Find the linearization L(x) of the function at a. f(x) = x^4 + 2x^2, a = 1

We can say that nearly all of the students got between a 54 and a 96, that 95% got between a 61 and an 89, and about two-thirds got between a 68 and an 82, but there may be other conclusions one may wish to draw.

to determine the nature of the solutions use the discriminant

Given a quadratic equation in standard form : ax² + bx + c = 0

then the discriminant is b² - 4ac

• If b² - 4ac > 0 , then there are 2 real and distinct solutions

• If b² - 4ac = 0, there are 2 real and equal roots

• If b² - 4ac < 0 , there are no real solutions

for x² - 3x + 8 = 0 with a = 1, b= - 3 and c = 8

b² - 4ac = (- 3)² - (4 × 1 × 8 ) = 9 - 32 = - 23

Hence there are no real solutions to the equation

Yes. For example, the shape I will use is the circle.

No matter how you rotate the circle, it will always look the same. If you reflect the circle over any drawen line in which it passes through the middle, the two halves created would be congruent.

~Rise Above the Ordinary, Senpai

In this case we do not know for how long have they worked. But lets assume that they both will fix the car in an hour.

Case 1: Lets talk about Abe first.

Abe will charge $70.00 per hour plus a part which costs $130.00.

Now, the total cost to be paid to Abe to fix the car is [tex]70+130=200[/tex] dollars.

So we will have to pay $200.00 to Abe to fix the car.

Case 2: Lets talk about Gabe now,

Gabe can fix it for $80 an hour and finds the part just for $60.

Now, the total cost to be paid to Gabe to fix the car is [tex]80+40=120[/tex] dollars.

So we will have to pay $120.00 to Gabe.

Considering the two cases above we can ask Gabe to fix our car but there is another case.

Case 3: What if Abe finds a part for $60.00 rather $130.00

In that case, we will have to pay [tex]70+60=130[/tex] dollars in total to Abe.

Now, we need to pay $130.00 to Abe to fix the car.

Still we can see that we need to pay $10.00 less to Gabe so will ask Gabe to fix the car  (since [tex]130-120=10[/tex]).

Alright, so let's make 2 3/5 into an improper fraction.

2 x 5 = 10 + 3 = 13

So 13/5 / 11/25.

Keep, change, flip rule: 13/5 x 25/11.

Now you multiple the numerator and denominator from both fractions. (I'm not going to do the math for you. Hope this helped and sorry if my explanation is...yeah.)

The division of 2 3/5 by 1 1/25 is equal to 2.5.

To perform the division, convert the mixed numbers to improper fractions. 2 3/5 becomes 13/5, and 1 1/25 is 26/25. Now divide the fractions: (13/5) ÷ (26/25) = 13/5 * 25/26 = 325/130 = 2.5.

Answer:

  E.) △ABC with midpoints M and N.

Step-by-step explanation:

You want a related given statement to the scenario "in a triangle a segment joining the midpoints of two sides is one-half the length of the third side."

The scenario describes a triangle ABC with midpoints designated on two of the sides. There is no "plane R", angles 1 and 2, line l, point P. In triangle ABC, point B will not be between A and C.

These considerations eliminate choices A–D, leaving choice E:

  E.) △ABC with midpoints M and N

Answer:

The answers are:

m = 9   and     n = 15

Step-by-step explanation:

m/15 = n/25 = 12/20

  m/15 = 12/20

  m/15 = 3/5

  5m = 45

  m = 9

  n/25 = 12/20

  n/25 = 3/5

  5n = 75

  n = 15

m = 9 and n = 15

Find the length( l ) of the leg in the large right triangle using Pythagoras' identity

l = √(25² - 20²) = √225 = 15

the outer and inner right triangles are similar hence the ratios of corresponding sides are equal

[tex]\frac{25}{n}[/tex] = [tex]\frac{15}{m}[/tex] = [tex]\frac{20}{12}[/tex]

using [tex]\frac{25}{n}[/tex] = [tex]\frac{20}{12}[/tex] (cross-multiply )

20n = 300 ( divide both sides by 20 )

n = 15

using [tex]\frac{15}{m}[/tex] = [tex]\frac{20}{12}[/tex] ( cross-multiply )

20m = 180 ( divide both sides by 20 )

m = 9

x ≠ - 4, 3

the denominator of the fraction cannot equal zero as this would make the fraction undefined. Equating the denominator to zero and solving gives the values that x cannot be

solve x² + x - 12 = 0

(x + 4)(x - 3) = 0

equate each factor to zero abd solve for x

x + 4 = 0 ⇒ x = - 4

x - 3 = 0 ⇒ x = 3

restrictions on x are : x ≠ - 4, 3

Answer: Option C) Raj forgot the negative when substituting -15+9x for y.

Solution:

(1) 9x-y=15

(2) 2x+8y=28

Isolating y in the first equation. Subtracting 9x both sides of the equation:

(1) 9x-y-9x=15-9x

Subtracting:

(1) -y=15-9x

Multiplying both sides of the equation by -1:

(1) (-1)(-y)=(-1)(15-9x)

(1) y=-15+9x

Then Raj found the value of y. It's not option D.

Substitutng y by -15+9x in the second equation:

(2) 2x+8(-15+9x)=28

Then option C) is the answer: Raj forgot the negative when substituting -15+9x for y.

Eliminating the parentheses applying the distributive property in the multiplication:

(2) 2x-120+72x=28

Adding similar terms:

(2) 74x-120=28

Solving for x. Adding 120 both sides of the equation:

(2) 74x-120+120=28+120

Adding:

(2) 74x=148

Dividing both sides of the equation by 74:

(2) 74x/74=148/74

Dividing:

(2) x=2

Solving for y: Replacing x by 2 in the first equation:

(1) y=-15+9x

(1) y=-15+9(2)

Multiplying:

(1) y=-15+18

Subtracting:

(1) y=3  

If you were to think of this diagram as a map of intersecting roads, corresponding angles are the ones on the same corner:

NW corner: ∠1 and ∠3

NE corner: ∠5 and ∠7

SE corner: ∠6 and ∠8

SW corner: ∠2 and ∠4

The choices in bold font above are the only pairs of corresponding angles that are in your answer list:

Answer:

∠1 and ∠3  , ∠6 and ∠8  , ∠5 and ∠7  are corresponding angles

Step-by-step explanation:

Corresponding Angles are angles which occupy same relative position at intersection when a line intersects two lines.

In pair of corresponding angles, one angle is interior angle and other one is exterior angle.

Option 1:

∠1 is exterior angle and ∠3  is interior angle. Also Both are at relatively same position.

Thus they are Corresponding angles.

Option 2:

∠6 is interior angle and ∠8  is exterior angle. Also Both are at relatively same position.

Thus they are Corresponding angles.

Option 3:

∠2 and ∠8  both are exterior angle.

Thus they are not Corresponding angles.

Option 4:

∠5 is interior angle and ∠7 is exterior angle. Also Both are at relatively same position.

Thus they are Corresponding angles.

Option 5:

∠2 and ∠7 both are exterior angles.

Thus they are not corresponding angles.

Option 6:

∠3 and ∠6 both are interior angles.

Thus they are not corresponding angles.

she would need to ride for 61 minutes

15√2

area = s² = 450 ← s is length of side

to find s take the square root of both sides

s = [tex]\sqrt{450}[/tex] = [tex]\sqrt{2(9)(25)}[/tex]

  = √2 × √9 × √25 = √2 × 3 × 5 = 15√2

15√2 represents a side length of a square that has an area of 450 square inches.

The answer is option A.

The area of any quadrilateral can be determined by multiplying the length of its base by its height.

area = s² = 450 ← s is length of side

to find s take the square root of both sides

s =  √450 = √2(9)(25)

= √2 × √9 × √25 = √2 × 3 × 5 = 15√2

Since we know the shape here is square, we know that all sides are of equal length. From this, we can work backward by taking the square root of the area to find the length of one side.

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54 nickels and 27 dimes

1 dime = 10 cents = $0.1

1 nickel = 5 cents = $0.05

setting up 2 equations

let n = amount of nickels and d = amount of dimes, then

n + d = 81 → (1)

0.05n + 0.1d = 5.4 → (2)

multiply (2 ) by 10

0.5n + d = 54 → (3)

subtract (3) from (1) to eliminate d

0.5n = 27 ( divide both sides by 0.5 )

n = [tex]\frac{27}{0.5}[/tex] = 54

substitute n = 54 in (1)

54 + d = 81 ( subtract 54 from both sides )

d = 27

Mary has 54 nickels and 27 dimes

(-x³ +3x +4) -(2x³ +7x² -9) = -x³ +3x +4 -2x³ -7x² +9 . . . . eliminate parentheses

= x³(-1-2) +x²(-7) +x(3) +(4+9)

= -3x³ -7x² +3x +13 . . . matches the second choice.

Answer:

C. -1/2

Step-by-step explanation:

7π/6 radians is equivalent to (7π/6)(180°/π) = 210°, a 3rd-quadrant angle whose reference angle is 30°. The sine of angles in the 3rd quadrant is negative.

sin(30°) = 1/2

sin(210°) = -sin(30°) = -1/2

_____

In radians mode, your calculator can tell you this result directly.

C - [tex]\frac{1}{2}[/tex]

sin(7π / 6 )

note 7π\6 is in the third quadrant where sin is negative

the related acute angle to 7π/6 is 7π/6 - π = π/6

sin (7π/6) = - sin(π/6) = - [tex]\frac{1}{2}[/tex]

Answer:

h(0) is equal to 2.

Step-by-step explanation:

In order to find this, we first put 0 in for x in the g(x) equation.

g(x) = 2x - 1

g(0) = 2(0) - 1

g(0) = -1

Now that we have this, we can stick the answer for g(x) into the f(x) equation.

f(x) = 1 - g(x)

f(x) = 1 - -1

f(x) = 1 + 1

f(x) = 2

The value of [tex]h(0)[/tex] is 2.

It is given that,

Explanation:

We have,

[tex]h(x)=1-g(x)[/tex]

[tex]h(x)=1-(2x-1)[/tex]

[tex]h(x)=1-2x+1[/tex]

[tex]h(x)=2-2x[/tex]

Substitute [tex]x=0[/tex] in the above function.

[tex]h(0)=2-2(0)[/tex]

[tex]h(0)=2-0[/tex]

[tex]h(0)=2[/tex]

Thus, the value of [tex]h(0)[/tex] is 2.

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Note that both numbers are multiple of 3: you can simplify the ratio as follows

[tex] \dfrac{6}{603} = \dfrac{3\cdot 2}{3\cdot 201} = \dfrac{2}{201} [/tex]

The ratio can't be further simplified because 2 and 201 are coprime. So, the only thing you could do is write down the decimal expansion of the number.

For the record, its period is 33 digits long, and it is

[tex] 0.009950248756218905472636815920398 [/tex]

Answer:

0.00995025

Step-by-step explanation:

The marks on the line segments tell you they are the same length, and that the triangle is an equilateral triangle. That tells you the angles are the same size, and all are 60°. This lets you find x and y.

(7x+4)° = 60°

7x = 56 . . . . . . . . divide by °, subtract 4

x = 8 . . . . . . . . . . divide by 7

_____

(8y+12)° = 60°

8y = 48 . . . . . . . . divide by °, subtract 12

y = 6 . . . . . . . . . . divide by 8

other leg = 12 cm

using Pythagoras' identity with x as the side to be found, then

x = √(13² - 5² ) = √(169 - 25 ) =√144 = 12

Answer:

1

Step-by-step explanation:

Answer:

B. y = 2x + 29

Step-by-step explanation:

The given graph has a slope of 2 (a rise of 10 for a run of 5), so the last two chioices are not viable. Clearly a parallel line through the given point will have a positve y-intercept, so the first choice is not viable.

The appropriate choice is the second one:

... B. y = 2x + 29

Hence the line parallel to this is  y = 2x + 29.

Hence, option B is correct.

A straight group of points that stretch in opposing directions is what is known as a line. It is endless in both directions and lacks any ends. It is not thick. It only has one dimension.

In the given graph,

The line is passing through (0, 15) and (10, 35).

Therefore the slope of this lien is,

m  = (35-15)/(10-0)

    = 2

Now the parallel line to this line will have same slope.

Which passes through (3, 35),

Hence the line be ,

y - 35 = 2(x - 3)

y - 35 = 2x - 6

       y = 2x + 29

Hence the line is  y = 2x + 29.

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Answer:

The dog was running towards the trainer to receive a treat

Step-by-step explanation:

At the point on the graph where Time is 5 (seconds), the slope of the distance vs time curve is negative, indicating the dog is moving toward the trainer. The motivation of the dog is unknown, so the above answer choice involves speculation that is not supported by the problem statement.

Answer:B.The dog was running towards the trainer to receive a treat.

Step-by-step explanation:cuz im right

the 2 equations given are vertical angles which mean they would equal the same.

Set the two equations to equal each other to solve for x:

6(x-2) = 3x+30

Simplify the left side:

6x-12 = 3x+30

Add 12 to eac side:

6x = 3x+42

Subtract 3x from each side"

3x = 42

Divide both sides by 3:

X = 42/3

X = 14

Now you know X, replace x with 14 in the equation for DHG:

DHG = 6(x-2)

6(14-2)

Simplify:

6(12)

Multiply:

72

Angle DHG is 72 degrees.

∠Y = 64°

since the triangles are similar

∠Y = ∠C

∠C = 180° - (73 + 43 )° = 64° = ∠Y

Final answer:

The ratio of boys to girls in the class is 14:12, which simplifies to 7:6.

Explanation:

The ratio of boys to girls in the class is determined by comparing the number of boys to the number of girls.

Given that there are 14 boys and 12 girls, the ratio of boys to girls is:

14 boys : 12 girls

This can be simplified by dividing both numbers by the greatest common divisor, which is 2 in this case.

Hence, the simplified ratio is:

7 boys : 6 girls

Answer:

30°

Step-by-step explanation:

The sum of the angles of a quadrilateral is 360°. You have 3 angles given, so can find the fourth using that fact. (The double arcs on angles B and C mean those angles are congruent. Same symbols are used to mark same-size angles.)

... 360° = A + B + C + D

... 360° = A + 115° + 115° + 100°

... 360° -330° = A = 30°