f(x)=x^2+x-30

complete the square

Answer:

[tex](x-3)^{2} +(y+2)^{2}=9[/tex]

Step-by-step explanation:

we know that

the equation of a circle into center radius form is equal to

[tex](x-h)^{2} +(y-k)^{2}=r^{2}[/tex]

In this problem we have

center ( 3,-2)

radius r=3 units

substitute

[tex](x-3)^{2} +(y+2)^{2}=3^{2}[/tex]

[tex](x-3)^{2} +(y+2)^{2}=9[/tex]

Answer: A on edg

Step-by-step explanation:

Answer:

Option A. [tex]10\ units^{2}[/tex]

Step-by-step explanation:

we know that

The area of the rectangle is equal to

A=LW

where

L is the length of rectangle

W is the width of rectangle

we have

[tex]A(-3,1),B(-2,-1),C(2,1),D(1,3)[/tex]

Plot the vertices

see the attached figure

L=AD=BC

W=AB=DC

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Find the distance AD

[tex]A(-3,1),D(1,3)[/tex]

substitute in the formula

[tex]AD=\sqrt{(3-1)^{2}+(1+3)^{2}}[/tex]

[tex]AD=\sqrt{(2)^{2}+(4)^{2}}[/tex]

[tex]AD=\sqrt{20}[/tex]

[tex]AD=2\sqrt{5}\ units[/tex]

Find the distance AB

[tex]A(-3,1),B(-2,-1)[/tex]

substitute in the formula

[tex]AB=\sqrt{(-1-1)^{2}+(-2+3)^{2}}[/tex]

[tex]AB=\sqrt{(-2)^{2}+(1)^{2}}[/tex]

[tex]AB=\sqrt{5}[/tex]

[tex]AB=\sqrt{5}\ units[/tex]

Find the area

[tex]A=(2\sqrt{5})*(\sqrt{5})=10\ units^{2}[/tex]

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This result represents the total area under the curve y = x^2 + 4 between x = -3 and x = 2.

The area under the curve y = x^2 + 4 on the interval [-3,2] can be found using definite integration. The definite integral of a function gives us the net area between the function and the x-axis across the specified interval. To compute the area, we set up the integral from -3 to 2 of the function x^2 + 4.

To solve this, we integrate the function with respect to x:

This result represents the total area under the curve y = x^2 + 4 between x = -3 and x = 2.

Answer:

The point was reflected over the y-axis.

The point was translated left 6 units

Step-by-step explanation:

step 1

we know that

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite

In this problem

If you apply a reflection across the y-axis

(x.y)------> (-x,y)

(3,-2) ------> (-3,-2)

step 2

If you apply a translation to the left 6 units

The rule of the translation is equal to

(x,y)------> (x-6,y)

(3,-2) ------> (3-6,-2) ----> (-3,-2)

Answer: x÷(2÷5y)

Step-by-step explanation: this is because you have to first do the quotient of 2 and try then the answer will be divided by 5

Answer:

The quotient of x and the quotient of 2 and 5y.

Expression:

x/(2/5y)

Explanation:

The quotient means to divide the numbers. The “and” after quotient is what the number is dividing with. So, x us dividing with the division of 2 and 5y.

Hello There!

The value of the number "5" in the number 15,406 would be the value of 5,000

Answer:

24649-17424=7225 UNITS

Step-by-step explanation:

This step implies that Lara was using the Pythagoras theorem to find the missing length of the right triangle.

a²+b²=c², taking a and b to be the  two lengths adjoined by the right angle and c the hypotenuse.

Laura's step represents the step above.

157²=24649

132²=17424

157²-132²=c²

24649-17424=7225

Answer:

At 11:30 am they will arrive at their starting point together

Step-by-step explanation:

we know that

One of them completes one lap in 6 minutes

The second one in 9 minutes

The third one in 15 minutes

step 1

Find the least common multiple (LCM)

6=2*3

9=3²

15=3*5

so

LCM=(3²)*(2)*(5)=90 minutes

step 2

Find the number of laps of each jogger for the LCM

jogger 1

90/6=15 laps

jogger 2

90/9=10 laps

jogger 3

90/15=6 laps

If they start at 10:00 am

then

10:00 am + 90 minutes=11:30 am

Answer:

y = - 3x + 16

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{3}[/tex] x + 8 ← is in slope- intercept form

with slope m = [tex]\frac{1}{3}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3, so

y = - 3x + c ← is the partial equation of the perpendicular line

To find c substitute (6, - 2) into the partial equation

- 2 = - 18 + c ⇒ c = - 2 + 18 = 16

y = - 3x + 16 ← equation of perpendicular line

Answer:

p=0.125

Step-by-step explanation:

2p+6p=1

Add like terms

8p=1

Divide both sides by 8 to get p by itself

8p/8=1/8

p=0.125

Answer:

Simplify 4y + 7x = 2t and there you go that's your answer☺

Step-by-step explanation:

Bucket = y

Jars = x

Tubs = t

y + 5x = t

3y + 2x = t

Answer:

Number of jars in one tub is:

13

Step-by-step explanation:

Let b denote the buckets, j denotes the jars and t denotes the tubs

One bucket + 5 jars equal one tub

b+5j=t   ----------------(1)

Three buckets plus two jars equal two tubs

3b+2j=2t   ------------------(2)

equation (1)×3- equation (2)

3(b+5j)-(3b+2j)= 3t-2t

3b+15j-3b-2j= t

13j= t

Hence, Number of jars in one tub is:

13

Answer: It can not be a mixed number because if you divide -27 by 50 you get -0.54, so then if you turn -0.54 in fraction form it would be -27/50, so the fraction would stay the way it is. -27/50 is not an improper fraction. To be improper, the numerator must be greater than the denominator!

* Hopefully this helps:) Mark me the brainliest:)!!!

Answer:

You had it correctly chosen, (9, infinity)

Step-by-step explanation:

Good job =)

ANSWER

[9,∞)

EXPLANATION

The given radical function is ;

[tex]f(x) = \sqrt{x - 9} [/tex]

This function is defined if and only if the expression under the radical sign is greater than or equal to zero.

[tex]x - 9 \geqslant 0[/tex]

[tex]x \geqslant 9[/tex]

Or

In interval notation, we have

[9,∞)

ANSWER

a. 16

b. 1

c. 64

d. 64

EXPLANATION

We want to simplify the following exponential expressions

a.

[tex] {2}^{4} [/tex]

This implies that

[tex] {2}^{4} = 2 \times 2 \times 2 \times 2[/tex]

[tex] {2}^{4} = 16[/tex]

b. Any non-zero number exponent zero is 1.

This implies that,

[tex] {3}^{0} = 1[/tex]

c. The given exponentiial expression is,

[tex] {4}^{6} \times {4}^{ - 3} [/tex]

The bases are the same so we add the exponents.

[tex] {4}^{6} \times {4}^{ - 3} = {4}^{6 + - 3} [/tex]

This simplifies to,

[tex]{4}^{6} \times {4}^{ - 3} = {4}^{3} [/tex]

[tex]{4}^{6} \times {4}^{ - 3} = 4 \times 4 \times 4 = 64[/tex]

d. We want to simplify:

[tex] { ({2}^{3}) }^{2} [/tex]

This is the same as

[tex]{ ({2}^{3}) }{ ({2}^{3}) }[/tex]

We add the exponents now to get:

[tex]{2}^{3 + 3} = {2}^{6} = 64[/tex]

Answer:

-13 < 16

Step-by-step explanation:

(4 is x, -5 is y)

-5 - 8 < 4(4)

-13 < 16

It is true and is a solution

Answer:

The ordered pair is not a solution to the inequality because -13 < -16 is false.

Step-by-step explanation:

Step 1: Plug x and y into the inequality

-5 - 8 < -4(4)

Step 2: Simplify the inequality

-13 < -16

Step 3: Interpret and conclude

The ordered pair is not a solution to the inequality because -13 < -16 is false.

Answer:

The answer B

Step-by-step explanation:

Answer:

13/6

Step-by-step explanation:

-6 1/3 + 5 5/6

1. You can reduce the first equation to 2

-6 1/3, becomes -2 x 1/1. This is because 3 goes into itself 1 time, and it goes into 6, -2 times. Your new equation: -2 + 5 5/6

2. Multiply the 5's in 5 5/6 by each other to get...

25/6

Your new equation: -2 + 25/6

3. Multiply 6 by -2 to get -12

4. Now add the numerators(remember -12 is basically, -12/1) together to get your answers

-12 + 25/6 = 13/6

Hello There!

If we add -6 1/3 and 5 5/6 together, we will get a sum of -1/2

STEP 1 First, I like to convert mixed numbers into improper fractions because they are easier to work with. So, I would change -6 1/3 to -19/3. Then, I would change 5 and 5/6 to 35/6.

STEP 2 Applying the fraction formula for addition. (-19x6) + (35x3) and then i would put this over 6x3

STEP 3   -114+105

                      18

STEP 4

-9/18 = -1/2

Final answer:

To solve the equation ax - y = bx for x, add y to both sides, combine x terms, factor x out, and divide by (a - b) resulting in the solution x = y / (a - b).

Explanation:

To solve the given equation ax - y = bx for x, we aim to isolate x on one side of the equation:

First, we add y to both sides of the equation: ax = bx + y.

Next, we group the x terms together: ax - bx = y.

Then, we factor out x: x(a - b) = y.

Finally, we divide both sides by (a - b) to solve for x: x = y / (a - b).

So, the solution is x = y / (a - b).

Answer:

Kristen would be 7.5 yo and Nicole would be 24.5 years old

Step-by-step explanation:

let x= kristen's age

3x+2= nicole's age

(3x+2)+x=32

4x+2=32

4x=30

x=7.5

3(7.5)+2= 24.5

Answer:

The Average rate of change (the slope) is -4/3

Step-by-step explanation:

Find two Exact point like point A (-1,4) and point B (2,0)

Then count how many spaces does point A have to move left to right and down to get to point B.

since it moves down the number will be negative.

You will have to go 3 spaces to the right and 4 spaces down.

therefore giving you a slope of -4/3

To find the average rate of change for a given function, evaluate the function at the two given points and use the formula (f(2) - f(-1)) / (2 - (-1)).

To find the average rate of change for a given function, we need to calculate the difference in the values of the function between the two given points, and then divide that difference by the difference in the x-coordinates of the points. In this case, we are given x=-1 and x=2.

Let's evaluate the function at these two points:

f(-1) = ?, f(2) = ?

Once we have the values, we can calculate the average rate of change using the formula:

Average Rate of Change = (f(2) - f(-1)) / (2 - (-1))

Substitute the values and calculate to find the answer.

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Answer:

Step-by-step explanation:

the zeroes of a function basically mean when y = 0, so basically the x-intercept(s)

in this case, the zeroes are 3 and 6

Answer:

A. x = 3 and x = 6

Step-by-step explanation:

Zeros occur when the function crosses the x - axis. In this case, the quadratic function crosses the function when x = 3 and x = 6.

Answer: Option b

b. x greater or equal than 1.8

Step-by-step explanation:

In this problem we have the following inequality:

[tex]2x\leq 3(x-0.6)[/tex]

To solve it we must group the x on one side and the constants on the other side

[tex]2x\leq 3(x-0.6)[/tex]

Apply distributive property on the right side of the inequality

[tex]2x\leq 3x-3*0.6[/tex]

[tex]2x\leq 3x-1.8[/tex]

Subtract 3x on both sides of the inequality

[tex]2x-3x\leq 3x-3x-1.8[/tex]

[tex]-x\leq-1.8[/tex]

Multiply by -1 both sides of the inequality

[tex]x\geq 1.8[/tex]

The answer is the option b

Answer:

the answer is option B

Step-by-step explanation:

Answer: 3/5=0.60

Step-by-step explanation:

The p(a/b) is 3/5 = 0.6

The Bayes theorem predicts the likelihood that an event connected to any condition would occur. Use the concept of the conditional probability formula, P(Ei|A)=P(Ei∩A)P(A), to demonstrate the Bayes theorem (A). The Bayes' Theorem describes the likelihood that an event connected to any condition would occur.

Given

P(a) = P(student in karate ) = 3

P(b) =P(student in chess) = 5

P(a|b) = 3/5 = 0.60

To know more about Bayes theorem refer to :

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Answer:

2 2/5

Step-by-step explanation:

-1 3/5 ÷ -2/3

Change the mixed number to an improper fraction

-1 3/5 =  - (5*1 +3)/5 = -8/5

-8/5÷-2/3

Copy dot flip

-8/5 * -3/2

24/10

Divide top and bottom by 2

12/5

Change to a mixed number

12/5 = 2 2/5

11 is the base, meaning that it is the number being multiplied

3 is the exponent, meaning it tells you how many times you must multiply the base together

For this question we must multiply 11 together 3 times:

11*11*11 = 1331

Hope this helped!

The conjugate of the complex number 2 - 8i is 2 + 8i, found by changing the sign of the imaginary part from negative to positive.

The conjugate of a complex number is found by changing the sign of the imaginary part.

For a complex number with a real part of 2 and an imaginary part of -8i, the complex number is represented as 2 - 8i. To find its conjugate, we change the sign of the imaginary part, resulting in 2 + 8i.

The general form of a complex number is a + bi, where a is the real part and bi is the imaginary part.

The conjugate is then written as a - bi. Therefore, if we have the complex number z = 2 - 8i, the conjugate, denoted as [tex]\( \overline{z} \)[/tex], is 2 + 8i.

Answer: The graph is attached.

Step-by-step explanation:

The equation of the line in Slope-intercept form is:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

You can solve for "y":

[tex]2y<5x-10\\\\y<\frac{5}{2}x-\frac{10}{2}\\\\y<\frac{5}{2}x-5[/tex]

You need to rewrite the expression:

[tex]y=\frac{5}{2}x-5[/tex]

You can identify that the slope of this line is:

[tex]m=\frac{5}{2}[/tex]

And the y-intercept is:

[tex]b=-5[/tex]

Substitute [tex]y=0[/tex] and solve for "x" to know the x-intercept:

[tex]0=\frac{5}{2}x-5\\\\5*2=5x\\\\x=2[/tex]

Now you know that the line passes through the points (0,-5) and (2,0).

Since the inequality is "<", you know that the line must be dashed and the shaded region must be below the line [tex]y=\frac{5}{2}x-5[/tex].

Knowing this, you can graph it (Observe the graph attached)

To find the value of Lucy's house at the start of 2017, calculate a 5% increase each year from the initial £200,000 value in 2014. The compound value over the three years results in a house value of £231,525 at the start of 2017.

To calculate the value of Lucy's house at the start of 2017, we need to apply a 5% annual increase to the initial value of the house for three consecutive years (2014 to 2017).

Find the increase for the first year:

Initial value for 2014: £200,000

5% increase: £200,000 * 0.05 = £10,000

Value at the start of 2015: £200,000 + £10,000 = £210,000

Calculate the increase for the second year:

Value at the start of 2015: £210,000

5% increase: £210,000 * 0.05 = £10,500

Value at the start of 2016: £210,000 + £10,500 = £220,500

Calculate the increase for the third year:

Value at the start of 2016: £220,500

5% increase: £220,500 * 0.05 = £11,025

Value at the start of 2017: £220,500 + £11,025 = £231,525

Therefore, the value of Lucy's house at the start of 2017 would be £231,525.

Answer:

Shravan's age is 40 years old

Gaurav’s age is 30 years old

Step-by-step explanation:

Let

x-----> Shravan's age

y-----> Gaurav’s age

we know that

x=y+10 -----> equation A

(1/7)(x-5)=(1/5)(y-5) ----> equation B

substitute equation A in equation B and solve for y

(1/7)(y+10-5)=(1/5)(y-5)

(1/7)(y+5)=(1/5)(y-5)

5(y+5)=7(y-5)

5y+25=7y-35

7y-5y=25+35

2y=60

y=30 years

Find the value of x

x=y+10  ----> x=30+10=40 years

therefore

Shravan's age is 40 years old

Gaurav’s age is 30 years old