}x\\y\\z\\w\end{bmatrix}=\begin{bmatrix}-3\\12\\3\-3\end{bmatrix}[/tex]

which we can strip down to the augmented matrix,

[tex]\left[\begin{array}{cccc|c}2&-1&2&1&-3\\1&2&-3&1&12\\3&-1&-1&2&3\\-2&3&2&-3&-3\end{array}\right][/tex]

Now for the row operations:

• swap rows 1 and 2

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\2&-1&2&1&-3\\3&-1&-1&2&3\\-2&3&2&-3&-3\end{array}\right][/tex]

• add -2 (row 1) to row 2, -3 (row 1) to row 3, and 2 (row 1) to row 4

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&-7&8&-1&-33\\0&7&-4&-1&21\end{array}\right][/tex]

• add 7 (row 2) to -5 (row 3), and row 3 to row 4

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&16&-2&-24\\0&0&4&-2&-12\end{array}\right][/tex]

• multiply through rows 3 and 4 by 1/2

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&8&-1&-12\\0&0&2&-1&-6\end{array}\right][/tex]

• add -4 (row 4) to row 3

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&0&3&12\\0&0&2&-1&-6\end{array}\right][/tex]

• swap rows 3 and 4

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&-1&-6\\0&0&0&3&12\end{array}\right][/tex]

• multiply through row 4 by 1/3

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&-1&-6\\0&0&0&1&4\end{array}\right][/tex]

• add row 4 to row 3

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&0&-2\\0&0&0&1&4\end{array}\right][/tex]

• multiply through row 3 by 1/2

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]

• add -8 (row 3) and row 4 to row 2

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&0&0&-15\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]

• multiply through row 2 by -1/5

[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&1&0&0&3\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]

• add -2 (row 2) and 3 (row 3) and -1 (row 4) to row 1

[tex]\left[\begin{array}{cccc|c}1&0&0&0&-1\\0&1&0&0&3\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]

Then the solution to the system is (x, y, z, w) = (-1, 3, -1, 4).

Hello!

The answer is a.

Good luck! :)

Answer:

x=[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Hi there!

We are given the following equation:

[tex]\frac{4x}{5}[/tex]-[tex]\frac{1}{10}[/tex]=[tex]\frac{3}{10}[/tex]

and we need to find the value of x

To do this, we need to isolate the value of x with a coefficient of 1 (1x) on one side. The value of x, or everything else is on the other side

So let's get rid of [tex]\frac{1}{10}[/tex] from the left side by adding [tex]\frac{1}{10}[/tex] to both sides (-[tex]\frac{1}{10}[/tex]+[tex]\frac{1}{10}[/tex]=0).

[tex]\frac{4x}{5}[/tex]-[tex]\frac{1}{10}[/tex]=[tex]\frac{3}{10}[/tex]

  +[tex]\frac{1}{10}[/tex]  +[tex]\frac{1}{10}[/tex]

___________

[tex]\frac{4x}{5}[/tex]=[tex]\frac{3}{10}[/tex]+[tex]\frac{1}{10}[/tex]

as the fractions on the right side both have the same denominator, we can add them together

[tex]\frac{4x}{5}[/tex]=[tex]\frac{4}{10}[/tex]

Now we need to have the value of 1x. Currently we have [tex]\frac{4x}{5}[/tex].

In order to get x with a coefficient of 1, multiply both sides by the reciprocal of [tex]\frac{4}{5}[/tex], which is [tex]\frac{5}{4}[/tex]

[tex]\frac{5}{4}[/tex]×[tex]\frac{4x}{5}[/tex]=[tex]\frac{4}{10}[/tex]*[tex]\frac{5}{4}[/tex]

which simplifies down to

x=[tex]\frac{20}{40}[/tex]

Now reduce the fraction by dividing the numerator and denominator both by 20

x=[tex]\frac{1}{2}[/tex]

Hope this helps!  

Answer:

[tex]x = 28[/tex] ----- Banana

[tex]y = 54[/tex] ----- Almonds

[tex]z = 18[/tex] ---- Chocolate

Step-by-step explanation:

Let

[tex]x \to[/tex] banana

[tex]y \to[/tex] almonds

[tex]z \to[/tex] chocolate

So, we have:

[tex]x + y + z = 100[/tex] --- total used

[tex]4x + 8y + 6z = 652[/tex] -- i.e. 6.52 * 100 --- total sales from 100 pounds

[tex]y = 3z[/tex]

Required

The number of pounds of each (i.e. x, y and z)

Substitute [tex]y = 3z[/tex] in [tex]x + y + z = 100[/tex]

[tex]x + 3z + z = 100[/tex]

[tex]x + 4z = 100[/tex]

Make x the subject

[tex]x = 100 - 4z[/tex]

Substitute [tex]y = 3z[/tex] in [tex]4x + 8y + 6z = 652[/tex]

[tex]4x + 8 * 3z + 6z = 652[/tex]

[tex]4x + 24z + 6z = 652[/tex]

[tex]4x + 30z = 652[/tex]

Substitute [tex]x = 100 - 4z[/tex]

[tex]4(100 - 4z) + 30z = 652[/tex]

[tex]400 - 16z + 30z = 652[/tex]

Collect like terms

[tex]- 16z + 30z = 652-400[/tex]

[tex]14z = 252[/tex]

Divide by 14

[tex]z = 18[/tex]

Substitute [tex]z = 18[/tex] in [tex]x = 100 - 4z[/tex]

[tex]x = 100 - 4 * 18[/tex]

[tex]x = 100 - 72[/tex]

[tex]x = 28[/tex]

To calculate y, we have:

[tex]y = 3z[/tex]

[tex]y = 3 * 18[/tex]

[tex]y = 54[/tex]

Answer:

2x - 1

Step-by-step explanation:

that is the procedure above

Answer:

a. See the attached excel file for the frequency distribution table, and the attached photo for the histogram.

b. We have:

Mean = 16.7

Median = 15

Note: See the attached photo for the locations of Mean and Median on the histogram.

Step-by-step explanation:

a. Construct a frequency distribution of these days and display it as a histogram.

Note: See the attached excel file for the frequency distribution table, and the attached photo for the histogram.

b. Determine the mean and the median of the dad and mark their locations on the histogram.

From the attached excel file, we have:

Total of F = 10

Total of FX = 167

Therefore, we have:

Mean = 167 / 10 = 16.7

Median is the middle number after arranged the data in ascending or descending order. Using the ascending order, we have:

13 13 14 14 15 15 16 20 21 26

Since 15 and 15 are in the middle, their average are the median which is calculated as follows:

Median = (15 + 15) / 2 = 15

Note: See the attached photo for the locations of Mean and Median on the histogram.

Answer:

160cm^3

Step-by-step explanation:

5 x 4 x 8 = 160cm^3

Answer:

.

Step-by-step explanation:

.

Answer:

your can only divide then up in that specific sequence one time

Answer:

Slope: Undefined

Step-by-step explanation:

Since  x=1

is a vertical line, there is no y-intercept and the slope is undefined.  

y-intercept: No y-intercept

Answer:

C. 6

Step-by-step explanation:

Recall that inverse variation is given by:

[tex]\displaystyle y=\frac{k}{x}[/tex]

Where k is the constant of variation.

We know that y = 48 when x = 3. Substitute:

[tex]\displaystyle (48)=\frac{k}{(3)}[/tex]

Solve for k:

[tex]k=3(48)=144[/tex]

Hence, our equation is:

[tex]\displaystyle y=\frac{144}{x}[/tex]

We want to find x when y = 24. Substitute:

[tex]\displaystyle \frac{24}{1}=\frac{144}{x}[/tex]

Cross-multiply:

[tex]24x=144[/tex]

Divide both sides by 24. Hence:

[tex]x=6[/tex]

Our answer is C.

Answer:

0.1143 = 11.43% probability that all but one of them are using Chrome as their browser

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they use Chrome, or they do not. The probability of a person using Chrome is independent of any other person, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Chrome: 52.57%

This means that [tex]p = 0.5257[/tex]

Sample of 6 people

This means that [tex]n = 6[/tex]

What is the probability that all but one of them are using Chrome as their browser?

5 using Chrome, so:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{6,5}.(0.5257)^{5}.(1-0.5257)^{1} = 0.1143[/tex]

0.1143 = 11.43% probability that all but one of them are using Chrome as their browser

Answer:

the total number of participants required is 90

Step-by-step explanation:

Given the data in the question;

Factor A has three levels

Factor B has three levels

sample size n; ten participants

we have two Way ANOVA involving Factor A and Factor B.

Now,

{ Total # Participants Required } = { #Levels factor A } × { #Levels factor B } × { Sample size of each level }

we substitute

{ Total # Participants Required } = 3 × 3 × 10

{ Total # Participants Required } = 9 × 10

{ Total # Participants Required } = 90

Therefore, the total number of participants required is 90

Explanation:

There are 4 choices for first place, 3 choices for second place, and 2 choices for third place. Overall, there are 4*3*2 = 24 permutations.

Answer:

LCD????

[tex]2v^2x^3[/tex]

Step-by-step explanation:

Answer:

116ML every 3 hours, 928ML a day

Step-by-step explanation:

You said it yourself if there is 29ML in one once and you need 4 ounces every 3 hours then 29 x 4 = 116.

Answer:

[tex]P(Green\ and\ Green) = \frac{25}{144}[/tex]

Step-by-step explanation:

Given

[tex]Green=5[/tex]

[tex]Blue = 7[/tex]

Required

[tex]P(Green\ and\ Green)[/tex]

This is calculated as:

[tex]P(Green\ and\ Green) = P(Green) * P(Green)[/tex]

Since, it is a probability with replacement, we have:

[tex]P(Green\ and\ Green) = \frac{Green}{Total} * \frac{Green}{Total}[/tex]

So, we have:

[tex]P(Green\ and\ Green) = \frac{5}{12} * \frac{5}{12}[/tex]

[tex]P(Green\ and\ Green) = \frac{25}{144}[/tex]

9514 1404 393

Answer:

  a-b

Step-by-step explanation:

Add the two equations together:

  (ax +by) +(bx +ay) = (a² -b²) +(0)

  x(a +b) +y(a +b) = (a +b)(a -b)

  x + y = a - b . . . . . divide by (a+b), assuming a+b ≠ 0

This is one single number slightly over 17 thousand.

You may need to erase the comma when typing the answer in.

=========================================================

Explanation:

Let's say that another person steps in for Joe, Susan, John, and Meredith. I'll refer to this person as the teacher (perhaps these 9 friends are students on a field trip).

The 9 friends drops to 9-4 = 5 people when those four named people leave the group temporarily. Then it bumps up to 5+1 = 6 people when the teacher steps in. Wherever the teacher is located, the four friends that left will replace the teacher. This guarantees that those four friends stick together.

There are 6! = 6*5*4*3*2*1 = 720 ways to arrange those 6 people. The exclamation mark is a factorial symbol.

Within any of those 720 permutations, we have 4! = 4*3*2*1 = 24 ways to arrange those group of named people when they come back to replace the teacher.

So overall the answer is 4!*6! = 24*720 = 17,280

You may need to erase the comma when typing the answer in.

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

Side note: There are 9! = 362,880 ways to arrange all nine friends regardless if those four mentioned people stick together or not. We see that they stick together roughly (17,280)/(362,880) = 0.0476 = 4.76% of the time.

Answer:

y 9 5 473648

Step-by-step explanation:

Answer:

see graph

Step-by-step explanation:

Answer:

t could be all real numbers.

Step-by-step explanation:

The function D(t) is given by:

[tex]D(t)=-1.5t+12[/tex]

The domain is all the posible x-values for which the function is defined.

In our case, t could be all real numbers.

The answer is the first option.

I hope it helps you!

Answer:

If you are working with equilateral triangles, divide 180 by three to find the value of X. All of the angles of an equilateral triangle are equal. Solve for X in interesting lines by finding the value of one adjacent angle and subtracting it from 180 degrees.

Step-by-step explanation:

Answer:

x = 5 and y = 1.5

Step-by-step explanation:

hope this helps please like and mark as brainliest

I think it might be the 3rd option

Step-by-step explanation: