function g can be thought of as a translated (shifted) version of f(x)=|x|

Answer:

Option (3)

Step-by-step explanation:

Given question is incomplete; here is the complete question.

The function f(x) = –x2 – 4x + 5 is shown on the graph. Which statement about the function is true?

The domain of the function is all real numbers less than or equal to −2.

The domain of the function is all real numbers less than or equal to 9.

The range of the function is all real numbers less than or equal to −2.

The range of the function is all real numbers less than or equal to 9

By using a graph tool we get a parabola opening downwards.

Since domain of a function is represented by x-values and range by y-values.

Domain of the given function will be (-∞, ∞)

Range of the function will be (-∞, 9] Or a set of all real numbers less thn equal to 9.

Therefore, Option (3) will be the answer.

Step-by-step explanation:

here,

31 cup of milk require 41 cup of water.

1 cup of milk require 41/31 cup of water.

so, 41/31 cup of water is required for 1 cup of milk.

hope u get it..

Answer:

if you would travel 50km/h then the time will be 2.4hours

Step-by-step explanation:

speed=v1=60km/h

time=t1=2h

speed=v2=50km/h

time=t2=?

as we know that

v1×t1=v2×t2

evaluating the expression

(v1×t1)/v2=t2

putting values

[tex]\frac{60km/h*2h}{50km/h}=t2[/tex]

[tex]\frac{120km/h^2}{50km/h}=t2[/tex]

2.4hours=t2

i hope this will help you :)

Answer:

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = expected outcome/total outcome

Since a six-sided die is rolled, the total outcome will be the total number of possible siedes a die contain {1, 2, 3, 4, 5, 6} i.e 6 elements

If a number less than 2 is gotten, the expected outcome will be {1} i.e 1 element.

Probability of getting a number less than 2 = 1/6

If a prime number is gotten, the outcome will be the elements {2, 3, 5} i.e 3 elements.

The probability of getting a prime number = 3/6 = 1/2

The probability of getting a number less than 2 OR a prime number upon rolling a six-sided die will be 1/6*1/2 = 1/18

Answer:

Step-by-step explanation:

On a six-sided die, there is only one way to get a number less than 2, which is by rolling a 1.  So the probability of getting a number less than 2 is:

P left parenthesis l e s s space t h a n space 2 right parenthesis equals 1 over 6

There are three primes numbers when rolling a six-sided die, which are {2, 3, 5}.  So the probability of getting a prime number is:

P left parenthesis p r i m e right parenthesis equals 3 over 6

Since there is no overlap between these two events, the probability of getting a number less than 2 OR a prime number is:

P left parenthesis l e s s space t h a n space 2 space o r space p r i m e right parenthesis equals P left parenthesis l e s s space t h a n space 2 right parenthesis plus P left parenthesis p r i m e right parenthesis equals 1 over 6 plus 3 over 6 equals 4 over 6 equals 2 over 3

Answer is 2/3

Answer:

a

The Null hypothesis represented as

     [tex]H_0: \mu_1 - \mu_2 = 0[/tex]

The Alternative hypothesis represented as

     [tex]H_a: \mu_1 - \mu_2 < 0[/tex]

b

p-value =  P(Z <  -3.37  )  = 0.000376

c

There is insufficient evidence to conclude that graduate students score higher, on average, on the HPI than undergraduate students

Step-by-step explanation:

From the question we are told that

   The population size is  [tex]n= 650[/tex]

    The  sample size for graduates is  [tex]n_1 = 300[/tex]

     The sample  mean for graduates is [tex]\= x _1 = 148[/tex]

      The sample  standard deviation for graduates is [tex]\sigma_1 = 16[/tex]

    The  sample size for under-graduates is [tex]n _2 = 350[/tex]

         The sample  mean for under-graduates is [tex]\= x _2 = 153[/tex]

         The sample  standard deviation for graduates is [tex]\sigma_2 = 21[/tex]

The Null hypothesis represented as

     [tex]H_0: \mu_1 - \mu_2 = 0[/tex]

The Alternative hypothesis represented as

     [tex]H_a: \mu_1 - \mu_2 < 0[/tex]

Where [tex]\mu_1 \ and \ \mu_2[/tex] are the population mean

  Now the test statistic is mathematically represented as

          [tex]t = \frac{(\= x_1 - \= x_2 ) }{ \sqrt{ \frac{ (n_1 - 1 )\sigma_1 ^2 + (n_2 - 1)\sigma_2^2}{n_1 +n_2 -2} } * \sqrt{ \frac{1}{n_1} + \frac{1}{n_2} } }[/tex]

substituting values

       [tex]t = \frac{(148 - 153 ) }{ \sqrt{ \frac{ (300- 1 )16 ^2 + (350 - 1) 21^2}{300 +350 -2} } * \sqrt{ \frac{1}{300} + \frac{1}{350} } }[/tex]

      [tex]t = -3.37[/tex]

The p-values is mathematically evaluated as

     p-value =  P(Z <  -3.37  )  = 0.000376

The above answer is gotten using a p-value calculator  at (0.05) level of significance

     Looking the p-value we see that it is less than the level of significance (0.05)  so Null hypothesis is rejected

Hence there is insufficient evidence to conclude that graduate students score higher, on average, on the HPI than undergraduate students

Following are the two-Sample of the T-Test and CI:

[tex]\boxed{\boxed{\begin{matrix}Sample& N &Mean& StDev& SEMean\\ 1 &350 &153.0& 21.0 &1.1 \\ 2& 300& 148.0& 16.0& 0.92\end{matrix}}}[/tex]

Calculating the difference:

[tex]= \mu (1) - \mu (2)\\\\[/tex]

The estimated difference: [tex]5.00[/tex]

When the [tex]95\%[/tex] of CI so, the difference:[tex](2.09, 7.91)[/tex]

Therefore the T-Test difference value = 0

[tex]\to (vs \neq): T-Value = 3.37 \\\\\to P-Value = 0.001 \\\\\to DF = 648[/tex]

When the both use Pooled so, the StDev = 18.8583

Therefore, the final value of t is "3.37".

Learn more:

brainly.com/question/16380581

Answer: P(t) = 1.25.sin([tex]\frac{\pi}{3}[/tex].t) + 5.65

Step-by-step explanation: A motion repeating itself in a fixed time period is a periodic motion and can be modeled by the functions:

y = A.sin(B.t - C) + D or y = Acos(B.t - C) + D

where:

A is amplitude A=|A|

B is related to the period by: T = [tex]\frac{2.\pi}{B}[/tex]

C is the phase shift or horizontal shift: [tex]\frac{C}{B}[/tex]

D is the vertical shift

In this question, the motion of Pluto is modeled by a sine function and doesn't have phase shift, C = 0.

Amplitude:

a = [tex]\frac{largest - smallest}{2}[/tex]

At t=0, Pluto is the farthest from the sun, a distance 6.9 billions km away. At t=66, it is closest to the star, P(66) = 4.4 billions km. Then:

a = [tex]\frac{6.9-4.4}{2}[/tex]

a = 1.25

b

A time period for Pluto is T=66 years:

66 = [tex]\frac{2.\pi}{b}[/tex]

b = [tex]\frac{\pi}{33}[/tex]

Vertical Shift

It can be calculated as:

d = [tex]\frac{largest+smallest}{2}[/tex]

d = [tex]\frac{6.9+4.4}{2}[/tex]

d = 5.65

Knowing a, b and d, substitute in the equivalent positions and find P(t).

P(t) = a.sin(b.t) + d

P(t) = 1.25.sin([tex]\frac{\pi}{3}[/tex].t) + 5.65

The Pluto's distance from the sun as a function of time is

P(t) = 1.25.sin([tex]\frac{\pi}{3}[/tex].t) + 5.65

Answer:

P(t) = 1.25.sin(.t) + 5.65

Step-by-step explanation:

Answer:

6*2 = 12

Step-by-step explanation:

2 + 2 + 2 + 2 + 2 + 2 = 12

There are six 2's being added together

6*2 = 12

Answer: 2*6

Step-by-step explanation:

There are 6 2's shown in the question.  Thus, simply do 6*2.

Hope it helps <3

Answers:

A ' = (-2, -3)

B ' = (0, -3)

C ' = (-1, 1)

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

Explanation:

To apply an x axis reflection, we simply change the sign of the y coordinate from positive to negative, or vice versa. The x coordinate stays as is.

Algebraically, the reflection rule used can be written as [tex](x,y) \to (x,-y)[/tex]

Applying this rule to the three given points will mean....

The diagram is provided below.

Side note: Any points on the x axis will stay where they are. That isn't the case here, but its for any future problem where it may come up. This only applies to x axis reflections.

Answer:

(-2,-3)...(0,-3)...(-1,1)

Step-by-step explanation:

Answer:

a) 21.58% probability that exactly 3 people are repeat offenders

b) 97.91% probability that at least one person is a repeat offender

c) 3.69

d) 1.83

Step-by-step explanation:

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.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders

This means that [tex]p = 0.09[/tex]

41 people arrested for DUI in Illinois are selected at random.

This means that [tex]n = 41[/tex]

a. What is the probability that exactly 3 people are repeat offenders?

This is P(X = 3).

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

[tex]P(X = 3) = C_{41,3}.(0.09)^{3}.(0.91)^{38} = 0.2158[/tex]

21.58% probability that exactly 3 people are repeat offenders

b. What is the probability that at least one person is a repeat offender?

Either none are repeat offenders, or at least one is. The sum of the probabilities of these outcomes is 1. So

[tex]P(X = 0) + P(X \geq 1) = 1[/tex]

We want [tex]P(X \geq 1)[/tex].

Then

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = 0) = C_{41,0}.(0.09)^{0}.(0.91)^{41} = 0.0209[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0209 = 0.9791[/tex]

97.91% probability that at least one person is a repeat offender

c. What is the mean number of repeat offenders?

[tex]E(X) = np = 41*0.09 = 3.69[/tex]

d. What is the standard deviation of the number of repeat offenders?

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{41*0.09*0.91} = 1.83[/tex]

Answer:

First one is (x+2.4)

Second one is 4(x+2.4)=14.8

Step-by-step explanation:

Answer:

What expression would represent how far Bijan runs everyday?

✔ (x + 2.4)

What is the equation that represents his total distance after 4 days?

✔ 4(x + 2.4) = 14.8

Step-by-step explanation: I TOOK THE TEST

Answer:

1/7

Step-by-step explanation:

There are 7 cards, 1 of which is less than 2. Therefore, P (less then 2) = 1/7

Answer:

1/7

Step-by-step explanation:

The number from the list that is less than 2 is 1.

1 number out of a total of 7 numbers.

= 1/7

Answer:

A 90% confidence interval for the mean weight is [21.78 ounces, 21.98 ounces].

Step-by-step explanation:

We are given the weights, in the ounces, of a sample of 12 boxes below;

Weights (X): 21.88, 21.76, 22.14, 21.63, 21.81, 22.12, 21.97, 21.57, 21.75, 21.96, 22.20, 21.80.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                         P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean weight = [tex]\frac{\sum X}{n}[/tex] = 21.88 ounces

            s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex]  = 0.201 ounces

            n = sample of boxes = 12

            [tex]\mu[/tex] = population mean weight

Here for constructing a 90% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 90% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-1.796 < [tex]t_1_1[/tex] < 1.796) = 0.90  {As the critical value of t at 11 degrees of

                                                  freedom are -1.796 & 1.796 with P = 5%}  

P(-1.796 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.796) = 0.90

P( [tex]-1.796 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.796 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90

P( [tex]\bar X-1.796 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.796 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90

90% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.796 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.796 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                        = [ [tex]21.88-1.796 \times {\frac{0.201}{\sqrt{12} } }[/tex] , [tex]21.88+1.796 \times {\frac{0.201}{\sqrt{12} } }[/tex] ]

                                        = [21.78, 21.98]

Therefore, a 90% confidence interval for the mean weight is [21.78 ounces, 21.98 ounces].

Answer:

2049.

Step-by-step explanation:

2045 - 1983 = 62 years.

So the competition will take place in 1983 + 60 = 2043.

After 2045  the competition takes place in 2049.

Answer:

0.65

Step-by-step explanation:

There are 65 student that do sports as 20+20+25=65. In total there are 100 student and you find this by adding up all the values. Now all you do is divide 65/100 and get 0.65 and that is the probability a random student plays sports.

Answer:

Domain : (-∞, ∞)

Range : (-∞, ∞)

Step-by-step explanation:

Parent function (y = [tex]\sqrt[3]{x}[/tex] ) of the given function y = -[tex]\sqrt[3]{x}[/tex] has been shown as the dotted line on the graph.

Solid curve represents the function,

y = [tex]-\sqrt[3]{x}[/tex]

Therefore, Domain of this function will be (-∞, ∞) Or x ∈ set of all real numbers.

And Range of the function will be (-∞, ∞) Or y ∈ set of all real numbers

Answer:

CI: {0.4085; 0.6647}

Step-by-step explanation:

The confidence interval for a proportion (p) is given by:

[tex]p \pm z*\sqrt{\frac{(1-p)*p}{n} }[/tex]

Where n is the sample size, and z is the z-score for the desired confidence interval. The score for a 90% confidence interval is 1.645. The proportion of depositors who ask for cash back is:

[tex]p=\frac{22}{41}=0.536585[/tex]

Thus the confidence interval is:

[tex]0.536585 \pm 1.645*\sqrt{\frac{(1-0.536585)*0.536585}{41}}\\0.536585 \pm 0.128109\\L=0.4085\\U=0.6647[/tex]

The confidence interval for the proportion of all depositors who ask for cash back is CI: {0.4085; 0.6647}

Answer:

xy-19x+3y-57

Step-by-step explanation:

Once again, FOIL is the way to go!

First, Outside, Inside, Last

xy-19x+3y-57

Answer:

xy-19x+3y-57

Step-by-step explanation:

(x+3)(y-19)

FOIL

first: xy

outer: -19x

inner 3y

last  -57

Add them together

xy-19x+3y-57

Answer:

Given,

X=2

y=-2

z=3

Now,

[tex]3x + y - z \\ = 3 \times 2 + ( - 2) - 3 \\ = 6 + ( - 2) - 3 \\ = 6 - 2 - 3 \\ = 4 - 3 \\ = 1[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

1

Step-by-step explanation:

3X+Y-Z

Where X = 2, Y = -2 amd Z = 3

=> 3(2)+(-2)-(3)

=> 6-2-3

=> 4-3

=> 1

Answer:

so

slope is calculated this way:

[tex] \frac{3 - 6}{2 - 1} = \frac{ - 3}{1} = - 3[/tex]

let's calculate y init by:

3 = -3×2 + b

b = 9

so equation is:

y=-3x+9

Answer:

he additive inverse of:

a)  [tex]-6x^2-x-2[/tex] is : [tex]6x^2+x+2[/tex]

b)  [tex]6x^2-x+2[/tex]  is :  [tex]-6x^2+x-2[/tex]

c)  [tex]6x^2+x-2[/tex]  is :  [tex]-6x^2-x+2[/tex]

d)  [tex]6x^2+x+2[/tex]  is :  [tex]-6x^2-x-2[/tex]

Step-by-step explanation:

You need to consider that the additive inverse of a polynomial is that polynomial that consists of the opposite of each term of the polynomial given.

Then, the additive inverse of:

a)  [tex]-6x^2-x-2[/tex] is :  [tex]6x^2+x+2[/tex]

b)  [tex]6x^2-x+2[/tex]  is :  [tex]-6x^2+x-2[/tex]

c)  [tex]6x^2+x-2[/tex]  is :  [tex]-6x^2-x+2[/tex]

d)  [tex]6x^2+x+2[/tex]  is :  [tex]-6x^2-x-2[/tex]

Answer:

(190-5a)°

Step-by-step explanation:

Sum of internal angles of a triangle equals to 180°

If the third angle is x, then we have:

The third angle is: (190-5a)°

Answer:

area = 36 ft²

Step-by-step explanation:

no figure has been given ..

therefore,  area of a triangle = 1/2 * b * h

assume b = 6 ft

assume h = 12 ft

area = 1/2 * 6 * 12

area = 36 ft²

Answer:

The common difference is 1/2

Step-by-step explanation:

Data obtained from the question include:

3rd term (a3) = 0

Common difference (d) =.?

From the question given, we were told that the 7th term (a7) and the 4th term (a4) are related by the following equation:

a7 – 2a4 = 1

Recall:

a7 = a + 6d

a4 = a + 3d

a3 = a + 2d

Note: 'a' is the first term, 'd' is the common difference. a3, a4 and a7 are the 3rd, 4th and 7th term respectively.

But, a3 = 0

a3 = a + 2d

0 = a + 2d

Rearrange

a = – 2d

Now:

a7 – 2a4 = 1

Substituting the value of a7 and a4, we have

a + 6d – 2(a + 3d) = 1

Sustitute the value of 'a' i.e –2d into the above equation, we have:

–2d + 6d – 2(–2d + 3d) = 1

4d –2(d) = 1

4d –2d = 1

2d = 1

Divide both side by 2

d = 1/2

Therefore, the common difference is 1/2

***Check:

d = 1/2

a = –2d = –2 x 1/2 = –1

a3 = 0

a3 = a + 2d

0 = –1 + 2(1/2)

0 = –1 + 1

0 = 0

a7 = a + 6d = –1 + 6(1/2) = –1 + 3 = 2

a4 = a + 3d = –1 + 3(1/2) = –1 + 3/2

= (–2 + 3)/2 = 1/2

a7 – 2a4 = 1

2 – 2(1/2 = 1

2 – 1 = 1

1 = 1

Answer:

Step-by-step explanation:

Given:

  c/2 -5 = 7

  Step 1: c/2 -5 +5 = 7 +5

  Step 2: c/2 +0 = 12

  Step 3: c/2 = 12

  Step 4: 2(c/2) = 12(2)

  Step 5: c = 24

Find:

  The property that justifies each step of the solution.

Solution:

  Step 1: addition property of equality (lets you add the same to both sides)

  Step 2: integers are closed to addition

  Step 3: identity property of addition (adding 0 changes nothing)

  Step 4: multiplication property of equality

  Step 5: closure of real numbers to multiplication; identity property of multiplication

_____

It is hard to say what "property" you want to claim when you simplify an arithmetic expression. Above, we have used the property that the sets of integers and real numbers are closed to addition and multiplication. That is, adding or multiplying real numbers gives a real number.

In Step 5, we can rearrange 2(c/2) to c(2/2) using the commutative property of multiplication. 2/2=1, and c×1 = c. The latter is due to the identity element for multiplication: multiplying by 1 changes nothing.

Apart from the arithmetic, the other properties used are properties of equality.  Those let you perform any operation on an equation, as long as you do it to both sides of the equation. The operations we have performed in this fashion are adding 5 and multiplying by 2.

Answer:

Step 1 ~ addition property of equality

Step 2 ~ additive inverses

Step 3 ~ additive identity

Step 4 ~ multiplication property of equality

Explanation:

Addition property of equality means that If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal. In this problem, they added 5 to both sides to make the equation balanced.

Additive inverses means what you add to a number to get zero.  The negative of a number. -5 + 5 = 0.

Additive identity means that the sum of a number and 0 is that number.

Multiplication property of equality states that when you multiply both sides of an equation by the same number, the two sides remain equal. In this problem, they multiplied 2 to both sides to get rid of the denominator in the fraction.

Answer:

c = 6.25

Step-by-step explanation:

We are given the following piecewise function:

[tex]\left \{ {{cx^{2} + 2x, x < 3} \atop {3x^{3} - cx, x \geq 3}} \right[/tex]

Continuous function:

A function f(x) is continuous, at a point a, if:

[tex]\lim_{x \to a} f(x)[/tex] exists and [tex]\lim_{x \to a} f(x) = f(a)[/tex]

In this question:

Piece-wise function, so we have to verify if the limit exists.

The function changes at x = 3. So we verify at a = 3.

It will exist if:

[tex]\lim_{x \to 3^{-}} f(x) = \lim_{x \to 3^{+}} f(x)[/tex]

To the left:

Less than 3.

[tex]\lim_{x \to 3^{-}} f(x) = \lim_{x \to 3^{-}} cx^{2} + 2x = c*(3)^{2} + 2*3 = 9c + 6[/tex]

To the right:

Greater than 3.

[tex]\lim_{x \to 3^{+}} f(x) = \lim_{x \to 3^{+}} 3x^{3} - cx = 3*3^{3} - 3c = 81 - 3c[/tex]

f continuous:

They have to be equal:

[tex]\lim_{x \to 3^{-}} f(x) = \lim_{x \to 3^{+}} f(x)[/tex]

[tex]9c + 6 = 81 - 3c[/tex]

[tex]12c = 75[/tex]

[tex]c = \frac{75}{12}[/tex]

[tex]c = 6.25[/tex]

Answer:

B. -1.

Step-by-step explanation:

[tex]i^1[/tex] = i

[tex]i^2 = -1[/tex]

[tex]i^3 = -i[/tex]

[tex]i^4 = 1[/tex]

...And it keeps going in a pattern, from i to -1 to -i to 1. And so, we have four values.

34 / 4 = 8 with a remainder of 2. That means that the value of [tex]i^{34}[/tex] is the same thing as [tex]i^2\\[/tex], so it is B. -1.

Hope this helps!

Answer:

a) P(A∩B) = 0.29

b) P1 = 0.1

c) P = 0.35

Step-by-step explanation:

Let's call A the event that the motorist stop at the first signal, and B the event that the motorist stop at the second signal.

From the question we know:

P(A) = 0.39

P(B) = 0.54

P(A∪B) = 0.64

Where P(A∪B) is the probability that he stop in the first, the second or both signals. Additionally, P(A∪B) can be calculated as:

P(A∪B)  = P(A) + P(B) - P(A∩B)

Where P(A∩B) is the probability that he stops at both signals.

So, replacing the values and solving for P(A∩B), we get:

0.64 = 0.39 + 0.54 - P(A∩B)

P(A∩B) = 0.29

Then, the probability P1 that he just stop at the first signal can be calculated as:

P1 = P(A) - P(A∩B) = 0.39 - 0.29 = 0.1

At the same way, the probability P2 that he just stop at the second signal can be calculated as:

P2 = P(B) - P(A∩B) = 0.54 - 0.29 = 0.25

Finally, the probability P that he stops at exactly one signal is:

P = P1 + P2 = 0.1 + 0.25 = 0.35

Hey there! :)

Answer:

Last option. (-1, 0) and (0, 6).

Step-by-step explanation:

Solve this system by setting the two equations equal to each other:

6x + 6 = -x² + 5x + 6

Rearrange the equation:

x² + 6x + 6 - 5x - 6 = 0

Combine like terms:

x² + x = 0

Factor out x:

x(x + 1) = 0

Set each factor equal to 0:

x = 0

x + 1 = 0

x = -1

These are the x values of the solutions. Plug these into an equation to solve for y:

y = 6(0) + 6

y = 6

-------

y = 6(-1) + 6

y = -6 + 6

y = 0

Therefore, the solutions to the equation are (-1, 0) and (0, 6).

Step-by-step explanation:

yeah,when 15-7=8

the number is 8