The function f(x)=−5x^2+3 is defined over the domain −4

For this case we must find the roots of the following equation:

[tex]3x ^ 2-4x + 2 = 0[/tex]

We have that the roots will come from:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

Where:

[tex]a = 3\\b = -4\\c = 2[/tex]

Substituting the values:

[tex]x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (3) (2)}} {2 (3)}\\x = \frac {4 \pm \sqrt {16-24}} {6}\\x = \frac {4 \pm \sqrt {-8}} {6}\\x = \frac {4 \pm \sqrt {-1 * 8}} {6}\\x = \frac {4 \pmi \sqrt {2 ^ 2 * 2}} {6}\\x = \frac {4 \pm2i \sqrt {2}} {6}\\x = \frac {2 \pmi \sqrt {2}} {3}[/tex]

We have two complex roots:

[tex]x_ {1} = \frac {2 + i \sqrt {2}} {3}\\x_ {2} = \frac {2-i \sqrt {2}} {3}[/tex]

Answer:

[tex]x_ {1} = \frac {2 + i \sqrt {2}} {3}\\x_ {2} = \frac {2-i \sqrt {2}} {3}[/tex]

Answer:

a.$247

Step-by-step explanation:

39×5=195

195+52=247

Answer:

The answer is $247 (Option A)

Step-by-step explanation:

Pamela will have the car for 5 days.

The cost per renting is variable, and it increases as the days do.

5*$39= $195

And the LDW (Loss Damage Waiver) is an only once cost of $52

You can get the total rental cost by adding both of them:

$195+$52= $247 (Option A)

Answer:

See below.

Step-by-step explanation:

All the equations are one-step equations.

In each case, see what operation is being done to the variable, and do the opposite operation to both sides.

1.

t + 1.32 = 3.48

1.32 is being added to t.

Subtract 1.32 from both sides.

t + 1.32 - 1.32 = 3.48 - 1.32

t = 2.16

2.

b - 4.22 = 7.08

4.22 is being subtracted from b.

Add 4.22 to both sides.

b - 4.22 + 4.22 = 7.08 + 4.22

b = 11.3

4.

h + 4/9 = 7/9

4/9 is being added to h.

Subtract 4/9 from both sides.

h + 4/9 - 4/9 = 7/9 - 4/9

h = 3/9

h = 1/3

5.

-5/8 = x - 1/4

1/4 is being subtracted from x.

Add 1/4 to both sides.

-5/8 + 1/4 = x - 1/4 + 1/4

-5/8 + 2/8 = x

-3/8 = x

x = -3/8

7.

3.2c = 9.6

c is being multiplied by 3.2.

Divide both sides by 3.2.

3.2c/3.2 = 9.6/3.2

c = 3

8.

-5.04 = 1.26d

c is being multiplied by 1.26.

Divide both sides by 1.26.

-5.04/1.26 = 1.26d/1.26

-4 = d

d = -4

10.

-2/3 = 3/4t

t is being multiplied by 3/4.

Divide both sides by 3/4 which is the same as multiplying both sides by 4/3.

-2/3 * 4/3 = 3/4t * 4/3

-8/9 = t

t = -8/9

11.

w/2.5 = 4.2

w is being divided by 2.5.

Multiply both sides by 2.5.

w/2.5 * 2.5 = 4.2 * 2.5

w = 10.5

Answer:

The second choice

Step-by-step explanation:

The histogram shows the following:

3 children are within the ages of 5-10

7 children are within the ages of 11-13

4 children are within the ages of 14-18

So all you need to do is find the set of data that shows that fit the intervals. So find the data that have three values within 5 to 10; seven values with the 11-13; and four values within 14 to 18.

Answer:

(2,4)

Step-by-step explanation:

We have the system:

y=x+2

y=3x-2.

This is already setup for substitution.

I'm going to replace my first y with what the second y equals.

That is, I'm going to write 3x-2=x+2.

Time to solve the following for x:

3x-2=x+2

Subtract x on both sides:

2x-2= 2

Add 2 on both sides:

2x. = 4

Divide both sides by 2:

x. = 2

Now that we know x=2 and we have an equation that relates x to y: either y=x+2 or y=3x-2, doesn't matter which we use, we can find y.

So we y=x+2 with x=2 which means y=2+2=4.

So the solution, the intersection, is (2,4).

Answer:

(2, 4 )

Step-by-step explanation:

Given the 2 equations

y = x + 2 → (1)

y = 3x - 2 → (2)

Substitute y = 3x - 2 into (1)

3x - 2 = x + 2 ( subtract x from both sides )

2x - 2 = 2 ( add 2 to both sides )

2x = 4 ( divide both sides by 2 )

x = 2

Substitute x = 2 into (1) for the corresponding value of y

y = x + 2 = 2 + 2 = 4

As a check

Substitute x = 2 into the 2 equations and check validity

(1) → y = 2 + 2 = 4 ← Correct

(2) → y = (3 × 2) - 2 = 6 - 2 = 4 ← Correct

Solution is (2, 4 )

For this case we have that by definition[tex]\pi[/tex] equals 180 degrees.

We must convert 135 degrees to radians, then:

[tex]135 * \frac {\pi} {180} =\\135 * \frac {3.14} {180} =\\\frac {423.9} {180} = 2.355[/tex]

Rounding off we have:

2.4 radians.

Answer:

2.4 radians

Final answer:

To find the length of the pole, we can use the Pythagorean theorem.

Explanation:

To find the length of the pole, we can use the Pythagorean theorem. Since the base of the pole is 7 feet away from the wall and the top of the pole reaches 21 feet up the wall, we can envision a right triangle with the pole as the hypotenuse. Using the Pythagorean theorem, we can calculate:

c^2 = a^2 + b^2

Where c is the length of the pole, a is the base length (7 feet), and b is the height reached by the pole (21 feet).

Plugging in the values, we get:

c^2 = 7^2 + 21^2

Solving for c, we find that the length of the pole is √(7^2 + 21^2) feet.

Answer:

the answer is A. f(x +1) = -2f(x)

Step-by-step explanation:

every new number in the sequence is multiplied by -2, making it -2f(x).

Answer:

(D) f(x+1)=2f(x)

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

30 x 40 x 50 x 60 x 70 = 252,000,000

There are six zeros at the end. So there are 6 terminal zeros.

Answer:

Given an exponential function of the form

y = a*(b)^x

The values of b that will result in the desired percentage values are:

Case 1

b = 23% decrease

1 - 0.23 = 0.77

y = a*(0.77)^x

Case 2

b = 8% increase

1 + 0.08 = 1.08

y = a*(1.08)^x

Case 3

b = 15% decrease

1 - 0.15= 0.85

y = a*(0.85)^x

Case 4

b = 120% increase

1 + 1.2 = 2.2

y = a*(2.2)^x

See attached picture for examples

The value of b in an exponential function is calculated as : For a 23% decrease = 0.77, For an 8% increase = 1.08, For a 15% decrease = 0.85, For a 120% increase = 2.20.

The student is trying to determine the corresponding exponential function base value (b) for a given percent rate of change.

In an exponential function y = abx, a positive b models exponential growth, while a value of b less than 1 models exponential decay.

We can convert the percent increase or decrease to a decimal and then add or subtract it from 1 to find the corresponding value of b.

For a 23% decrease, b = 1 - 0.23 = 0.77.

For an 8% increase, b = 1 + 0.08 = 1.08.

For a 15% decrease, b = 1 - 0.15 = 0.85.

For a 120% increase, b = 1 + 1.20 = 2.20.

Answer:

[tex]\large\boxed{5\dfrac{1}{3}\ units}[/tex]

Step-by-step explanation:

ΔZYW and ΔWYX are similar. Therefore corresponding sides are in proportion:

[tex]\dfrac{ZY}{YW}=\dfrac{YW}{YX}[/tex]

We have:

[tex]ZY=3,\ YW=4,\ YX = a[/tex]

Substitute:

[tex]\dfrac{3}{4}=\dfrac{4}{a}[/tex]          cross multiply

[tex]3a=(4)(4)[/tex]

[tex]3a=16[/tex]          divide both sides by 3

[tex]a=\dfrac{16}{3}\\\\a=5\dfrac{1}{3}[/tex]

Answer:

Hello guys im also here for that answer

Step-by-step explanation:

Answer:

c) -20x^2+14x+12

all real numbers

Step-by-step explanation:

So (fg)(x)=f(x)g(x)=(-4x-2)(5x-6).

Need find the expression in standard form we need to use foil:

First:  (-4x)(5x)=-20x^2

Outer: (-4x)(-6)=24x

Inner:  (-2)(5x)=-10x

Last:  (-2)(-6)=12

--------------------------Add like terms:

-20x^2+14x+12

Polynomials have domain all real numbers.

There are no restrictions on what x can be.  For every number you plug in, you will get a number back.  

Answer:

c.-20x^2 + 14x + 12; all real numbers

Step-by-step explanation:

f(x) = -4x - 2

g(x) = 5x - 6

Therefore, -20x^2 + 14x + 12; all real numbers.

Answer:

look at explanation:

Step-by-step explanation:

1st picture: angle bisector

2nd picture: angle bisector

3rd picture: perpendicular bisector

4th picture: angle bisector

5th picture: perpendicular bisector

6th picture: perpendicular bisector

Answer:

(0,7)

Step-by-step explanation:

This equation you are given is in slope-intercept form, the form y=mx+b.

It is called slope-intercept from because it gives us the slope and the y-intercept.

The slope is m.

The y-intercept is b.

If we compare y=8x+7 to y=mx+b, we should make the conclusion that m=8 and b=7.

This tells the slope is 8 while the y-intercept is 7.

The y-intercept is 7 is sometimes required to be represented by a point.  Since it is the y-intercept, the x is 0 so the point that represents the y-intercept is (0,7).

Answer:

0,7

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Given

x³ - 4x² - 3 divided by x + 1

Write the coefficients of the polynomial in descending order, including a zero for any terms not included in the polynomial.

In this case a 0 is required to denote the x- term

Division by ( x + h) is evaluated for x = - h, hence

division by x + 1 is evaluated for x = - 1, hence

- 1 | 1  - 4  0  - 3 ← is the required synthetic division → A

Answer:

8.555 in.

Step-by-step explanation:

So the area of the square is x^2.

This makes that the area of the circle is x^2 - 20 pie.

The radius of the circle is half of the diameter, so it is 0,5x.

The formula for the circle area is:

Area = pie * r^2.

x^2 - 20 pie = pie * (0,5x)^2

x^2 - 20 pie = pie * 0,25x^2

x^2 - pie * 0,25x^2 = 20 pie

x^2 * (1 - 0,25 pie) = 20 pie

x^2 = 20pie / (1 - 0,25 pie)

x = square root (20pie / (1 - 0,25 pie)) = 17.11

So the radius is 0,5 * 17.11 = 8.555 in.

Answer:

1

Step-by-step explanation:

(f °g)(3) = f(g(3)) = f(-13) = 1

Step-by-step explanation:

Write a proportion.  3 laps is to 2 km as 5 laps is to x km.

3 / 2 = 5 / x

Cross multiply:

3x = 10

Divide:

x = 10/3

x = 3⅓

Madison will have run 3⅓ kilometers.

Answer:a and b

Step-by-step explanation:

Answer:

[tex]A\subset B[/tex]

Step-by-step explanation:

Let A and B, be two non-empty sets, then set A is a subset of set B if all elements in set A can be found in set B.

The given sets are:

A={1,2} and B={1,2,3,4}

We can observe that, all the elements in set A are also in set B.

This means that set A is a subset of B.

We write this as:

[tex]A\subset B[/tex]

The correct answer is option D.

Answer:

A. 30

Step-by-step explanation:

30*.08=24

Answer:

-18a⁷b⁷ + 42a²b⁵

Step-by-step explanation:

  (3a⁵b⁶ - 7b⁴)(-6a²b)

= (3a⁵b⁶)(-6a²b) – (7b⁴)(-6a²b)     Distributed the 6a²b term

= -18a⁷b⁷ - (-42a²b⁵)                     Multiplied and added exponents

= -18a⁷b⁷ + 42a²b⁵                       Removed parentheses

Answer: -16

Step-by-step explanation:

input is x

output is y

9x-7=y

9(-1)-7=y

-9-7=-16

Answer:

The answer is -16

Step-by-step explanation:

input is x

output is y

9x-7=y

9(-1)-7=y

-9-7=-16

y= mx+b ( equation for slope)

y= 4/5x-3

The slope (m)is 4/5

The y- intercept(b) is -3

Answer: slope is 4/5

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

In this case:

m = 4/5

b = -3

This means that 4/5 is the slope of this line.

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

y=1/6x+1 because the formula is written as y=mx+b

Answer:

y=1/6x+1

Step-by-step explanation:

slope is the change in y over the change in . 2-1 is 1 and 6-0 is 6 so the slope will be 1/6. the y intercept is given by the second coordinate (0,1) which is why you add 1.

Answer:

Geometric Sequence.

[tex]a_{n}=(2)^{n-1}[/tex]

Step-by-step explanation:

The x-coordinates represent the number of terms of the sequence while the y-coordinates represent the term of the sequence. So the series shown on the graph is:

1, 2, 4, 8

We can see that the ratio of two consecutive terms of the above sequence is constant. i.e.

2/1 = 2

4/2 = 2

8/4 = 2

Such a sequence in which the ratio of two consecutive terms is a constant is known as Geometric Sequence and this constant ratio is known as common ratio.

The general term of a geometric sequence is represented as:

[tex]a_{n}=a_{1}(r)^{n-1}[/tex]

Using the values for the given sequence we get:

[tex]a_{n}=1(2)^{n-1}[/tex]

[tex]a_{n}=(2)^{n-1}[/tex]

Where n represents the number of term.

Answer:

Step-by-step explanation:

We will check whether the given pair x = 3 and y = 2 is the solution of the first equation.

4(3) - 5(2) = 12 - 10 = 2 CORRECT

Put x = 3 and y = 2 to the equation 6x + 7y = Q:

Q = 6(3) + 7(2)

Q = 18 + 14

Q = 32

Answer:

A, C, E

Step-by-step explanation:

substitute for x in each option and check if the value of y satisfies the inequality

Answer:

Option A, C and E

Step-by-step explanation:

We have to find points which are solution to the linear inequality ( y<0.5x + 2)

(a) For (-3, -2)

-2 < (0.5 × 3 + 2)

-2 < 1.5 + 2

-2 < 3.5

True, It's a solution.

(b) For (-2, 1)

1 < 0.5 × (-2) + 2

1 < -1 + 2

1 < 1

False, it's not a solution

(c) For (-1, -2)

-2 < 0.5 (-1) +2

-2 < -1 + 2

-2 < 1

True, It's a solution.

(d) For (-1, 2)

2 < 0.5 (-1) + 2

2 < -1 + 2

2 < 1

False, It's not the solution.

(e) For (1, -2)

-2 < 0.5 (1) + 2

-2 < 2.5

True It's a solution

Therefore, Option A, C and E are the solutions.

Answer: 190°

Step-by-step explanation:

Angle CAE is 1/2 times the measure of arc CBA, therefore:

95° x 2=190°

The  measure of arc CBA =190°

To understand the relationship between angle CAE and arc CBA, we need to delve into the properties of angles and arcs in circles. Here is a step-by-step explanation:

Step 1: Understanding Inscribed Angles

In a circle, an inscribed angle is an angle formed by two chords that intersect on the circle. The measure of an inscribed angle is always half the measure of the intercepted arc.

Step 2: Relationship between Angle CAE and Arc CBA

Given:

- Angle CAE is inscribed in the circle.

- Arc CBA is the intercepted arc for angle CAE.

According to the properties of inscribed angles:

[tex]\[ \text{Measure of Angle CAE} = \frac{1}{2} \times \text{Measure of Arc CBA} \][/tex]

Step 3: Using the Given Information

Let's denote:

[tex]- \( \angle CAE \)[/tex] as the measure of angle CAE.

[tex]- \( \text{Arc CBA} \)[/tex] as the measure of arc CBA.

From the given information, the measure of arc CBA is 95°. Using the inscribed angle property:

[tex]\[ \angle CAE = \frac{1}{2} \times \text{Arc CBA} \][/tex]

[tex]\[ \angle CAE = \frac{1}{2} \times 95^\circ \][/tex]

[tex]\[ \angle CAE = 47.5^\circ \][/tex]

However, if we are interpreting the problem differently and consider that angle CAE is given as 95°, and we need to find the measure of the arc intercepted by this angle when doubled, then we would calculate:

[tex]\[ \text{Arc CBA} = 2 \times \angle CAE \][/tex]

[tex]\[ \text{Arc CBA} = 2 \times 95^\circ \][/tex]

[tex]\[ \text{Arc CBA} = 190^\circ \][/tex]

Therefore, if angle CAE is half the measure of arc CBA, and given the angle CAE as 95°:

[tex]\[ \text{Arc CBA} = 2 \times 95^\circ = 190^\circ \][/tex]

This shows that the measure of arc CBA is 190°.

Answer:

R(p) = -6p^2 + 60p....

Step-by-step explanation:

Revenue, R = quantity sold * price

Price = p

Quantity sold = q = -6p + 60

R(p) = q*p

where q=-6p + 60

= (-6p + 60) * p = -6p^2 + 60p

Answer: R(p) = -6p^2 + 60p....

Answer:

Draw a line across  the points (6,0) and (0,3)

Step-by-step explanation:

This is the equation of a line, so it is enough to find two points (x,y), locate them and draw a straight line passing trough then,

Having said that, lets start.

The first easy point to find is the one that makes y=0, so we have the following equation: 0=-1/2 x +3, which gives that x=6, this point is (6,0)

The other easy point to find is the one that makes x=0, so we have the following equation y=-1/2 * 0 +3, which gives that y=3, this point is (0,3)

We have two points (6,0) and (0,3)